GAMMs LabPhon 18
Jalal Al-Tamimi
Newcastle University6 June 2018; updated 10 August 2022
1 Loading packages
library(ggplot2);library(mgcv);library(itsadug);library(tidyverse);library(gganimate); library(doParallel)Le chargement a nécessité le package : nlme
This is mgcv 1.8-39. For overview type 'help("mgcv-package")'.
Le chargement a nécessité le package : plotfunctions
Attachement du package : ‘plotfunctions’
L'objet suivant est masqué depuis ‘package:ggplot2’:
alpha
Loaded package itsadug 2.4 (see 'help("itsadug")' ).
Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
── Attaching packages ────────────────────────────────────────────────── tidyverse 1.3.1 ──
✓ tibble 3.1.6 ✓ dplyr 1.0.8
✓ tidyr 1.2.0 ✓ stringr 1.4.0
✓ readr 2.1.2 ✓ forcats 0.5.1
✓ purrr 0.3.4
── Conflicts ───────────────────────────────────────────────────── tidyverse_conflicts() ──
x plotfunctions::alpha() masks ggplot2::alpha()
x dplyr::collapse() masks nlme::collapse()
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()
No renderer backend detected. gganimate will default to writing frames to separate files
Consider installing:
- the `gifski` package for gif output
- the `av` package for video output
and restarting the R session
Le chargement a nécessité le package : foreach
Attachement du package : ‘foreach’
Les objets suivants sont masqués depuis ‘package:purrr’:
accumulate, when
Le chargement a nécessité le package : iterators
Le chargement a nécessité le package : parallel2 Demo Linear Model vs GAM
In this demo, data obtained from a Jordanian Arabic speaker producing the word /du:d/ “worm” is used. F2 frequencies obtained at 5 ms interval from onset to midpoint of the vowel are used. Let’s plot the F2 frequencies by interval number. The second plot displays a linear regression line superimposed on the plot. As can be seen, the linear regression line is not able to cope with the curviness of the data, and is unable to cope with it. The third plot superimposes a spline obtained from a GAM model.
demoGAMProd <- read.csv("dataProd_duud.csv")
head(demoGAMProd)ggplot.demo1 <- ggplot(demoGAMProd,aes(x=IntervalsN,y=F2))+
geom_point()+theme_bw(base_size = 20)+coord_cartesian(ylim=c(600,1800))+
labs(y = "F2 Hz", x = "Intervals number")
ggplot.demo1
ggplot.demo2 <- ggplot(demoGAMProd,aes(x=IntervalsN,y=F2))+
geom_point()+theme_bw(base_size = 20)+coord_cartesian(ylim=c(600,1800))+
labs(y = "F2 Hz", x = "Intervals number")+geom_smooth(method = lm, se=F)
ggplot.demo2`geom_smooth()` using formula 'y ~ x'
ggplot.demo3 <- ggplot(demoGAMProd,aes(x=IntervalsN,y=predict(bam(F2 ~ s(IntervalsN, bs="cr"), data = demoGAMProd))))+
geom_point()+theme_bw(base_size = 20)+coord_cartesian(ylim=c(600,1800))+
labs(y = "F2 Hz", x = "Intervals number")+geom_smooth(method = lm, formula = y ~ splines::bs(x, 3),se=F)
ggplot.demo3
3 Actual data analyses
This data is obtained from a single speaker producing various consonants in the frame VCV, with V = symmetric /i: a: u:/ (=vowel) and C is one of 17 consonants put into five contexts “plain”, “velar”, “uvular”, “pharyngealised” and “pharyngeal” (=context). The data is from Ultrasound Tongue Imaging. Tongue contours were obtained at the consonant onset, midpoint and offset (=time). A total of 51 words (=word) were obtained and these were repeated 3 times. Tongue splines were extracted with X-Y coordinates (=y outcome). 42 Fan positions (=Fan) were extracted and these are used as a normalisation between contexts. The outcome is y, the predictors are Fan, time, context and vowel, and the random factor is word.
3.1 Creating new variables
Before running the actual GAM model on the data, we need to:
- Create two new variables for context and vowel. These will be “ordered” predictors and sum coded
- To run an Auto-Regressive Model, we need to find the autocorrelation in the dataframe:
- We rearrange the data by time, ID, and Fan
- We add a new variable “start” that marks the start of Fan
pharDF <- read.csv("resultsFull.c_NoRelNoz.csv")
str(pharDF)'data.frame': 18900 obs. of 23 variables:
$ X.1 : int 1 2 3 4 5 6 7 8 9 10 ...
$ ID : int 1 2 3 7 8 9 10 11 12 13 ...
$ Client.Surname : chr "Sara" "Sara" "Sara" "Sara" ...
$ Time.of.sample.in.recording: num 3.84 5.37 2.37 5.3 2.26 ...
$ Prompt : chr "2aataa.... 2aataa.... 2aataa.... 2aattaa.... 2aattaa.... 2aattaa" "2aataa.... 2aataa.... 2aataa.... 2aattaa.... 2aattaa.... 2aattaa" "2aataa.... 2aataa.... 2aataa.... 2aattaa.... 2aattaa.... 2aattaa" "2aataa.... 2aataa.... 2aataa.... 2aattaa.... 2aattaa.... 2aattaa" ...
$ word : chr "2aataa" "2aataa" "2aataa" "2aataa" ...
$ context : chr "plain" "plain" "plain" "plain" ...
$ consonant : chr "t" "t" "t" "t" ...
$ consType : chr "plosive" "plosive" "plosive" "plosive" ...
$ vowel : chr "aa" "aa" "aa" "aa" ...
$ labelNew : chr "CL_Mid" "CL_Mid" "CL_Mid" "CL_Ons" ...
$ label : chr "CL_Mid" "CL_Mid" "CL_Mid" "CL_Ons" ...
$ repetition : int 2 3 1 3 1 2 3 1 2 2 ...
$ Fan : int 1 1 1 1 1 1 1 1 1 1 ...
$ x : num 18.8 18.9 21.5 19.1 17.7 ...
$ y : num 15.6 15.6 14.1 15.5 16.3 ...
$ vowel2 : chr "a<U+02D0>" "a<U+02D0>" "a<U+02D0>" "a<U+02D0>" ...
$ labelNew2 : int 2 2 2 1 1 1 3 3 3 2 ...
$ context.ord : chr "plain" "plain" "plain" "plain" ...
$ vowel.ord : chr "aa" "aa" "aa" "aa" ...
$ fan_line : int 1 1 1 1 1 1 1 1 1 1 ...
$ X : num 18.8 18.9 21.5 19.1 17.7 ...
$ Y : num 15.6 15.6 14.1 15.5 16.3 ...levels(pharDF$context)NULLpharDF$context <- factor(pharDF$context,
levels = c("plain","velar","uvular","pharyngealised","pharyngeal"))
levels(pharDF$vowel)NULLpharDF$vowel <- factor(pharDF$vowel,
levels = c("ii","aa","uu"))
levels(pharDF$labelNew)NULLpharDF$labelNew <- factor(pharDF$labelNew,
levels = c("CL_Ons","CL_Mid","CL_Off"))
pharDF$ID <- as.numeric(pharDF$ID)
pharDF$Fan <- as.numeric(pharDF$Fan)
pharDF$labelNew2 <- as.numeric(pharDF$labelNew2)
pharDF$time <- pharDF$labelNew2
pharDF$word <- as.factor(pharDF$word)
pharDF$context.ord <- as.ordered(pharDF$context)
contrasts(pharDF$context.ord) <- "contr.treatment"
pharDF$vowel.ord <- as.ordered(pharDF$vowel)
contrasts(pharDF$vowel.ord) <- "contr.treatment"
## to find autocorrelation in the data. Rearrange dataframe and add a variable "start" to indicate
## when Fan == 1
pharDF <- arrange(pharDF, time, ID, Fan)
pharDF$start <- pharDF$Fan==1
ncores = 10
3.2 Visualising the data
Before running anything, we start by visualising the data and use an animated figure
pl <- ggplot(pharDF, aes(x=Fan, y=y, col=context, frame=time)) +
facet_grid(vowel ~ context) +
geom_line(aes(group=ID))+theme_bw()+
transition_manual(time)
animate(pl, width=800, height=300)nframes and fps adjusted to match transition
Rendering [=================>-------------------------------------] at 2.7 fps ~ eta: 1s
Rendering [====================================>------------------] at 2.1 fps ~ eta: 0s
Rendering [=======================================================] at 2.2 fps ~ eta: 0s
[1] "./gganim_plot0001.png" "./gganim_plot0002.png" "./gganim_plot0003.png"
attr(,"frame_vars")3.3 Running our first GAM model
This is our first GAM model. This will be used to find the level of autocorrelation in the data. Our model has double non-linear predictors (fan and time), two factor predictors (context and vowel) and one random effect (word). Interactions between fan and time are used. In addition, by context*vowel interaction is added to account for the two-way interaction with respect to each of fan and time. The function itsadug::acf_resid is used, and we display the level of autocorrelation for each of the “Fan”, the “time”, the “context”, the “vowel” finally the “word”
mdl.sys.time1 <- system.time(phar.gam.noAR <- bam(y ~ context.ord*vowel.ord +
## 1d smooths
s(Fan, bs="cr", k=10) +
s(time, bs="cr", k=3) +
## 1d smooths * factors
s(Fan, k=10, bs="cr", by=context.ord) +
s(Fan, k=10, bs="cr", by=vowel.ord) +
s(Fan, k=10, bs="cr", by=interaction(context.ord, vowel.ord)) +
s(time, k=3, bs="cr", by=context.ord) +
s(time, k=3, bs="cr", by=vowel.ord) +
s(time, k=3, bs="cr", by=interaction(context.ord, vowel.ord)) +
## 2d smooths
ti(Fan, time, bs="cr", k=c(10,3))+
## 2d smooths * factors
ti(Fan, time, bs="cr", k=c(10,3), by=context.ord)+
ti(Fan, time, bs="cr", k=c(10,3), by=vowel.ord)+
ti(Fan, time, bs="cr", k=c(10,3),by=interaction(context.ord, vowel.ord)) +
## random smooths by word
s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
data=pharDF, nthreads = ncores, method="fREML", discrete = TRUE))
mdl.sys.time1utilisateur système écoulé
85.518 0.460 23.230 3.3.1 Summary and Rho
summary(phar.gam.noAR)
Family: gaussian
Link function: identity
Formula:
y ~ context.ord * vowel.ord + s(Fan, bs = "cr", k = 10) + s(time,
bs = "cr", k = 3) + s(Fan, k = 10, bs = "cr", by = context.ord) +
s(Fan, k = 10, bs = "cr", by = vowel.ord) + s(Fan, k = 10,
bs = "cr", by = interaction(context.ord, vowel.ord)) + s(time,
k = 3, bs = "cr", by = context.ord) + s(time, k = 3, bs = "cr",
by = vowel.ord) + s(time, k = 3, bs = "cr", by = interaction(context.ord,
vowel.ord)) + ti(Fan, time, bs = "cr", k = c(10, 3)) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = context.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = vowel.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = interaction(context.ord,
vowel.ord)) + s(Fan, word, bs = "fs", k = 10, m = 1,
xt = list(bs = "tp")) + s(time, word, bs = "fs", k = 3, m = 1,
xt = list(bs = "tp"))
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 35.7762 0.3566 100.340 < 2e-16 ***
context.ordvelar 1.8198 0.5042 3.609 0.000308 ***
context.orduvular 2.4191 0.7973 3.034 0.002415 **
context.ordpharyngealised 0.8235 0.4784 1.721 0.085191 .
context.ordpharyngeal 0.5458 0.6176 0.884 0.376842
vowel.ordaa 0.6929 0.4784 1.449 0.147483
vowel.orduu 0.9109 0.4784 1.904 0.056902 .
context.ordvelar:vowel.ordaa -0.6105 0.6950 -0.878 0.379757
context.orduvular:vowel.ordaa -2.7389 1.1162 -2.454 0.014142 *
context.ordpharyngealised:vowel.ordaa -1.2107 0.6574 -1.841 0.065572 .
context.ordpharyngeal:vowel.ordaa 0.6388 0.8587 0.744 0.456955
context.ordvelar:vowel.orduu -2.0721 0.6950 -2.981 0.002875 **
context.orduvular:vowel.orduu -3.1064 1.1162 -2.783 0.005390 **
context.ordpharyngealised:vowel.orduu -1.7974 0.6574 -2.734 0.006266 **
context.ordpharyngeal:vowel.orduu -0.6710 0.8587 -0.781 0.434568
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df
s(Fan) 7.660e+00 7.704e+00
s(time) 2.394e-04 2.554e-04
s(Fan):context.ordvelar 6.639e+00 6.821e+00
s(Fan):context.orduvular 6.694e+00 6.905e+00
s(Fan):context.ordpharyngealised 7.574e+00 7.651e+00
s(Fan):context.ordpharyngeal 2.753e-04 3.002e-04
s(Fan):vowel.ordaa 6.945e+00 7.093e+00
s(Fan):vowel.orduu 7.107e+00 7.251e+00
s(Fan):interaction(context.ord, vowel.ord)plain.ii 6.900e+00 7.166e+00
s(Fan):interaction(context.ord, vowel.ord)velar.ii 1.001e+00 1.001e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.ii 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 6.652e+00 6.946e+00
s(Fan):interaction(context.ord, vowel.ord)plain.aa 4.221e+00 4.458e+00
s(Fan):interaction(context.ord, vowel.ord)velar.aa 3.245e+00 3.416e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.aa 1.001e+00 1.001e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 6.391e+00 6.683e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)plain.uu 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)velar.uu 7.436e+00 7.671e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.uu 5.422e+00 5.722e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 4.064e+00 4.307e+00
s(time):context.ordvelar 8.318e-01 8.432e-01
s(time):context.orduvular 5.462e-04 5.894e-04
s(time):context.ordpharyngealised 6.189e-04 6.586e-04
s(time):context.ordpharyngeal 6.224e-04 6.734e-04
s(time):vowel.ordaa 3.347e-04 3.594e-04
s(time):vowel.orduu 2.055e-04 2.185e-04
s(time):interaction(context.ord, vowel.ord)plain.ii 1.784e+00 1.798e+00
s(time):interaction(context.ord, vowel.ord)velar.ii 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)uvular.ii 1.678e+00 1.697e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.ii 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.ii 1.853e+00 1.864e+00
s(time):interaction(context.ord, vowel.ord)plain.aa 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)velar.aa 1.805e+00 1.818e+00
s(time):interaction(context.ord, vowel.ord)uvular.aa 1.001e+00 1.001e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.aa 1.559e+00 1.581e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.aa 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)plain.uu 1.474e+00 1.496e+00
s(time):interaction(context.ord, vowel.ord)velar.uu 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)uvular.uu 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.uu 1.645e+00 1.665e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.uu 1.000e+00 1.000e+00
ti(time,Fan) 8.224e+00 9.815e+00
ti(time,Fan):context.ordvelar 9.022e+00 1.126e+01
ti(time,Fan):context.orduvular 1.360e+01 1.549e+01
ti(time,Fan):context.ordpharyngealised 8.357e+00 1.052e+01
ti(time,Fan):context.ordpharyngeal 6.037e+00 7.684e+00
ti(time,Fan):vowel.ordaa 1.304e+01 1.466e+01
ti(time,Fan):vowel.orduu 1.247e+01 1.438e+01
ti(time,Fan):interaction(context.ord, vowel.ord)plain.ii 7.203e+00 8.133e+00
ti(time,Fan):interaction(context.ord, vowel.ord)velar.ii 1.933e+00 1.972e+00
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.ii 1.871e+00 1.967e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 1.533e+01 1.686e+01
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 1.114e+01 1.317e+01
ti(time,Fan):interaction(context.ord, vowel.ord)plain.aa 1.062e+01 1.277e+01
ti(time,Fan):interaction(context.ord, vowel.ord)velar.aa 1.355e+01 1.580e+01
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.aa 1.000e+00 1.001e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 1.010e+00 1.013e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 4.450e+00 5.272e+00
ti(time,Fan):interaction(context.ord, vowel.ord)plain.uu 9.520e+00 1.153e+01
ti(time,Fan):interaction(context.ord, vowel.ord)velar.uu 4.587e+00 5.521e+00
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.uu 8.803e+00 1.102e+01
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 1.001e+00 1.001e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 1.303e+01 1.513e+01
s(Fan,word) 3.433e+02 4.850e+02
s(time,word) 9.173e+01 1.200e+02
F p-value
s(Fan) 109.757 < 2e-16 ***
s(time) 0.002 0.999412
s(Fan):context.ordvelar 7.719 < 2e-16 ***
s(Fan):context.orduvular 10.417 < 2e-16 ***
s(Fan):context.ordpharyngealised 32.030 < 2e-16 ***
s(Fan):context.ordpharyngeal 0.061 0.996573
s(Fan):vowel.ordaa 11.843 < 2e-16 ***
s(Fan):vowel.orduu 16.429 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)plain.ii 42.972 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)velar.ii 215.288 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)uvular.ii 38.402 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 164.512 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 14.980 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)plain.aa 28.096 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)velar.aa 29.473 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)uvular.aa 18.151 2.07e-05 ***
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 19.330 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 43.132 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)plain.uu 156.421 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)velar.uu 23.373 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)uvular.uu 6.384 2.37e-06 ***
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 127.985 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 10.190 < 2e-16 ***
s(time):context.ordvelar 5.863 0.026195 *
s(time):context.orduvular 0.391 0.987883
s(time):context.ordpharyngealised 0.457 0.986153
s(time):context.ordpharyngeal 0.631 0.983553
s(time):vowel.ordaa 0.124 0.994670
s(time):vowel.orduu 0.161 0.995269
s(time):interaction(context.ord, vowel.ord)plain.ii 9.361 0.003289 **
s(time):interaction(context.ord, vowel.ord)velar.ii 0.441 0.506426
s(time):interaction(context.ord, vowel.ord)uvular.ii 0.757 0.389453
s(time):interaction(context.ord, vowel.ord)pharyngealised.ii 2.293 0.129933
s(time):interaction(context.ord, vowel.ord)pharyngeal.ii 2.669 0.070209 .
s(time):interaction(context.ord, vowel.ord)plain.aa 0.000 0.998328
s(time):interaction(context.ord, vowel.ord)velar.aa 1.832 0.156321
s(time):interaction(context.ord, vowel.ord)uvular.aa 0.000 0.996139
s(time):interaction(context.ord, vowel.ord)pharyngealised.aa 1.713 0.332576
s(time):interaction(context.ord, vowel.ord)pharyngeal.aa 0.011 0.917418
s(time):interaction(context.ord, vowel.ord)plain.uu 7.232 0.010802 *
s(time):interaction(context.ord, vowel.ord)velar.uu 0.095 0.758498
s(time):interaction(context.ord, vowel.ord)uvular.uu 0.016 0.901081
s(time):interaction(context.ord, vowel.ord)pharyngealised.uu 3.424 0.121664
s(time):interaction(context.ord, vowel.ord)pharyngeal.uu 0.101 0.750587
ti(time,Fan) 3.008 0.000751 ***
ti(time,Fan):context.ordvelar 2.533 0.004742 **
ti(time,Fan):context.orduvular 14.433 < 2e-16 ***
ti(time,Fan):context.ordpharyngealised 1.260 0.401719
ti(time,Fan):context.ordpharyngeal 1.841 0.097808 .
ti(time,Fan):vowel.ordaa 9.638 < 2e-16 ***
ti(time,Fan):vowel.orduu 5.402 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)plain.ii 9.158 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)velar.ii 8.937 0.000385 ***
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.ii 6.314 0.004897 **
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 47.129 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 15.427 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)plain.aa 5.973 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)velar.aa 15.279 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.aa 18.581 1.64e-05 ***
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 134.167 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 3.090 0.007342 **
ti(time,Fan):interaction(context.ord, vowel.ord)plain.uu 9.768 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)velar.uu 7.195 3.01e-06 ***
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.uu 3.492 6.80e-05 ***
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 6.160 0.013055 *
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 16.508 < 2e-16 ***
s(Fan,word) 30.757 < 2e-16 ***
s(time,word) 11.488 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Rank: 1282/1303
R-sq.(adj) = 0.986 Deviance explained = 98.6%
fREML = 35486 Scale est. = 2.2096 n = 18900rho_est <- start_value_rho(phar.gam.noAR)
rho_est[1] 0.94167493.3.2 ACF first GAM
The five plots below show the autocorrelation in the residuals. As can be see, the first plot using Fan, has a complete zero correlations. It is possible that because the various fan points obtained alongside the tongue contour are already correlated with each other, and hence the correlations between fan 1 to 2, 2 to 3, 41 to 42 are already taken into account by the model. The four additional plots show the autocorrelation in the residuals for time, context, vowel and word. All of these predictors are showing autocorrelations between their successive data points. This means that for a specific time (onset, midpoint or offset), there is already correlations between tongue splines obtained at the onset, the midpoint and the offset. It is crucial to tell the model to account for this, otherwise there is overconfidence in the estimates.
3.3.2.1 ACF by Fan
acf_resid(phar.gam.noAR,split_pred=list(pharDF$Fan),main = "Average ACF No.AR by Fan",cex.lab=1.5,cex.axis=1.5)
3.3.2.2 ACF by Time
acf_resid(phar.gam.noAR,split_pred=list(pharDF$time),main = "Average ACF No.AR by Time",cex.lab=1.5,cex.axis=1.5)
3.3.2.3 ACF by Context
acf_resid(phar.gam.noAR,split_pred=list(pharDF$context.ord),main = "Average ACF No.AR by Context",cex.lab=1.5,cex.axis=1.5)
3.3.2.4 ACF by Vowel
acf_resid(phar.gam.noAR,split_pred=list(pharDF$vowel.ord),main = "Average ACF No.AR by Vowel",cex.lab=1.5,cex.axis=1.5)
3.3.2.5 ACF by Word
acf_resid(phar.gam.noAR,split_pred=list(pharDF$word),main = "Average ACF No.AR by Word",cex.lab=1.5,cex.axis=1.5)
3.4 Running our second Autoregressive GAM
Our second GAM model is identical to the first, but takes into account the autocorrelation. By including AR.start and rho, we are using information obtained from original model to account for the autocorrelation
mdl.sys.time2 <- system.time(phar.gam.AR <- bam(y ~ context.ord*vowel.ord +
## 1d smooths
s(Fan, bs="cr", k=10) +
s(time, bs="cr", k=3) +
## 1d smooths * factors
s(Fan, k=10, bs="cr", by=context.ord) +
s(Fan, k=10, bs="cr", by=vowel.ord) +
s(Fan, k=10, bs="cr", by=interaction(context.ord, vowel.ord)) +
s(time, k=3, bs="cr", by=context.ord) +
s(time, k=3, bs="cr", by=vowel.ord) +
s(time, k=3, bs="cr", by=interaction(context.ord, vowel.ord)) +
## 2d smooths
ti(Fan, time, bs="cr", k=c(10,3))+
## 2d smooths * factors
ti(Fan, time, bs="cr", k=c(10,3), by=context.ord)+
ti(Fan, time, bs="cr", k=c(10,3), by=vowel.ord)+
ti(Fan, time, bs="cr", k=c(10,3), by=interaction(context.ord, vowel.ord))+
## random smooths by word
s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
data=pharDF,
AR.start=pharDF$start, rho=rho_est, nthreads = ncores, method="fREML", discrete = TRUE))
mdl.sys.time2utilisateur système écoulé
89.537 0.438 21.479 3.4.1 Summary
summary(phar.gam.AR)
Family: gaussian
Link function: identity
Formula:
y ~ context.ord * vowel.ord + s(Fan, bs = "cr", k = 10) + s(time,
bs = "cr", k = 3) + s(Fan, k = 10, bs = "cr", by = context.ord) +
s(Fan, k = 10, bs = "cr", by = vowel.ord) + s(Fan, k = 10,
bs = "cr", by = interaction(context.ord, vowel.ord)) + s(time,
k = 3, bs = "cr", by = context.ord) + s(time, k = 3, bs = "cr",
by = vowel.ord) + s(time, k = 3, bs = "cr", by = interaction(context.ord,
vowel.ord)) + ti(Fan, time, bs = "cr", k = c(10, 3)) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = context.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = vowel.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = interaction(context.ord,
vowel.ord)) + s(Fan, word, bs = "fs", k = 10, m = 1,
xt = list(bs = "tp")) + s(time, word, bs = "fs", k = 3, m = 1,
xt = list(bs = "tp"))
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 35.7836 0.3498 102.295 < 2e-16 ***
context.ordvelar 1.8356 0.4947 3.711 0.000207 ***
context.orduvular 2.4247 0.7819 3.101 0.001933 **
context.ordpharyngealised 0.8374 0.4693 1.785 0.074347 .
context.ordpharyngeal 0.5581 0.6059 0.921 0.356992
vowel.ordaa 0.7040 0.4693 1.500 0.133574
vowel.orduu 0.9126 0.4693 1.945 0.051834 .
context.ordvelar:vowel.ordaa -0.6253 0.6818 -0.917 0.359087
context.orduvular:vowel.ordaa -2.7150 1.0942 -2.481 0.013103 *
context.ordpharyngealised:vowel.ordaa -1.2354 0.6450 -1.915 0.055454 .
context.ordpharyngeal:vowel.ordaa 0.6256 0.8423 0.743 0.457665
context.ordvelar:vowel.orduu -2.0672 0.6818 -3.032 0.002434 **
context.orduvular:vowel.orduu -3.1006 1.0949 -2.832 0.004632 **
context.ordpharyngealised:vowel.orduu -1.8018 0.6448 -2.794 0.005209 **
context.ordpharyngeal:vowel.orduu -0.6707 0.8424 -0.796 0.425971
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df
s(Fan) 8.724e+00 8.770e+00
s(time) 2.974e-04 5.341e-04
s(Fan):context.ordvelar 6.974e+00 7.161e+00
s(Fan):context.orduvular 7.046e+00 7.244e+00
s(Fan):context.ordpharyngealised 7.697e+00 7.763e+00
s(Fan):context.ordpharyngeal 7.952e-05 9.977e-05
s(Fan):vowel.ordaa 7.050e+00 7.217e+00
s(Fan):vowel.orduu 7.190e+00 7.348e+00
s(Fan):interaction(context.ord, vowel.ord)plain.ii 7.559e+00 7.824e+00
s(Fan):interaction(context.ord, vowel.ord)velar.ii 3.153e+00 3.478e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.ii 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 7.113e+00 7.446e+00
s(Fan):interaction(context.ord, vowel.ord)plain.aa 4.307e+00 4.695e+00
s(Fan):interaction(context.ord, vowel.ord)velar.aa 1.001e+00 1.001e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.aa 1.001e+00 1.001e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 6.680e+00 7.045e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 1.000e+00 1.000e+00
s(Fan):interaction(context.ord, vowel.ord)plain.uu 1.000e+00 1.001e+00
s(Fan):interaction(context.ord, vowel.ord)velar.uu 7.606e+00 7.872e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.uu 6.575e+00 6.962e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 1.000e+00 1.001e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 4.828e+00 5.252e+00
s(time):context.ordvelar 7.306e-01 9.105e-01
s(time):context.orduvular 4.284e-04 8.150e-04
s(time):context.ordpharyngealised 5.822e-04 1.036e-03
s(time):context.ordpharyngeal 1.193e-03 2.282e-03
s(time):vowel.ordaa 2.588e-04 4.807e-04
s(time):vowel.orduu 4.581e-04 8.308e-04
s(time):interaction(context.ord, vowel.ord)plain.ii 1.459e+00 1.703e+00
s(time):interaction(context.ord, vowel.ord)velar.ii 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)uvular.ii 1.579e+00 1.821e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.ii 1.000e+00 1.001e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.ii 1.793e+00 1.957e+00
s(time):interaction(context.ord, vowel.ord)plain.aa 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)velar.aa 1.758e+00 1.926e+00
s(time):interaction(context.ord, vowel.ord)uvular.aa 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.aa 1.340e+00 1.560e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.aa 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)plain.uu 1.138e+00 1.256e+00
s(time):interaction(context.ord, vowel.ord)velar.uu 1.000e+00 1.001e+00
s(time):interaction(context.ord, vowel.ord)uvular.uu 1.000e+00 1.000e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.uu 1.447e+00 1.689e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.uu 1.001e+00 1.001e+00
ti(time,Fan) 5.065e+00 6.412e+00
ti(time,Fan):context.ordvelar 7.295e+00 9.281e+00
ti(time,Fan):context.orduvular 1.523e+01 1.650e+01
ti(time,Fan):context.ordpharyngealised 1.254e+01 1.431e+01
ti(time,Fan):context.ordpharyngeal 1.682e+00 2.235e+00
ti(time,Fan):vowel.ordaa 1.314e+01 1.464e+01
ti(time,Fan):vowel.orduu 1.216e+01 1.371e+01
ti(time,Fan):interaction(context.ord, vowel.ord)plain.ii 8.345e+00 8.839e+00
ti(time,Fan):interaction(context.ord, vowel.ord)velar.ii 6.120e+00 7.798e+00
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.ii 1.001e+00 1.002e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 1.653e+01 1.749e+01
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 1.579e+01 1.733e+01
ti(time,Fan):interaction(context.ord, vowel.ord)plain.aa 1.079e+01 1.331e+01
ti(time,Fan):interaction(context.ord, vowel.ord)velar.aa 1.559e+01 1.702e+01
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.aa 1.001e+00 1.001e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 1.326e+00 1.435e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 7.798e+00 1.031e+01
ti(time,Fan):interaction(context.ord, vowel.ord)plain.uu 1.165e+01 1.401e+01
ti(time,Fan):interaction(context.ord, vowel.ord)velar.uu 5.552e+00 6.490e+00
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.uu 1.093e+01 1.411e+01
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 2.277e+00 2.785e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 1.516e+01 1.691e+01
s(Fan,word) 3.770e+02 4.890e+02
s(time,word) 1.415e+01 1.250e+02
F p-value
s(Fan) 146.962 < 2e-16 ***
s(time) 0.026 0.99701
s(Fan):context.ordvelar 9.096 < 2e-16 ***
s(Fan):context.orduvular 9.053 < 2e-16 ***
s(Fan):context.ordpharyngealised 34.585 < 2e-16 ***
s(Fan):context.ordpharyngeal 0.004 0.99950
s(Fan):vowel.ordaa 12.329 < 2e-16 ***
s(Fan):vowel.orduu 16.218 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)plain.ii 5.550 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)velar.ii 1.402 0.22305
s(Fan):interaction(context.ord, vowel.ord)uvular.ii 0.000 0.99998
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 0.000 0.99998
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 3.041 0.00232 **
s(Fan):interaction(context.ord, vowel.ord)plain.aa 0.706 0.54776
s(Fan):interaction(context.ord, vowel.ord)velar.aa 0.000 0.99998
s(Fan):interaction(context.ord, vowel.ord)uvular.aa 0.000 0.99998
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 3.347 0.00160 **
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 0.000 0.99999
s(Fan):interaction(context.ord, vowel.ord)plain.uu 0.000 0.99999
s(Fan):interaction(context.ord, vowel.ord)velar.uu 6.458 < 2e-16 ***
s(Fan):interaction(context.ord, vowel.ord)uvular.uu 2.243 0.03089 *
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 0.000 0.99999
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 2.282 0.03235 *
s(time):context.ordvelar 2.978 0.09965 .
s(time):context.orduvular 0.192 0.99001
s(time):context.ordpharyngealised 0.443 0.98291
s(time):context.ordpharyngeal 0.405 0.97575
s(time):vowel.ordaa 0.030 0.99697
s(time):vowel.orduu 0.224 0.98911
s(time):interaction(context.ord, vowel.ord)plain.ii 14.401 5.19e-05 ***
s(time):interaction(context.ord, vowel.ord)velar.ii 0.916 0.33842
s(time):interaction(context.ord, vowel.ord)uvular.ii 0.567 0.48825
s(time):interaction(context.ord, vowel.ord)pharyngealised.ii 4.530 0.03329 *
s(time):interaction(context.ord, vowel.ord)pharyngeal.ii 1.855 0.15363
s(time):interaction(context.ord, vowel.ord)plain.aa 0.000 0.99948
s(time):interaction(context.ord, vowel.ord)velar.aa 1.609 0.19535
s(time):interaction(context.ord, vowel.ord)uvular.aa 0.001 0.97747
s(time):interaction(context.ord, vowel.ord)pharyngealised.aa 2.081 0.21691
s(time):interaction(context.ord, vowel.ord)pharyngeal.aa 0.015 0.90163
s(time):interaction(context.ord, vowel.ord)plain.uu 14.364 0.00011 ***
s(time):interaction(context.ord, vowel.ord)velar.uu 0.187 0.66604
s(time):interaction(context.ord, vowel.ord)uvular.uu 0.027 0.87099
s(time):interaction(context.ord, vowel.ord)pharyngealised.uu 4.750 0.03422 *
s(time):interaction(context.ord, vowel.ord)pharyngeal.uu 0.165 0.68517
ti(time,Fan) 0.043 0.99990
ti(time,Fan):context.ordvelar 0.991 0.39702
ti(time,Fan):context.orduvular 9.891 < 2e-16 ***
ti(time,Fan):context.ordpharyngealised 3.070 8.96e-05 ***
ti(time,Fan):context.ordpharyngeal 0.054 0.92423
ti(time,Fan):vowel.ordaa 4.595 < 2e-16 ***
ti(time,Fan):vowel.orduu 3.936 5.12e-07 ***
ti(time,Fan):interaction(context.ord, vowel.ord)plain.ii 11.080 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)velar.ii 0.900 0.63496
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.ii 0.000 1.00000
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 18.888 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 7.897 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)plain.aa 2.172 0.00777 **
ti(time,Fan):interaction(context.ord, vowel.ord)velar.aa 5.689 < 2e-16 ***
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.aa 0.000 1.00000
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 0.000 0.99973
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 1.413 0.16403
ti(time,Fan):interaction(context.ord, vowel.ord)plain.uu 2.310 0.00357 **
ti(time,Fan):interaction(context.ord, vowel.ord)velar.uu 1.727 0.12905
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.uu 1.500 0.11389
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 0.080 0.97179
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 6.158 < 2e-16 ***
s(Fan,word) 12.279 < 2e-16 ***
s(time,word) 0.190 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Rank: 1284/1303
R-sq.(adj) = 0.984 Deviance explained = 98.5%
fREML = 12752 Scale est. = 1.6981 n = 189003.4.2 ACF second GAM
The following five plots show (in the same order as above) the autocorrelation in the residuals. As can be seen, for all five plots, the levels of autocorrelations in the residuals are reduced massively. We have now more confidence in our estimates, and can continue work
3.4.2.1 ACF by Fan
acf_resid(phar.gam.AR,split_pred=list(pharDF$Fan),main = "Average ACF AR by Fan",cex.lab=1.5,cex.axis=1.5)
3.4.2.2 ACF by Time
acf_resid(phar.gam.AR,split_pred=list(pharDF$time),main = "Average ACF AR by Time",cex.lab=1.5,cex.axis=1.5)
3.4.2.3 ACF by Context
acf_resid(phar.gam.AR,split_pred=list(pharDF$context.ord),main = "Average ACF AR by Context",cex.lab=1.5,cex.axis=1.5)
3.4.2.4 ACF by Vowel
acf_resid(phar.gam.AR,split_pred=list(pharDF$vowel.ord),main = "Average ACF AR by Vowel",cex.lab=1.5,cex.axis=1.5)
3.4.2.5 ACF by Word
acf_resid(phar.gam.AR,split_pred=list(pharDF$word),main = "Average ACF AR by Word",cex.lab=1.5,cex.axis=1.5)
3.4.3 Gam Check
gam.check(phar.gam.AR)
Method: fREML Optimizer: perf chol
$grad
[1] -4.495788e-05 -1.416679e-04 -8.724631e-07 -3.369139e-05 -2.322772e-05 -2.646267e-05
[7] -3.934153e-05 8.572465e-06 8.587223e-06 -6.083851e-05 -1.765828e-05 -6.894936e-05
[13] 7.645017e-06 1.132933e-05 3.365540e-05 -7.907573e-05 -1.394622e-05 -7.157765e-05
[19] -9.047854e-05 -2.281925e-05 1.471309e-05 -7.980586e-05 -3.026176e-05 2.033256e-08
[25] -1.358484e-04 -6.164180e-05 -1.347668e-04 -1.221928e-04 -1.359857e-04 2.845275e-08
[31] -6.222191e-05 -3.619593e-08 -1.309497e-04 2.290468e-09 -6.255144e-05 -4.840882e-08
[37] -5.999826e-05 -3.398253e-08 -6.173596e-05 -3.697374e-08 -1.404164e-04 -6.020312e-05
[43] 1.088059e-07 -1.516741e-04 1.320886e-07 -4.487331e-08 -8.561040e-09 1.888781e-08
[49] -1.303608e-08 5.673040e-09 -9.978420e-08 -5.220367e-08 2.270234e-07 1.380112e-07
[55] 4.946025e-07 9.444100e-08 2.411116e-07 1.656954e-08 -8.164500e-05 1.610296e-09
[61] -3.780627e-08 -8.289301e-09 -4.829854e-05 -5.810627e-05 -3.609381e-08 7.586333e-08
[67] -3.783145e-09 -6.419241e-08 9.913513e-08 -1.850878e-07 -5.265704e-07 -8.102783e-08
[73] -3.352521e-05 -9.251367e-05 -1.012569e-04 -2.177566e-09 5.302926e-07 -3.395690e-07
[79] -2.511117e-07 -6.949732e-08 -9.181318e-05 -4.868114e-09 -3.533558e-08 7.032578e-08
[85] 6.009735e-09 5.400447e-09 -1.280399e-07 1.015886e-07 4.694833e-05 -1.064926e-12
[91] -1.449279e-04 1.127987e-12 3.939912e-04
$hess
[,1] [,2] [,3] [,4] [,5] [,6]
3.880516e+00 -9.231245e-09 3.352108e-02 -6.079133e-02 -7.561573e-02 -1.306881e-06
-9.231245e-09 1.416279e-04 -2.396216e-09 -1.217396e-09 -7.030217e-10 -4.475964e-15
3.352108e-02 -2.396216e-09 3.063521e+00 -5.037472e-02 4.452336e-02 -1.541643e-06
-6.079133e-02 -1.217396e-09 -5.037472e-02 3.088378e+00 -1.087565e-01 -1.243132e-06
-7.561573e-02 -7.030217e-10 4.452336e-02 -1.087565e-01 3.699925e+00 -5.288553e-07
-1.306881e-06 -4.475964e-15 -1.541643e-06 -1.243132e-06 -5.288553e-07 2.646208e-05
-7.386708e-02 -5.397808e-10 1.241113e-02 -2.294418e-02 -1.046438e-01 1.544368e-06
-6.651738e-02 -2.084358e-09 -9.398017e-02 -1.082492e-01 -4.609894e-02 -1.120971e-06
3.168294e-02 -2.353574e-09 -1.362277e-01 3.010183e-02 7.470902e-02 3.039897e-07
1.886826e-03 -1.242707e-09 -1.130408e-01 1.760305e-02 3.081848e-02 -2.694112e-06
[,7] [,8] [,9] [,10] [,11] [,12]
-7.386708e-02 -6.651738e-02 3.168294e-02 1.886826e-03 5.634728e-06 3.846927e-07
-5.397808e-10 -2.084358e-09 -2.353574e-09 -1.242707e-09 2.582525e-12 -1.359434e-12
1.241113e-02 -9.398017e-02 -1.362277e-01 -1.130408e-01 2.045724e-07 -2.959935e-06
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1.289316e-01 9.395547e-02 -6.922503e-02 5.777377e-01 1.290994e-05 1.423419e-05
[,13] [,14] [,15] [,16] [,17] [,18]
-5.203275e-02 -8.101122e-03 -6.829396e-06 2.440404e-05 1.113617e-02 4.098931e-07
6.902940e-10 -3.832186e-10 1.963794e-13 1.194605e-11 3.511318e-10 1.220394e-13
1.127289e-01 2.892477e-01 9.334737e-05 1.030646e-06 9.302451e-02 -7.417308e-06
9.433554e-02 2.432500e-02 8.628293e-07 2.193618e-05 1.151931e-02 -2.872032e-06
5.312686e-02 -3.631227e-02 1.776242e-06 3.720593e-06 -2.713051e-02 -8.078355e-07
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1.757226e-01 5.750532e-02 1.626081e-05 9.207492e-06 -2.017819e-04 -2.358560e-06
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-9.759511e-02 6.825345e-02 1.612873e-04 6.002560e-05 1.210630e-01 -7.466222e-06
[,19] [,20] [,21] [,22] [,23] [,24]
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1.184043e-05 5.174802e-02 4.686380e-01 3.625668e-06 -1.190407e-02 4.983402e-07
1.945853e-05 -1.620299e-02 -1.270778e-02 6.448958e-06 -2.083891e-02 1.360887e-06
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1.296229e-06 1.337902e-01 1.507348e-04 9.768909e-06 3.165542e-02 -1.767604e-04
[,25] [,26] [,27] [,28] [,29] [,30]
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1.330483e-09 -4.288783e-10 5.291355e-08 2.658805e-09 -2.295977e-09 -1.082912e-06
-1.839684e-08 -2.241399e-09 4.802360e-08 3.441774e-10 -2.833924e-09 -1.578634e-06
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[,31] [,32] [,33] [,34] [,35] [,36]
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2.454251e-15 -2.846024e-11 1.063626e-13 -1.711038e-10 1.112930e-13 5.148062e-10
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4.851659e-09 1.633855e-05 3.734111e-08 -2.442146e-07 -3.179787e-09 3.388410e-04
[,37] [,38] [,39] [,40] [,41] [,42]
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4.044007e-14 -4.276019e-11 -1.159225e-13 -3.915910e-10 -4.382897e-14 5.337302e-15
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3.923203e-10 4.480139e-06 5.576079e-10 -8.524391e-06 -5.902612e-10 3.976194e-11
-4.424200e-09 6.698160e-05 -1.086912e-08 -5.806584e-05 2.810178e-08 9.665810e-11
[,43] [,44] [,45] [,46] [,47] [,48]
4.961272e-05 1.569969e-09 -6.248696e-05 -1.063685e-04 1.212921e-04 1.734702e-04
2.727882e-06 -1.189373e-08 -1.218900e-06 7.683570e-08 -2.496446e-07 2.176618e-08
1.290101e-05 1.040451e-09 -2.582515e-05 1.390319e-06 3.765130e-04 1.394995e-04
1.596921e-05 -1.873458e-10 2.686613e-05 -4.526913e-05 -2.571018e-05 -7.577537e-05
2.473865e-05 1.424518e-09 -2.978307e-05 -3.012419e-04 9.855081e-05 1.640293e-04
4.451673e-10 -8.546503e-13 7.289116e-10 -6.077916e-10 1.021675e-09 1.999488e-10
1.961332e-05 3.668778e-09 -1.382468e-04 -6.308237e-04 2.610396e-04 -6.269350e-05
7.275647e-05 -3.390595e-09 6.481517e-05 1.574318e-04 1.679877e-04 2.093997e-04
1.822809e-05 -1.430880e-09 -4.446656e-04 -3.921748e-04 -2.730952e-04 2.446572e-04
7.712028e-05 -2.224655e-09 7.509315e-05 2.753300e-05 1.000807e-04 -3.240569e-04
[,49] [,50] [,51] [,52] [,53] [,54]
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4.765585e-06 2.521469e-05 -1.036905e-04 -3.865351e-04 1.097437e-04 9.632640e-05
1.107460e-03 6.677721e-03 2.036808e-04 4.465681e-04 -9.070326e-06 -1.481947e-04
1.079891e-05 5.009462e-05 8.715721e-04 1.757358e-03 -8.285945e-06 -9.043058e-05
-1.675060e-09 6.426617e-12 -1.765829e-09 2.586346e-09 8.383160e-09 1.008948e-08
-8.564795e-05 -3.040854e-04 5.740880e-06 1.081109e-04 8.537711e-05 1.424100e-04
-3.171806e-05 -1.674678e-04 6.286227e-05 1.946736e-04 -1.182877e-05 -7.175743e-05
6.608251e-05 1.335481e-04 -6.633133e-06 2.574265e-06 7.719769e-05 1.881947e-04
4.652378e-05 4.943491e-05 -3.893308e-05 -1.977136e-04 8.065448e-05 -2.325817e-05
[,55] [,56] [,57] [,58] [,59] [,60]
7.779693e-05 -1.371318e-04 -4.285991e-04 -1.113889e-05 1.054221e-08 1.277034e-05
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1.422042e-05 -4.489022e-04 -3.423386e-04 -2.277916e-05 -2.490271e-08 4.991327e-06
9.661978e-10 -2.577332e-10 -6.478925e-09 -6.341739e-10 -4.903237e-14 2.937526e-11
-4.237246e-04 -9.505363e-04 -7.281194e-04 1.067245e-04 -7.888064e-08 -2.196882e-05
-9.200836e-06 -1.511014e-04 -1.416398e-03 -3.006152e-04 1.082006e-08 2.104007e-06
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-4.614063e-05 1.437906e-04 4.221458e-05 6.518958e-05 8.098373e-09 3.462061e-06
[,61] [,62] [,63] [,64] [,65] [,66]
-7.745547e-05 1.741222e-04 -3.463914e-08 -1.542720e-07 -2.265386e-04 -8.852772e-05
2.716727e-08 2.634004e-08 1.404968e-12 1.471061e-11 8.212657e-08 -6.281976e-08
-8.068890e-05 -8.254552e-04 -8.745653e-11 2.076558e-09 7.353201e-05 4.578471e-04
2.898750e-06 1.809928e-04 8.175340e-09 2.237611e-08 -7.012344e-05 -5.493256e-05
-8.887564e-06 1.412022e-04 -1.026374e-08 -7.568038e-08 1.373583e-05 4.562690e-05
2.458730e-09 2.489184e-09 1.112567e-12 4.086080e-12 -3.898017e-09 3.965688e-10
-1.401805e-04 -4.301723e-04 -6.819771e-08 -3.231013e-07 -2.199648e-04 -4.998866e-04
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9.012389e-05 6.973290e-05 3.438449e-08 2.098704e-07 3.159693e-04 1.350864e-03
-3.861760e-04 -3.696667e-04 3.685551e-08 1.153315e-07 1.798065e-04 1.690016e-04
[,67] [,68] [,69] [,70] [,71] [,72]
5.550998e-08 -4.230004e-04 1.347997e-05 -1.429260e-04 -1.805754e-04 6.355694e-05
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1.394714e-06 -3.267243e-04 6.104505e-05 -8.467440e-05 2.691489e-05 -5.686220e-05
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-1.895297e-09 -1.611598e-09 8.588749e-09 1.816996e-09 4.673649e-10 1.822324e-09
-3.754149e-05 1.288706e-04 4.010423e-05 9.380054e-06 -4.227716e-04 -1.151053e-03
2.339128e-07 6.626226e-05 7.563158e-06 -8.123387e-06 2.015915e-04 -7.553682e-05
2.740743e-05 -8.852078e-04 -3.315583e-05 -6.615090e-04 3.109355e-04 1.259760e-04
4.205022e-05 -9.460767e-05 2.131245e-05 8.107435e-05 1.057420e-03 -6.067939e-04
[,73] [,74] [,75] [,76] [,77] [,78]
-3.505856e-08 -1.462401e-08 5.758811e-08 2.379183e-06 -2.156888e-04 1.527339e-05
1.342997e-11 -1.357342e-13 -1.494040e-11 -1.972284e-13 -3.055093e-07 -1.295831e-08
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3.814156e-10 -5.932430e-09 -2.611136e-08 -1.736375e-07 -4.220483e-04 -6.233044e-05
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7.909948e-13 -1.382118e-13 2.620552e-12 8.930481e-12 2.887069e-08 -2.223846e-08
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1.825399e-08 1.929210e-08 -7.124301e-09 -2.896370e-06 3.532382e-04 5.196455e-04
-4.675594e-08 7.135731e-09 -4.897608e-08 -3.293468e-06 1.803410e-05 -2.412502e-04
[,79] [,80] [,81] [,82] [,83] [,84]
3.398022e-05 2.944639e-05 -7.838411e-09 -1.648772e-06 1.287580e-05 1.227354e-04
-1.385051e-06 8.982407e-08 9.014620e-14 2.507491e-12 -2.221692e-07 1.107679e-07
2.674542e-04 6.402785e-04 3.330847e-09 -1.778458e-05 2.559663e-05 2.371739e-04
2.647604e-04 4.608897e-04 -3.197002e-08 -7.643634e-06 6.250969e-04 -7.288908e-04
4.205654e-04 5.685452e-04 -9.495112e-09 -5.508952e-06 5.026475e-05 6.965235e-05
1.280436e-08 9.769795e-09 8.361440e-14 -5.388466e-11 -1.445034e-09 -1.528459e-09
3.048675e-04 6.051042e-04 -7.492241e-09 -1.179487e-05 -5.460006e-06 -2.865809e-05
-2.045172e-04 -4.839180e-04 1.084807e-08 -1.009710e-05 5.382291e-05 1.331002e-04
-2.401406e-04 -1.252667e-03 -3.211251e-08 3.382290e-06 2.113107e-05 2.874313e-04
-5.747380e-04 -3.152930e-04 2.288397e-09 -2.511918e-06 -4.040092e-06 7.206640e-05
[,85] [,86] [,87] [,88] [,89] [,90]
-8.777671e-06 1.414501e-05 -1.205317e-05 3.142690e-05 9.270843e-03 4.065915e-17
-1.491851e-08 -1.170314e-09 -4.793302e-07 2.488867e-08 6.030278e-09 -3.723499e-23
-3.848509e-05 -3.686426e-05 -1.400584e-05 2.748247e-06 5.805769e-01 4.693900e-17
-6.602956e-07 1.384728e-05 7.747518e-06 7.809550e-05 -4.941868e-01 1.140126e-16
4.350306e-05 7.549797e-05 3.562933e-05 2.343392e-04 -5.510659e-02 9.726937e-17
-2.481791e-10 1.394424e-09 -7.109867e-10 -4.300773e-09 -7.863366e-06 2.172329e-21
4.655552e-05 1.285271e-04 -1.878453e-05 1.348932e-04 4.475946e-01 9.110115e-17
-3.561916e-05 -1.506822e-06 7.091318e-06 8.576493e-05 6.089240e-02 1.791356e-16
-9.233890e-06 -2.698747e-05 1.927428e-05 1.082807e-04 -7.976729e-01 -2.184689e-16
1.871155e-05 -7.351948e-05 -8.549989e-05 1.253963e-06 -4.869340e-02 -1.775974e-16
[,91] [,92] [,93]
-3.744708e-10 -3.754766e-17 -3.862284e+00
-4.218537e-09 -1.591030e-21 -7.014975e-06
1.079393e-09 1.068495e-16 -3.486955e+00
-2.952418e-09 4.361281e-17 -3.522822e+00
-6.925414e-10 -1.013151e-17 -3.848667e+00
-1.150989e-13 2.763347e-21 -1.329747e-05
-1.507948e-09 -1.344285e-16 -3.524951e+00
9.086843e-09 4.192677e-17 -3.594991e+00
4.910376e-11 4.297865e-18 -3.279486e+00
1.622137e-09 9.054853e-17 -1.076270e+00
[ getOption("max.print") est atteint -- 83 lignes omises ]
Model rank = 1284 / 1303
Basis dimension (k) checking results. Low p-value (k-index<1) may
indicate that k is too low, especially if edf is close to k'.
k' edf
s(Fan) 9.00e+00 8.72e+00
s(time) 2.00e+00 2.97e-04
s(Fan):context.ordvelar 9.00e+00 6.97e+00
s(Fan):context.orduvular 9.00e+00 7.05e+00
s(Fan):context.ordpharyngealised 9.00e+00 7.70e+00
s(Fan):context.ordpharyngeal 9.00e+00 7.95e-05
s(Fan):vowel.ordaa 9.00e+00 7.05e+00
s(Fan):vowel.orduu 9.00e+00 7.19e+00
s(Fan):interaction(context.ord, vowel.ord)plain.ii 9.00e+00 7.56e+00
s(Fan):interaction(context.ord, vowel.ord)velar.ii 9.00e+00 3.15e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.ii 9.00e+00 1.00e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 9.00e+00 1.00e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 9.00e+00 7.11e+00
s(Fan):interaction(context.ord, vowel.ord)plain.aa 9.00e+00 4.31e+00
s(Fan):interaction(context.ord, vowel.ord)velar.aa 9.00e+00 1.00e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.aa 9.00e+00 1.00e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 9.00e+00 6.68e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 9.00e+00 1.00e+00
s(Fan):interaction(context.ord, vowel.ord)plain.uu 9.00e+00 1.00e+00
s(Fan):interaction(context.ord, vowel.ord)velar.uu 9.00e+00 7.61e+00
s(Fan):interaction(context.ord, vowel.ord)uvular.uu 9.00e+00 6.57e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 9.00e+00 1.00e+00
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 9.00e+00 4.83e+00
s(time):context.ordvelar 2.00e+00 7.31e-01
s(time):context.orduvular 2.00e+00 4.28e-04
s(time):context.ordpharyngealised 2.00e+00 5.82e-04
s(time):context.ordpharyngeal 2.00e+00 1.19e-03
s(time):vowel.ordaa 2.00e+00 2.59e-04
s(time):vowel.orduu 2.00e+00 4.58e-04
s(time):interaction(context.ord, vowel.ord)plain.ii 2.00e+00 1.46e+00
s(time):interaction(context.ord, vowel.ord)velar.ii 2.00e+00 1.00e+00
s(time):interaction(context.ord, vowel.ord)uvular.ii 2.00e+00 1.58e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.ii 2.00e+00 1.00e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.ii 2.00e+00 1.79e+00
s(time):interaction(context.ord, vowel.ord)plain.aa 2.00e+00 1.00e+00
s(time):interaction(context.ord, vowel.ord)velar.aa 2.00e+00 1.76e+00
s(time):interaction(context.ord, vowel.ord)uvular.aa 2.00e+00 1.00e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.aa 2.00e+00 1.34e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.aa 2.00e+00 1.00e+00
s(time):interaction(context.ord, vowel.ord)plain.uu 2.00e+00 1.14e+00
s(time):interaction(context.ord, vowel.ord)velar.uu 2.00e+00 1.00e+00
s(time):interaction(context.ord, vowel.ord)uvular.uu 2.00e+00 1.00e+00
s(time):interaction(context.ord, vowel.ord)pharyngealised.uu 2.00e+00 1.45e+00
s(time):interaction(context.ord, vowel.ord)pharyngeal.uu 2.00e+00 1.00e+00
ti(time,Fan) 1.80e+01 5.06e+00
ti(time,Fan):context.ordvelar 1.80e+01 7.29e+00
ti(time,Fan):context.orduvular 1.80e+01 1.52e+01
ti(time,Fan):context.ordpharyngealised 1.80e+01 1.25e+01
ti(time,Fan):context.ordpharyngeal 1.80e+01 1.68e+00
ti(time,Fan):vowel.ordaa 1.80e+01 1.31e+01
ti(time,Fan):vowel.orduu 1.80e+01 1.22e+01
ti(time,Fan):interaction(context.ord, vowel.ord)plain.ii 1.80e+01 8.34e+00
ti(time,Fan):interaction(context.ord, vowel.ord)velar.ii 1.80e+01 6.12e+00
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.ii 1.80e+01 1.00e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 1.80e+01 1.65e+01
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 1.80e+01 1.58e+01
ti(time,Fan):interaction(context.ord, vowel.ord)plain.aa 1.80e+01 1.08e+01
ti(time,Fan):interaction(context.ord, vowel.ord)velar.aa 1.80e+01 1.56e+01
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.aa 1.80e+01 1.00e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 1.80e+01 1.33e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 1.80e+01 7.80e+00
ti(time,Fan):interaction(context.ord, vowel.ord)plain.uu 1.80e+01 1.17e+01
ti(time,Fan):interaction(context.ord, vowel.ord)velar.uu 1.80e+01 5.55e+00
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.uu 1.80e+01 1.09e+01
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 1.80e+01 2.28e+00
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 1.80e+01 1.52e+01
s(Fan,word) 5.00e+02 3.77e+02
s(time,word) 1.50e+02 1.41e+01
k-index p-value
s(Fan) 1.03 0.975
s(time) 1.02 0.830
s(Fan):context.ordvelar 1.03 0.970
s(Fan):context.orduvular 1.03 0.980
s(Fan):context.ordpharyngealised 1.03 0.980
s(Fan):context.ordpharyngeal 1.03 0.975
s(Fan):vowel.ordaa 1.03 0.980
s(Fan):vowel.orduu 1.03 1.000
s(Fan):interaction(context.ord, vowel.ord)plain.ii 1.03 0.980
s(Fan):interaction(context.ord, vowel.ord)velar.ii 1.03 0.990
s(Fan):interaction(context.ord, vowel.ord)uvular.ii 1.03 0.985
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 1.03 0.990
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 1.03 0.970
s(Fan):interaction(context.ord, vowel.ord)plain.aa 1.03 0.975
s(Fan):interaction(context.ord, vowel.ord)velar.aa 1.03 0.980
s(Fan):interaction(context.ord, vowel.ord)uvular.aa 1.03 0.980
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 1.03 0.980
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 1.03 0.970
s(Fan):interaction(context.ord, vowel.ord)plain.uu 1.03 0.985
s(Fan):interaction(context.ord, vowel.ord)velar.uu 1.03 0.975
s(Fan):interaction(context.ord, vowel.ord)uvular.uu 1.03 0.970
s(Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 1.03 0.970
s(Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 1.03 0.980
s(time):context.ordvelar 1.02 0.870
s(time):context.orduvular 1.02 0.825
s(time):context.ordpharyngealised 1.02 0.840
s(time):context.ordpharyngeal 1.02 0.830
s(time):vowel.ordaa 1.02 0.825
s(time):vowel.orduu 1.02 0.880
s(time):interaction(context.ord, vowel.ord)plain.ii 1.02 0.850
s(time):interaction(context.ord, vowel.ord)velar.ii 1.02 0.890
s(time):interaction(context.ord, vowel.ord)uvular.ii 1.02 0.850
s(time):interaction(context.ord, vowel.ord)pharyngealised.ii 1.02 0.860
s(time):interaction(context.ord, vowel.ord)pharyngeal.ii 1.02 0.880
s(time):interaction(context.ord, vowel.ord)plain.aa 1.02 0.850
s(time):interaction(context.ord, vowel.ord)velar.aa 1.02 0.835
s(time):interaction(context.ord, vowel.ord)uvular.aa 1.02 0.900
s(time):interaction(context.ord, vowel.ord)pharyngealised.aa 1.02 0.870
s(time):interaction(context.ord, vowel.ord)pharyngeal.aa 1.02 0.860
s(time):interaction(context.ord, vowel.ord)plain.uu 1.02 0.905
s(time):interaction(context.ord, vowel.ord)velar.uu 1.02 0.865
s(time):interaction(context.ord, vowel.ord)uvular.uu 1.02 0.860
s(time):interaction(context.ord, vowel.ord)pharyngealised.uu 1.02 0.870
s(time):interaction(context.ord, vowel.ord)pharyngeal.uu 1.02 0.835
ti(time,Fan) 0.98 0.120
ti(time,Fan):context.ordvelar 0.98 0.155
ti(time,Fan):context.orduvular 0.98 0.135
ti(time,Fan):context.ordpharyngealised 0.98 0.100 .
ti(time,Fan):context.ordpharyngeal 0.98 0.135
ti(time,Fan):vowel.ordaa 0.98 0.120
ti(time,Fan):vowel.orduu 0.98 0.130
ti(time,Fan):interaction(context.ord, vowel.ord)plain.ii 0.98 0.160
ti(time,Fan):interaction(context.ord, vowel.ord)velar.ii 0.98 0.185
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.ii 0.98 0.100 .
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.ii 0.98 0.165
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.ii 0.98 0.150
ti(time,Fan):interaction(context.ord, vowel.ord)plain.aa 0.98 0.155
ti(time,Fan):interaction(context.ord, vowel.ord)velar.aa 0.98 0.145
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.aa 0.98 0.165
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.aa 0.98 0.130
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.aa 0.98 0.125
ti(time,Fan):interaction(context.ord, vowel.ord)plain.uu 0.98 0.180
ti(time,Fan):interaction(context.ord, vowel.ord)velar.uu 0.98 0.165
ti(time,Fan):interaction(context.ord, vowel.ord)uvular.uu 0.98 0.125
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngealised.uu 0.98 0.095 .
ti(time,Fan):interaction(context.ord, vowel.ord)pharyngeal.uu 0.98 0.090 .
s(Fan,word) 1.03 0.980
s(time,word) 1.02 0.865
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
3.5 Significance testing second Autoregressive GAM
To test for significance of context, we run a model with a ML as method and evaluate significance through a maximum likelihood estimate.
3.5.1 Models
We ran three models
- A full model with all predictors (phar.gam.AR.ML)
- A reduced model without any terms associated with the predictor “context” (phar.gam.AR.ML.Min.Context)
- An intercept only model (=Null) without any terms associated with the predictor “vowel” (phar.gam.AR.ML.Min.ContextAndVowel)
mdl.sys.time3 <- system.time(phar.gam.AR.ML <- bam(y ~ context.ord*vowel.ord +
# 1d smooths
s(Fan, bs="cr",k=10) +
s(time, bs="cr", k=3) +
# 1d smooth * factor
s(Fan, k=10, bs="cr", by=context.ord) +
s(Fan, k=10, bs="cr", by=vowel.ord) +
s(Fan, k=10, bs="cr", by=interaction(context.ord, vowel.ord)) +
s(time, k=3, bs="cr", by=context.ord) +
s(time, k=3, bs="cr", by=vowel.ord) +
s(time, k=3, bs="cr", by=interaction(context.ord, vowel.ord)) +
# 2d smooth
ti(Fan, time, bs="cr", k=c(10,3))+
ti(Fan, time, bs="cr", k=c(10,3),by=context.ord)+
ti(Fan, time, bs="cr", k=c(10,3),by=vowel.ord)+
ti(Fan, time, bs="cr", k=c(10,3),by=interaction(context.ord, vowel.ord))+
# random smooths by word
s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
data=pharDF,
method="ML",
AR.start=pharDF$start, rho=rho_est, nthreads = ncores, discrete = TRUE))
mdl.sys.time3utilisateur système écoulé
21433.768 179.089 12276.728 mdl.sys.time4 <- system.time(phar.gam.AR.ML.Min.Context <- bam(y ~ vowel.ord +
# 1d smooths
s(Fan, bs="cr",k=10) +
s(time, bs="cr", k=3) +
# 1d smooth * factor
##s(Fan, k=10, bs="cr", by=context.ord) +
s(Fan, k=10, bs="cr", by=vowel.ord) +
##s(Fan, k=10, bs="cr", by=context.ord:vowel.ord) +
##s(time, k=3, bs="cr", by=context.ord) +
s(time, k=3, bs="cr", by=vowel.ord) +
##s(time, k=3, bs="cr", by=context.ord:vowel.ord) +
# 2d smooth
ti(Fan, time, bs="cr", k=c(10,3))+
##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord)+
###ti(Fan, time, bs="cr", k=c(10,3),by=vowel.ord)+
##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord:vowel.ord)+
# random smooths by word
s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
data=pharDF,
method="ML",
AR.start=pharDF$start, rho=rho_est, nthreads = ncores, discrete = TRUE))
mdl.sys.time4utilisateur système écoulé
474.920 7.668 251.698 mdl.sys.time5 <- system.time(phar.gam.AR.ML.Min.ContextAndVowel <- bam(y ~ 1 +
# 1d smooths
s(Fan, bs="cr",k=10) +
s(time, bs="cr", k=3) +
# 1d smooth * factor
##s(Fan, k=10, bs="cr", by=context.ord) +
###s(Fan, k=10, bs="cr", by=vowel.ord) +
##s(Fan, k=10, bs="cr", by=context.ord:vowel.ord) +
##s(time, k=3, bs="cr", by=context.ord) +
###s(time, k=3, bs="cr", by=vowel.ord) +
##s(time, k=3, bs="cr", by=context.ord:vowel.ord) +
# 2d smooth
##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord)+
###ti(Fan, time, bs="cr", k=c(10,3),by=vowel.ord)+
##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord:vowel.ord)+
# random smooths by word
s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
data=pharDF,
method="ML",
AR.start=pharDF$start, rho=rho_est, nthreads = ncores, discrete = TRUE))
mdl.sys.time5utilisateur système écoulé
832.054 13.665 387.945 3.5.2 Model comparison
Then we compare results of these models as shown below.
3.5.2.1 Effect of Context vs null
compareML(phar.gam.AR.ML, phar.gam.AR.ML.Min.Context)phar.gam.AR.ML: y ~ context.ord * vowel.ord + s(Fan, bs = "cr", k = 10) + s(time,
bs = "cr", k = 3) + s(Fan, k = 10, bs = "cr", by = context.ord) +
s(Fan, k = 10, bs = "cr", by = vowel.ord) + s(Fan, k = 10,
bs = "cr", by = interaction(context.ord, vowel.ord)) + s(time,
k = 3, bs = "cr", by = context.ord) + s(time, k = 3, bs = "cr",
by = vowel.ord) + s(time, k = 3, bs = "cr", by = interaction(context.ord,
vowel.ord)) + ti(Fan, time, bs = "cr", k = c(10, 3)) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = context.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = vowel.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = interaction(context.ord,
vowel.ord)) + s(Fan, word, bs = "fs", k = 10, m = 1,
xt = list(bs = "tp")) + s(time, word, bs = "fs", k = 3, m = 1,
xt = list(bs = "tp"))
phar.gam.AR.ML.Min.Context: y ~ vowel.ord + s(Fan, bs = "cr", k = 10) + s(time, bs = "cr",
k = 3) + s(Fan, k = 10, bs = "cr", by = vowel.ord) + s(time,
k = 3, bs = "cr", by = vowel.ord) + ti(Fan, time, bs = "cr",
k = c(10, 3)) + s(Fan, word, bs = "fs", k = 10, m = 1, xt = list(bs = "tp")) +
s(time, word, bs = "fs", k = 3, m = 1, xt = list(bs = "tp"))
Chi-square test of ML scores
-----
AIC difference: -2736.64, model phar.gam.AR.ML has lower AIC.3.5.2.2 Effect of Vowel vs Null
compareML(phar.gam.AR.ML,phar.gam.AR.ML.Min.ContextAndVowel)phar.gam.AR.ML: y ~ context.ord * vowel.ord + s(Fan, bs = "cr", k = 10) + s(time,
bs = "cr", k = 3) + s(Fan, k = 10, bs = "cr", by = context.ord) +
s(Fan, k = 10, bs = "cr", by = vowel.ord) + s(Fan, k = 10,
bs = "cr", by = interaction(context.ord, vowel.ord)) + s(time,
k = 3, bs = "cr", by = context.ord) + s(time, k = 3, bs = "cr",
by = vowel.ord) + s(time, k = 3, bs = "cr", by = interaction(context.ord,
vowel.ord)) + ti(Fan, time, bs = "cr", k = c(10, 3)) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = context.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = vowel.ord) + ti(Fan,
time, bs = "cr", k = c(10, 3), by = interaction(context.ord,
vowel.ord)) + s(Fan, word, bs = "fs", k = 10, m = 1,
xt = list(bs = "tp")) + s(time, word, bs = "fs", k = 3, m = 1,
xt = list(bs = "tp"))
phar.gam.AR.ML.Min.ContextAndVowel: y ~ 1 + s(Fan, bs = "cr", k = 10) + s(time, bs = "cr", k = 3) +
s(Fan, word, bs = "fs", k = 10, m = 1, xt = list(bs = "tp")) +
s(time, word, bs = "fs", k = 3, m = 1, xt = list(bs = "tp"))
Chi-square test of ML scores
-----
AIC difference: -3053.28, model phar.gam.AR.ML has lower AIC.3.5.2.3 Effect of Context vs Vowel
compareML(phar.gam.AR.ML.Min.Context,phar.gam.AR.ML.Min.ContextAndVowel)phar.gam.AR.ML.Min.Context: y ~ vowel.ord + s(Fan, bs = "cr", k = 10) + s(time, bs = "cr",
k = 3) + s(Fan, k = 10, bs = "cr", by = vowel.ord) + s(time,
k = 3, bs = "cr", by = vowel.ord) + ti(Fan, time, bs = "cr",
k = c(10, 3)) + s(Fan, word, bs = "fs", k = 10, m = 1, xt = list(bs = "tp")) +
s(time, word, bs = "fs", k = 3, m = 1, xt = list(bs = "tp"))
phar.gam.AR.ML.Min.ContextAndVowel: y ~ 1 + s(Fan, bs = "cr", k = 10) + s(time, bs = "cr", k = 3) +
s(Fan, word, bs = "fs", k = 10, m = 1, xt = list(bs = "tp")) +
s(time, word, bs = "fs", k = 3, m = 1, xt = list(bs = "tp"))
Chi-square test of ML scores
-----
AIC difference: -316.64, model phar.gam.AR.ML.Min.Context has lower AIC.From the results above, both “context” and “vowel” are improving the model fit. “Context” is improving the model fit more than “vowel” (see 3rd comparison)
3.6 Visualising smooths from second Autoregressive GAM
We use the function itsadug::plot_smooth to plot the five smooths for context “plain”, “velar”, “uvular”, “pharyngealised” and “pharyngeal”, in each of the vowel contexts /i: a: u:/ at the onset, midpoint and offset.
The results show that at the midpoint and offset, the three contexts, uvular, pharyngealised and pharyngeal are different from each other: uvular has a higher tongue position (y coordinate); intermediate in pharyngealised and lower and fronted in pharyngeal. At the onset, the same pattern is seen though to a lower degree in /a:/.
3.6.1 Vowel /i:/
3.6.1.1 Onset
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="ii",time=1),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /i:/ at Onset",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="ii",time=1),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="ii",time=1),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="ii",time=1),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="ii",time=1),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.1.2 Midpoint
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="ii",time=2),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /i:/ at Mid",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="ii",time=2),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="ii",time=2),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="ii",time=2),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="ii",time=2),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.1.3 Offset
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="ii",time=3),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /i:/ at Offset",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="ii",time=3),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="ii",time=3),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="ii",time=3),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="ii",time=3),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.2 Vowel /a:/
3.6.2.1 Onset
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="aa",time=1),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /a:/ at Onset",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="aa",time=1),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="aa",time=1),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="aa",time=1),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="aa",time=1),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.2.2 Midpoint
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="aa",time=2),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /a:/ at Mid",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="aa",time=2),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="aa",time=2),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="aa",time=2),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="aa",time=2),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.2.3 Offset
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="aa",time=3),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /a:/ at Offset",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="aa",time=3),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="aa",time=3),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="aa",time=3),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="aa",time=3),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.3 Vowel /u:/
3.6.3.1 Onset
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="uu",time=1),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /u:/ at Onset",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="uu",time=1),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="uu",time=1),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="uu",time=1),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="uu",time=1),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.3.2 Midpoint
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="uu",time=2),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /u:/ at Mid",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="uu",time=2),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="uu",time=2),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="uu",time=2),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="uu",time=2),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
3.6.3.3 Offset
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="uu",time=3),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
main="GAM smooths in /u:/ at Offset",hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): plain.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="uu",time=3),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): velar.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="uu",time=3),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): uvular.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="uu",time=3),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngealised.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="uu",time=3),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)Summary:
* context.ord : factor; set to the value(s): pharyngeal.
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 30 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"),
col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
NA
NA3.7 Visualising Difference smooths from second Autoregressive GAM
We use the function itsadug::plot_diff to plot the differences between the following pairs: “pharyngealised” vs “plain”; “uvular” vs “pharyngealised” and “pharyngealised” vs “pharyngeal”, in each of the vowel contexts /i: a: u:/ at the onset, midpoint and offset.
The results show that:
- Pharyngealised vs Plain: pharyngealised is different in tongue shape. There is an increase in y coordinates (Fan 15-22) indicating “retraction”, decrease (Fan 25-35) indicating “depression” of the tongue and potential difference in larynx height (Fan 5-10)
- Uvular vs Pharyngealised: differences depend of vowels (Fan 15-34): uvular is fronter in /i:/ (Fan 22-34); “raised” in /a:/ (Fan 22-28) and /u:/ (Fan 15-25)
- Pharyngealised vs Pharyngeal: Pharyngealised is “retracted”/backed to mid-position (Fan 15-25), with “depression” of the tongue (Fan 22-35) and potential lowered larynx (Fan 5-10).
3.7.1 Pharyngealised vs Plain
3.7.1.1 Onset
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=1,vowel.ord="ii"),main = "difference pharyngealised vs plain Onset",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
10.939394 - 23.363636
26.262626 - 38.686869plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=1,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
11.353535 - 22.535354
25.434343 - 35.373737plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=1,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
4.313131 - 9.282828
15.080808 - 23.363636
25.848485 - 37.858586legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.1.2 Midpoint
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=2,vowel.ord="ii"),main = "difference pharyngealised vs plain Midpoint",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
4.727273 - 24.191919
25.848485 - 41.171717plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=2,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
13.838384 - 23.363636
25.848485 - 36.616162plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=2,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
5.141414 - 8.454545
15.080808 - 24.191919
26.676768 - 39.515152legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.1.3 Offset
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=3,vowel.ord="ii"),main = "difference pharyngealised vs plain Offset",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
5.969697 - 25.020202
26.676768 - 41.171717plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=3,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
1.828283 - 6.797980
14.666667 - 23.363636
26.262626 - 34.959596plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
xlab="",cond=list(time=3,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
14.252525 - 23.777778
26.676768 - 38.686869legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.2 Uvular vs Pharyngealised
3.7.2.1 Onset
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=1,vowel.ord="ii"),main = "difference uvular vs pharyngealised Onset",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Difference is not significant.plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=1,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
24.606061 - 30.404040plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=1,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Difference is not significant.legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.2.2 Midpoint
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=2,vowel.ord="ii"),main = "difference uvular vs pharyngealised Midpoint",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
20.878788 - 32.474747plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=2,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
19.636364 - 28.747475
35.787879 - 37.858586plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=2,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
18.808081 - 25.434343legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.2.3 Offset
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=3,vowel.ord="ii"),main = "difference uvular vs pharyngealised Offset",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
22.949495 - 33.303030plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=3,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
21.707071 - 29.989899plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
xlab="",cond=list(time=3,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
19.222222 - 25.848485legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.3 Pharyngealised vs Pharyngeal
3.7.3.1 Onset
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=1,vowel.ord="ii"),main = "difference pharyngealised vs pharyngeal Onset",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
15.080808 - 26.262626plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=1,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
3.898990 - 5.141414
13.838384 - 21.707071
25.020202 - 36.202020plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=1,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 1.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
14.666667 - 21.707071
27.090909 - 31.646465legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.3.2 Midpoint
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=2,vowel.ord="ii"),main = "difference pharyngealised vs pharyngeal Midpoint",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
2.242424 - 9.696970
15.494949 - 26.262626
29.989899 - 38.272727plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=2,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
3.070707 - 7.626263
16.737374 - 21.292929
24.606061 - 34.131313plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=2,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 2.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
1.000000 - 13.838384
17.151515 - 25.020202legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
3.7.3.3 Offset
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=3,vowel.ord="ii"),main = "difference pharyngealised vs pharyngeal Offset",
col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): ii.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
14.666667 - 26.262626
29.161616 - 39.101010plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=3,vowel.ord="aa"),add=TRUE,
col='red',mark.diff = TRUE,col.diff = "red",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): aa.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
4.313131 - 7.626263
24.606061 - 33.717172plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
xlab="",cond=list(time=3,vowel.ord="uu"),add=TRUE,
col='blue',mark.diff = TRUE,col.diff = "blue",
ylim=c(-15,15),hide.label=T,rm.ranef=T)Summary:
* vowel.ord : factor; set to the value(s): uu.
* Fan : numeric predictor; with 100 values ranging from 1.000000 to 42.000000.
* time : numeric predictor; set to the value(s): 3.
* word : factor; set to the value(s): 2aa3aa. (Might be canceled as random effect, check below.)
* NOTE : The following random effects columns are canceled: s(Fan,word),s(time,word)
Fan window(s) of significant difference(s):
1.000000 - 14.666667
18.393939 - 24.606061
28.747475 - 31.646465legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1,
legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
4 System Information
sessionInfo()R version 4.1.3 (2022-03-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Rocky Linux 8.6 (Green Obsidian)
Matrix products: default
BLAS: /opt/R/4.1.3/lib64/R/lib/libRblas.so
LAPACK: /opt/R/4.1.3/lib64/R/lib/libRlapack.so
locale:
[1] LC_CTYPE=fr_FR.UTF-8 LC_NUMERIC=C LC_TIME=fr_FR.UTF-8
[4] LC_COLLATE=fr_FR.UTF-8 LC_MONETARY=fr_FR.UTF-8 LC_MESSAGES=fr_FR.UTF-8
[7] LC_PAPER=fr_FR.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=fr_FR.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] parallel stats graphics grDevices utils datasets methods base
other attached packages:
[1] doParallel_1.0.17 iterators_1.0.14 foreach_1.5.2 gganimate_1.0.7
[5] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.8 purrr_0.3.4
[9] readr_2.1.2 tidyr_1.2.0 tibble_3.1.6 tidyverse_1.3.1
[13] itsadug_2.4.1 plotfunctions_1.4 mgcv_1.8-39 nlme_3.1-155
[17] ggplot2_3.3.5
loaded via a namespace (and not attached):
[1] Rcpp_1.0.8.3 lubridate_1.8.0 lattice_0.20-45 prettyunits_1.1.1
[5] assertthat_0.2.1 digest_0.6.29 utf8_1.2.2 plyr_1.8.7
[9] R6_2.5.1 cellranger_1.1.0 backports_1.4.1 reprex_2.0.1
[13] evaluate_0.15 httr_1.4.2 pillar_1.7.0 rlang_1.0.2
[17] progress_1.2.2 readxl_1.4.0 rstudioapi_0.13 Matrix_1.4-0
[21] rmarkdown_2.13 labeling_0.4.2 splines_4.1.3 munsell_0.5.0
[25] broom_0.7.12 compiler_4.1.3 modelr_0.1.8 xfun_0.30
[29] pkgconfig_2.0.3 htmltools_0.5.2 tidyselect_1.1.2 codetools_0.2-18
[33] fansi_1.0.3 crayon_1.5.1 tzdb_0.3.0 dbplyr_2.1.1
[37] withr_2.5.0 grid_4.1.3 jsonlite_1.8.0 gtable_0.3.0
[41] lifecycle_1.0.1 DBI_1.1.2 magrittr_2.0.3 scales_1.1.1
[45] cli_3.2.0 stringi_1.7.6 farver_2.1.0 fs_1.5.2
[49] xml2_1.3.3 ellipsis_0.3.2 generics_0.1.2 vctrs_0.4.0
[53] tools_4.1.3 glue_1.6.2 tweenr_1.0.2 hms_1.1.1
[57] rsconnect_0.8.25 fastmap_1.1.0 yaml_2.3.5 colorspace_2.0-3
[61] rvest_1.0.2 knitr_1.38 haven_2.4.3 ---
title: "GAMMs LabPhon 18"
author: 
  name: "Jalal Al-Tamimi"
  affiliation: "Newcastle University"
date: "6 June 2018; updated 10 August 2022"
output: 
  html_notebook:
    number_sections: true
    toc: true
    toc_depth: 4
    toc_float:
      collapsed: true
---

# Loading packages 
```{r warning=FALSE, message=FALSE, error=FALSE}

library(ggplot2);library(mgcv);library(itsadug);library(tidyverse);library(gganimate); library(doParallel)
```

# Demo Linear Model vs GAM
In this demo, data obtained from a Jordanian Arabic speaker producing the word /du:d/ "worm" is used. F2 frequencies obtained at 5 ms interval from onset to midpoint of the vowel are used.
Let's plot the F2 frequencies by interval number. The second plot displays a linear regression line superimposed on the plot. As can be seen, the linear regression line is not able to cope with the curviness of the data, and is unable to cope with it. The third plot superimposes a spline obtained from a GAM model.

```{r}
demoGAMProd <- read.csv("dataProd_duud.csv")
head(demoGAMProd)
```


```{r warning=FALSE, message=FALSE, error=FALSE}
ggplot.demo1 <- ggplot(demoGAMProd,aes(x=IntervalsN,y=F2))+
                geom_point()+theme_bw(base_size = 20)+coord_cartesian(ylim=c(600,1800))+
                labs(y = "F2 Hz", x = "Intervals number")
ggplot.demo1

ggplot.demo2 <- ggplot(demoGAMProd,aes(x=IntervalsN,y=F2))+
  geom_point()+theme_bw(base_size = 20)+coord_cartesian(ylim=c(600,1800))+
  labs(y = "F2 Hz", x = "Intervals number")+geom_smooth(method = lm, se=F)

ggplot.demo2

ggplot.demo3 <- ggplot(demoGAMProd,aes(x=IntervalsN,y=predict(bam(F2 ~ s(IntervalsN, bs="cr"), data = demoGAMProd))))+
  geom_point()+theme_bw(base_size = 20)+coord_cartesian(ylim=c(600,1800))+
  labs(y = "F2 Hz", x = "Intervals number")+geom_smooth(method = lm, formula = y ~ splines::bs(x, 3),se=F)

ggplot.demo3

```

# Actual data analyses
This data is obtained from a single speaker producing various consonants in the frame VCV, with V = symmetric /i: a: u:/ (=vowel) and C is one of 17 consonants put into five contexts "plain", "velar", "uvular", "pharyngealised" and "pharyngeal" (=context). The data is from Ultrasound Tongue Imaging. Tongue contours were obtained at the consonant onset, midpoint and offset (=time). A total of 51 words (=word) were obtained and these were repeated 3 times. Tongue splines were extracted with X-Y coordinates (=y outcome). 42 Fan positions (=Fan) were extracted and these are used as a normalisation between contexts.
The outcome is y, the predictors are Fan, time, context and vowel, and the random factor is word.

## Creating new variables
Before running the actual GAM model on the data, we need to:

1. Create two new variables for context and vowel. These will be "ordered" predictors and sum coded
2. To run an Auto-Regressive Model, we need to find the autocorrelation in the dataframe:
  + We rearrange the data by time, ID, and Fan 
  + We add a new variable "start" that marks the start of Fan
  

```{r warning=FALSE, message=FALSE, error=FALSE}
pharDF <- read.csv("resultsFull.c_NoRelNoz.csv")
str(pharDF)

levels(pharDF$context)
pharDF$context <- factor(pharDF$context, 
                                levels = c("plain","velar","uvular","pharyngealised","pharyngeal"))
levels(pharDF$vowel)
pharDF$vowel <- factor(pharDF$vowel, 
                              levels = c("ii","aa","uu"))
levels(pharDF$labelNew)
pharDF$labelNew <- factor(pharDF$labelNew, 
                                 levels = c("CL_Ons","CL_Mid","CL_Off"))


pharDF$ID <- as.numeric(pharDF$ID)
pharDF$Fan <- as.numeric(pharDF$Fan)
pharDF$labelNew2 <- as.numeric(pharDF$labelNew2)
pharDF$time <- pharDF$labelNew2
pharDF$word <- as.factor(pharDF$word)



pharDF$context.ord <- as.ordered(pharDF$context)
contrasts(pharDF$context.ord) <- "contr.treatment"

pharDF$vowel.ord <- as.ordered(pharDF$vowel)
contrasts(pharDF$vowel.ord) <- "contr.treatment"

## to find autocorrelation in the data. Rearrange dataframe and add a variable "start" to indicate 
## when Fan == 1
pharDF <- arrange(pharDF, time, ID, Fan)
pharDF$start <- pharDF$Fan==1
ncores = 10

```
## Visualising the data

Before running anything, we start by visualising the data and use an animated figure

```{r warning=FALSE, message=FALSE, error=FALSE}
pl <- ggplot(pharDF, aes(x=Fan, y=y, col=context, frame=time)) +
  facet_grid(vowel ~ context) +
  geom_line(aes(group=ID))+theme_bw()+
transition_manual(time)
animate(pl, width=800, height=300)

```


## Running our first GAM model
This is our first GAM model. This will be used to find the level of autocorrelation in the data. Our model has double non-linear predictors (fan and time), two factor predictors (context and vowel) and one random effect (word). Interactions between fan and time are used. In addition, by context*vowel interaction is added to account for the two-way interaction with respect to each of fan and time.
The function itsadug::acf_resid is used, and we display the level of autocorrelation for each of the "Fan", the "time", the "context", the "vowel" finally the "word"

```{r warning=FALSE, message=FALSE, error=FALSE}

mdl.sys.time1 <- system.time(phar.gam.noAR <- bam(y ~ context.ord*vowel.ord +
                        ## 1d smooths
                        s(Fan, bs="cr", k=10) +
                        s(time, bs="cr", k=3) +
                        ## 1d smooths * factors
                        s(Fan, k=10, bs="cr", by=context.ord) +
                        s(Fan, k=10, bs="cr", by=vowel.ord) +
                        s(Fan, k=10, bs="cr", by=interaction(context.ord, vowel.ord)) +
                        s(time, k=3, bs="cr", by=context.ord) +
                        s(time, k=3, bs="cr", by=vowel.ord) +
                        s(time, k=3, bs="cr", by=interaction(context.ord, vowel.ord)) +
                        ## 2d smooths
                        ti(Fan, time, bs="cr", k=c(10,3))+
                        ## 2d smooths * factors
                        ti(Fan, time, bs="cr", k=c(10,3), by=context.ord)+
                        ti(Fan, time, bs="cr", k=c(10,3), by=vowel.ord)+
                        ti(Fan, time, bs="cr", k=c(10,3),by=interaction(context.ord, vowel.ord)) +
                        ## random smooths by word
                        s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
                        s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
                        data=pharDF, nthreads = ncores, method="fREML", discrete = TRUE))
mdl.sys.time1
```

### Summary and Rho

```{r warning=FALSE, message=FALSE, error=FALSE}
summary(phar.gam.noAR)

rho_est <- start_value_rho(phar.gam.noAR)
rho_est
```

### ACF first GAM
The five plots below show the autocorrelation in the residuals. As can be see, the first plot using Fan, has a complete zero correlations. It is possible that because the various fan points obtained alongside the tongue contour are already correlated with each other, and hence the correlations between fan 1 to 2, 2 to 3, 41 to 42 are already taken into account by the model. 
The four additional plots show the autocorrelation in the residuals for time, context, vowel and word. All of these predictors are showing autocorrelations between their successive data points. This means that for a specific time (onset, midpoint or offset), there is already correlations between tongue splines obtained at the onset, the midpoint and the offset. It is crucial to tell the model to account for this, otherwise there is overconfidence in the estimates. 

#### ACF by Fan

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.noAR,split_pred=list(pharDF$Fan),main = "Average ACF No.AR by Fan",cex.lab=1.5,cex.axis=1.5)
```

#### ACF by Time

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.noAR,split_pred=list(pharDF$time),main = "Average ACF No.AR by Time",cex.lab=1.5,cex.axis=1.5)
```

#### ACF by Context

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.noAR,split_pred=list(pharDF$context.ord),main = "Average ACF No.AR by Context",cex.lab=1.5,cex.axis=1.5)
```

#### ACF by Vowel

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.noAR,split_pred=list(pharDF$vowel.ord),main = "Average ACF No.AR by Vowel",cex.lab=1.5,cex.axis=1.5)
```

#### ACF by Word

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.noAR,split_pred=list(pharDF$word),main = "Average ACF No.AR by Word",cex.lab=1.5,cex.axis=1.5)
```


## Running our second Autoregressive GAM

Our second GAM model is identical to the first, but takes into account the autocorrelation. By including AR.start and rho, we are using information obtained from original model to account for the autocorrelation
```{r warning=FALSE, message=FALSE, error=FALSE}
mdl.sys.time2 <- system.time(phar.gam.AR <- bam(y ~ context.ord*vowel.ord +
                       ## 1d smooths
                       s(Fan, bs="cr", k=10) +
                       s(time, bs="cr", k=3) +
                       ## 1d smooths * factors
                       s(Fan, k=10, bs="cr", by=context.ord) +
                       s(Fan, k=10, bs="cr", by=vowel.ord) +
                       s(Fan, k=10, bs="cr", by=interaction(context.ord, vowel.ord)) +
                       s(time, k=3, bs="cr", by=context.ord) +
                       s(time, k=3, bs="cr", by=vowel.ord) +
                       s(time, k=3, bs="cr", by=interaction(context.ord, vowel.ord)) +
                       ## 2d smooths
                       ti(Fan, time, bs="cr", k=c(10,3))+
                       ## 2d smooths * factors
                       ti(Fan, time, bs="cr", k=c(10,3), by=context.ord)+
                       ti(Fan, time, bs="cr", k=c(10,3), by=vowel.ord)+
                       ti(Fan, time, bs="cr", k=c(10,3),  by=interaction(context.ord, vowel.ord))+
                       ## random smooths by word
                       s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
                       s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
                       data=pharDF,
                       AR.start=pharDF$start, rho=rho_est, nthreads = ncores, method="fREML", discrete = TRUE))
mdl.sys.time2
```


### Summary

```{r warning=FALSE, message=FALSE, error=FALSE}
summary(phar.gam.AR)
```

### ACF second GAM
The following five plots show (in the same order as above) the autocorrelation in the residuals. As can be seen, for all five plots, the levels of autocorrelations in the residuals are reduced massively. We have now more confidence in our estimates, and can continue work

#### ACF by Fan

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.AR,split_pred=list(pharDF$Fan),main = "Average ACF AR by Fan",cex.lab=1.5,cex.axis=1.5)
```


#### ACF by Time

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.AR,split_pred=list(pharDF$time),main = "Average ACF AR by Time",cex.lab=1.5,cex.axis=1.5)
```

#### ACF by Context

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.AR,split_pred=list(pharDF$context.ord),main = "Average ACF AR by Context",cex.lab=1.5,cex.axis=1.5)
```


#### ACF by Vowel

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.AR,split_pred=list(pharDF$vowel.ord),main = "Average ACF AR by Vowel",cex.lab=1.5,cex.axis=1.5)
```

#### ACF by Word

```{r warning=FALSE, message=FALSE, error=FALSE}
acf_resid(phar.gam.AR,split_pred=list(pharDF$word),main = "Average ACF AR by Word",cex.lab=1.5,cex.axis=1.5)
```


### Gam Check

```{r}
gam.check(phar.gam.AR)
```


## Significance testing second Autoregressive GAM
To test for significance of context, we run a model with a ML as method and evaluate significance through a maximum likelihood estimate. 

### Models
We ran three models

1. A full model with all predictors (phar.gam.AR.ML)
2. A reduced model without any terms associated with the predictor "context" (phar.gam.AR.ML.Min.Context)
3. An intercept only model (=Null) without any terms associated with the predictor "vowel" (phar.gam.AR.ML.Min.ContextAndVowel)

```{r warning=FALSE, message=FALSE, error=FALSE}
mdl.sys.time3 <- system.time(phar.gam.AR.ML <- bam(y ~ context.ord*vowel.ord +
                           # 1d smooths
                           s(Fan, bs="cr",k=10) +
                           s(time, bs="cr", k=3) +
                           # 1d smooth * factor
                           s(Fan, k=10, bs="cr", by=context.ord) +
                           s(Fan, k=10, bs="cr", by=vowel.ord) +
                           s(Fan, k=10, bs="cr", by=interaction(context.ord, vowel.ord)) +
                           s(time, k=3, bs="cr", by=context.ord) +
                           s(time, k=3, bs="cr", by=vowel.ord) +
                           s(time, k=3, bs="cr", by=interaction(context.ord, vowel.ord)) +
                           # 2d smooth
                           ti(Fan, time, bs="cr", k=c(10,3))+
                           ti(Fan, time, bs="cr", k=c(10,3),by=context.ord)+
                           ti(Fan, time, bs="cr", k=c(10,3),by=vowel.ord)+
                           ti(Fan, time, bs="cr", k=c(10,3),by=interaction(context.ord, vowel.ord))+                      
                           # random smooths by word
                           s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
                           s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
                           data=pharDF,
                           method="ML", 
                           AR.start=pharDF$start, rho=rho_est, nthreads = ncores, discrete = TRUE))

mdl.sys.time3



mdl.sys.time4 <- system.time(phar.gam.AR.ML.Min.Context <- bam(y ~ vowel.ord +
                                      # 1d smooths
                                      s(Fan, bs="cr",k=10) +
                                      s(time, bs="cr", k=3) +
                                      # 1d smooth * factor
                                      ##s(Fan, k=10, bs="cr", by=context.ord) +
                                      s(Fan, k=10, bs="cr", by=vowel.ord) +
                                      ##s(Fan, k=10, bs="cr", by=context.ord:vowel.ord) +
                                      ##s(time, k=3, bs="cr", by=context.ord) +
                                      s(time, k=3, bs="cr", by=vowel.ord) +
                                      ##s(time, k=3, bs="cr", by=context.ord:vowel.ord) +
                                      # 2d smooth
                                      ti(Fan, time, bs="cr", k=c(10,3))+
                                      ##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord)+
                                      ###ti(Fan, time, bs="cr", k=c(10,3),by=vowel.ord)+
                                      ##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord:vowel.ord)+                      
                                      # random smooths by word
                                      s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
                                      s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
                                      data=pharDF,
                                      method="ML", 
                                      AR.start=pharDF$start, rho=rho_est, nthreads = ncores, discrete = TRUE))
mdl.sys.time4

mdl.sys.time5 <- system.time(phar.gam.AR.ML.Min.ContextAndVowel <- bam(y ~ 1 +
                                    # 1d smooths
                                    s(Fan, bs="cr",k=10) +
                                    s(time, bs="cr", k=3) +
                                    # 1d smooth * factor
                                    ##s(Fan, k=10, bs="cr", by=context.ord) +
                                    ###s(Fan, k=10, bs="cr", by=vowel.ord) +
                                    ##s(Fan, k=10, bs="cr", by=context.ord:vowel.ord) +
                                    ##s(time, k=3, bs="cr", by=context.ord) +
                                    ###s(time, k=3, bs="cr", by=vowel.ord) +
                                    ##s(time, k=3, bs="cr", by=context.ord:vowel.ord) +
                                    # 2d smooth
                                    ##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord)+
                                    ###ti(Fan, time, bs="cr", k=c(10,3),by=vowel.ord)+
                                    ##ti(Fan, time, bs="cr", k=c(10,3),by=context.ord:vowel.ord)+                      
                                    # random smooths by word
                                    s(Fan, word, bs="fs", k=10, m=1, xt=list(bs = "tp")) +
                                    s(time, word, bs="fs", k=3, m=1, xt=list(bs = "tp")),
                                    data=pharDF,
                                    method="ML", 
                                    AR.start=pharDF$start, rho=rho_est, nthreads = ncores, discrete = TRUE))
mdl.sys.time5
```

### Model comparison
Then we compare results of these models as shown below.    

#### Effect of Context vs null
```{r warning=FALSE, message=FALSE, error=FALSE}
compareML(phar.gam.AR.ML, phar.gam.AR.ML.Min.Context)
```

#### Effect of Vowel vs Null
```{r warning=FALSE, message=FALSE, error=FALSE}
compareML(phar.gam.AR.ML,phar.gam.AR.ML.Min.ContextAndVowel)
```

#### Effect of Context vs Vowel
```{r warning=FALSE, message=FALSE, error=FALSE}
compareML(phar.gam.AR.ML.Min.Context,phar.gam.AR.ML.Min.ContextAndVowel)
```

From the results above, both "context" and "vowel" are improving the model fit. "Context" is improving the model fit more than "vowel" (see 3rd comparison)

## Visualising smooths from second Autoregressive GAM
We use the function itsadug::plot_smooth to plot the five smooths for context "plain", "velar", "uvular", "pharyngealised" and "pharyngeal", in each of the vowel contexts /i: a: u:/ at the onset, midpoint and offset.

The results show that at the midpoint and offset, the three contexts, uvular, pharyngealised and pharyngeal are different from each other: uvular has a higher tongue position (y coordinate); intermediate in pharyngealised and lower and fronted in pharyngeal. At the onset, the same pattern is seen though to a lower degree in /a:/.

### Vowel /i:/

#### Onset
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="ii",time=1),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /i:/ at Onset",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="ii",time=1),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="ii",time=1),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="ii",time=1),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="ii",time=1),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

#### Midpoint
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="ii",time=2),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /i:/ at Mid",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="ii",time=2),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="ii",time=2),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="ii",time=2),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="ii",time=2),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

#### Offset
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="ii",time=3),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /i:/ at Offset",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="ii",time=3),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="ii",time=3),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="ii",time=3),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="ii",time=3),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

### Vowel /a:/

#### Onset
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="aa",time=1),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /a:/ at Onset",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="aa",time=1),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="aa",time=1),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="aa",time=1),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="aa",time=1),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

#### Midpoint
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="aa",time=2),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /a:/ at Mid",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="aa",time=2),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="aa",time=2),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="aa",time=2),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="aa",time=2),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

#### Offset
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="aa",time=3),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /a:/ at Offset",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="aa",time=3),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="aa",time=3),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="aa",time=3),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="aa",time=3),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

### Vowel /u:/

#### Onset
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="uu",time=1),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /u:/ at Onset",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="uu",time=1),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="uu",time=1),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="uu",time=1),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="uu",time=1),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

#### Midpoint
```{r warning=FALSE, message=FALSE, error=FALSE}
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="uu",time=2),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /u:/ at Mid",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="uu",time=2),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="uu",time=2),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="uu",time=2),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="uu",time=2),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)
```

#### Offset
```{r warning=FALSE, message=FALSE, error=FALSE}

plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="plain",vowel.ord="uu",time=3),col="darkmagenta",ylim = c(10,65),ylab="",xlab="",
            main="GAM smooths in /u:/ at Offset",hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="velar",vowel.ord="uu",time=3),col="gray70",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="uvular",vowel.ord="uu",time=3),col="green",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngealised",vowel.ord="uu",time=3),col="red",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
plot_smooth(phar.gam.AR, view = "Fan",cond = list(context.ord="pharyngeal",vowel.ord="uu",time=3),col="blue",add=TRUE,ylim = c(10,65),hide.label=T,cex.axis=1.3,rm.ranef=T)
legend("topleft", legend=c("Plain", "Velar", "Uvular","Pharyngealised","Pharyngeal"), 
       col=c("darkmagenta","gray70","green","red","blue"), lwd=4)


```

## Visualising Difference smooths from second Autoregressive GAM
We use the function itsadug::plot_diff to plot the differences between the following pairs: "pharyngealised" vs "plain"; "uvular" vs "pharyngealised" and "pharyngealised" vs "pharyngeal", in each of the vowel contexts /i: a: u:/ at the onset, midpoint and offset.

The results show that: 

1. Pharyngealised vs Plain: pharyngealised is different in tongue shape. There is an increase in y coordinates (Fan 15-22) indicating "retraction", decrease (Fan 25-35) indicating "depression" of the tongue and potential difference in larynx height (Fan 5-10)
2. Uvular vs Pharyngealised: differences depend of vowels (Fan 15-34): uvular is fronter in /i:/ (Fan 22-34); "raised" in /a:/ (Fan 22-28) and /u:/ (Fan 15-25)
3. Pharyngealised vs Pharyngeal: Pharyngealised is "retracted"/backed to mid-position (Fan 15-25), with "depression" of the tongue (Fan 22-35) and potential lowered larynx (Fan 5-10).

### Pharyngealised vs Plain
#### Onset
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=1,vowel.ord="ii"),main = "difference pharyngealised vs plain Onset",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=1,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=1,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
```

#### Midpoint
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=2,vowel.ord="ii"),main = "difference pharyngealised vs plain Midpoint",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=2,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=2,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
```

#### Offset
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=3,vowel.ord="ii"),main = "difference pharyngealised vs plain Offset",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=3,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","plain")),
          xlab="",cond=list(time=3,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
```


### Uvular vs Pharyngealised

#### Onset
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=1,vowel.ord="ii"),main = "difference uvular vs pharyngealised Onset",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=1,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=1,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)

```

#### Midpoint
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=2,vowel.ord="ii"),main = "difference uvular vs pharyngealised Midpoint",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=2,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=2,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
```

#### Offset
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=3,vowel.ord="ii"),main = "difference uvular vs pharyngealised Offset",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=3,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("uvular","pharyngealised")),
          xlab="",cond=list(time=3,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
```


### Pharyngealised vs Pharyngeal

#### Onset
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=1,vowel.ord="ii"),main = "difference pharyngealised vs pharyngeal Onset",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=1,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=1,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
```

#### Midpoint
```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=2,vowel.ord="ii"),main = "difference pharyngealised vs pharyngeal Midpoint",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=2,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=2,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)
```

#### Offset

```{r warning=FALSE, message=FALSE, error=FALSE}
par(oma=c(1, 0, 0, 3.5),mgp=c(2, 1, 0))
plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=3,vowel.ord="ii"),main = "difference pharyngealised vs pharyngeal Offset",
          col='green',cex.main=1.1,mark.diff = TRUE,col.diff = "green",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=3,vowel.ord="aa"),add=TRUE,
          col='red',mark.diff =  TRUE,col.diff = "red",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)

plot_diff(phar.gam.AR, view="Fan",comp=list(context.ord=c("pharyngealised","pharyngeal")),
          xlab="",cond=list(time=3,vowel.ord="uu"),add=TRUE,
          col='blue',mark.diff =  TRUE,col.diff = "blue",
          ylim=c(-15,15),hide.label=T,rm.ranef=T)
legend(par('usr')[2], par('usr')[4], bty='n', xpd=NA,lty=1, 
       legend=c("/i:/", "/a:/", "/u:/"),col=c("green","red","blue"), lwd=4, cex=1.2)

```


# System Information

```{r}
sessionInfo()
```

