4.4 Generalised Linear Mixed-effects Models
Here we will look at an example when the outcome is binary. This simulated data is structured as follows. We asked one participant to listen to 165 sentences, and to judge whether these are “grammatical” or “ungrammatical”. There were 105 sentences that were “grammatical” and 60 “ungrammatical”. This fictitious example can apply in any other situation. Let’s think Geography: 165 lands: 105 “flat” and 60 “non-flat”, etc. This applies to any case where you need to “categorise” the outcome into two groups.
4.4.1 GLMM - Categorical predictors
Let’s run a first GLMM (Generalised Linear Model).
4.4.1.1 Simulating a new dataset
grammatical2 <- as.data.frame(
cbind("participant" = c("participant" = rep("p1", 165), rep("p2", 165)),
"grammaticality" = c("grammatical" = rep("grammatical", 105),
"ungrammatical" = rep("ungrammatical", 60),
"grammatical" = rep("grammatical", 105),
"ungrammatical" = rep("ungrammatical", 60)),
"response" = c("yes" = rep("yes", 100),
"no" = rep("no", 5),
"yes" = rep("yes", 10),
"no" = rep("no", 50),
"yes" = rep("yes", 90),
"no" = rep("no", 15),
"yes" = rep("yes", 30),
"no" = rep("no", 30))),
row.names = FALSE)
grammatical2 %>%
head(10)
## participant grammaticality response
## 1 p1 grammatical yes
## 2 p1 grammatical yes
## 3 p1 grammatical yes
## 4 p1 grammatical yes
## 5 p1 grammatical yes
## 6 p1 grammatical yes
## 7 p1 grammatical yes
## 8 p1 grammatical yes
## 9 p1 grammatical yes
## 10 p1 grammatical yes
4.4.1.2 Manipulations and a table
grammatical2 <- grammatical2 %>%
mutate(response = factor(response, levels = c("no", "yes")),
grammaticality = factor(grammaticality, levels = c("ungrammatical", "grammatical")))
grammatical2 %>%
select(response, grammaticality) %>%
group_by(response, grammaticality) %>%
table()
## grammaticality
## response ungrammatical grammatical
## no 80 20
## yes 40 190
4.4.1.3 Model estimation and results
4.4.1.3.1 Random Intercepts
The results below show the logodds for our model.
mdl.glmm <- grammatical2 %>%
glmer(response ~ grammaticality + (1|participant), data = ., family = binomial)
summary(mdl.glmm)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: response ~ grammaticality + (1 | participant)
## Data: .
##
## AIC BIC logLik -2*log(L) df.resid
## 290.8 302.2 -142.4 284.8 327
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1221 -0.6985 0.3203 0.3280 1.4317
##
## Random effects:
## Groups Name Variance Std.Dev.
## participant (Intercept) 0.005276 0.07264
## Number of obs: 330, groups: participant, 2
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.6940 0.2006 -3.459 0.000542 ***
## grammaticalitygrammatical 2.9475 0.3060 9.632 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## grmmtcltygr -0.615
4.4.1.3.2 Random Slopes
The results below show the logodds for our model.
mdl.glmmSlope <- grammatical2 %>%
glmer(response ~ grammaticality + (grammaticality|participant), data = ., family = binomial)
summary(mdl.glmmSlope)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: response ~ grammaticality + (grammaticality | participant)
## Data: .
##
## AIC BIC logLik -2*log(L) df.resid
## 280.3 299.2 -135.1 270.3 325
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2750 -0.4702 0.2339 0.3998 2.1269
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## participant (Intercept) 0.5992 0.774
## grammaticalitygrammatical 1.8089 1.345 -1.00
## Number of obs: 330, groups: participant, 2
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.7951 0.5875 -1.353 0.17593
## grammaticalitygrammatical 3.1739 1.0099 3.143 0.00167 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## grmmtcltygr -0.955
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
4.4.1.4 Model comparison
## Data: .
## Models:
## mdl.glmm: response ~ grammaticality + (1 | participant)
## mdl.glmmSlope: response ~ grammaticality + (grammaticality | participant)
## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)
## mdl.glmm 3 290.84 302.24 -142.42 284.84
## mdl.glmmSlope 5 280.25 299.25 -135.13 270.25 14.584 2 0.0006811 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Data: .
## Models:
## mdl.glmmSlope: response ~ grammaticality + (grammaticality | participant)
## mdl.glmmSlopeDec: response ~ grammaticality + (grammaticality || participant)
## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)
## mdl.glmmSlope 5 280.25 299.25 -135.13 270.25
## mdl.glmmSlopeDec 6 282.25 305.05 -135.13 270.25 0 1 1
The model comparisons show that the model with both random intercepts and random slopes is improving the model fit. The Is.Singular
message tells us that there is a chance there is a complete separation in the model.
4.4.1.5 Getting results
4.4.1.5.1 Model’s fit
print(tab_model(mdl.glmmSlope, file = paste0("outputs/mdl.glmmSlope.html")))
htmltools::includeHTML("outputs/mdl.glmmSlope.html")
response | |||
---|---|---|---|
Predictors | Odds Ratios | CI | p |
(Intercept) | 0.45 | 0.14 – 1.43 | 0.176 |
grammaticality [grammatical] |
23.90 | 3.30 – 172.99 | 0.002 |
Random Effects | |||
σ2 | 3.29 | ||
τ00 participant | 0.60 | ||
τ11 participant.grammaticalitygrammatical | 1.81 | ||
ρ01 participant | -1.00 | ||
N participant | 2 | ||
Observations | 330 | ||
Marginal R2 / Conditional R2 | 0.415 / NA |
4.4.1.5.2 Fixed effects
## (Intercept) grammaticalitygrammatical
## -0.7950773 3.1738527
## (Intercept)
## -0.7950773
## grammaticalitygrammatical
## 3.173853
4.4.1.5.3 Random effects
## (Intercept)
## p1 -1.50933642
## p2 -0.05609396
## grammaticalitygrammatical
## p1 4.414908
## p2 1.889839
4.4.1.5.4 Logodds to Odd ratios
Logodds can be modified to talk about the odds of an event.
## (Intercept)
## 0.4515463
## (Intercept)
## 10.79168
4.4.1.5.5 LogOdds to proportions
If you want to talk about the percentage “accuracy” of our model, then we can transform our loggodds into proportions. This shows that the proportion of “grammatical” receiving a “yes” response increases by 99% (or 95% based on our “true” coefficients).
## (Intercept)
## 0.3110795
## (Intercept)
## 0.9151944
4.4.1.5.6 Plotting
grammatical2 <- grammatical2 %>%
mutate(prob = predict(mdl.glmmSlope, type = "response"))
grammatical2 %>%
ggplot(aes(x = as.numeric(grammaticality), y = prob)) +
geom_point() +
geom_smooth(method = "glm",
method.args = list(family = "binomial"),
se = T) + theme_bw(base_size = 20)+
labs(y = "Probability", x = "")+
coord_cartesian(ylim = c(0,1))+
scale_x_discrete(limits = c("Ungrammatical", "Grammatical")) +
facet_grid(~ participant, margins = TRUE, scales = "free")
4.4.2 GLMM - Numeric predictors
In this example, we will run a GLM model using a similar technique to that used in Al-Tamimi (2017)
and Baumann & Winter (2018)
. We use the package LanguageR
and the dataset English
.
In the model above, we used the equation as lm(RTlexdec ~ AgeSubject). We were interested in examining the impact of age of subject on reaction time in a lexical decision task. In this section, we are interested in understanding how reaction time allows to differentiate the participants based on their age. We use AgeSubject
as our outcome and RTlexdec
as our predictor using the equation glm(AgeSubject ~ RTlexdec). We usually can use RTlexdec
as is, but due to a possible quasi separation and the fact that we may want to compare coefficients using multiple acoustic metrics, we will z-score our predictor. We run below two models, with and without z-scoring
For the glm model, we need to specify family = "binomial"
.
4.4.2.1 Without z-scoring of predictor
4.4.2.1.1 Model estimation
In the english
dataset, we have a random factor: “Word”. We include it here.
4.4.2.1.1.1 Random Intercepts
english2 <- english %>%
mutate(AgeSubject = factor(AgeSubject, levels = c("young", "old")))
mdl.glmm2 <- english2 %>%
glmer(AgeSubject ~ RTlexdec + (1|Word), data = ., family = "binomial")
summary(mdl.glmm2)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: AgeSubject ~ RTlexdec + (1 | Word)
## Data: .
##
## AIC BIC logLik -2*log(L) df.resid
## 3151.8 3171.1 -1572.9 3145.8 4565
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -26.3468 -0.3058 -0.0166 0.3893 4.0750
##
## Random effects:
## Groups Name Variance Std.Dev.
## Word (Intercept) 1.666e-15 4.082e-08
## Number of obs: 4568, groups: Word, 2197
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -128.6308 3.7928 -33.91 <2e-16 ***
## RTlexdec 19.6497 0.5792 33.93 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## RTlexdec -1.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
4.4.2.1.1.2 Random Slopes
mdl.glmmSlope2 <- english2 %>%
glmer(AgeSubject ~ RTlexdec + (RTlexdec|Word), data = ., family = "binomial")
summary(mdl.glmmSlope2)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: AgeSubject ~ RTlexdec + (RTlexdec | Word)
## Data: .
##
## AIC BIC logLik -2*log(L) df.resid
## 3075.6 3107.7 -1532.8 3065.6 4563
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3923 -0.2133 -0.0024 0.2512 5.8061
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Word (Intercept) 3325.68 57.669
## RTlexdec 80.01 8.945 -1.00
## Number of obs: 4568, groups: Word, 2197
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -179.980 10.570 -17.03 <2e-16 ***
## RTlexdec 27.535 1.621 16.99 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## RTlexdec -1.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
4.4.2.2 Model comparison
## Data: .
## Models:
## mdl.glmm2: AgeSubject ~ RTlexdec + (1 | Word)
## mdl.glmmSlope2: AgeSubject ~ RTlexdec + (RTlexdec | Word)
## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)
## mdl.glmm2 3 3151.8 3171.1 -1572.9 3145.8
## mdl.glmmSlope2 5 3075.6 3107.7 -1532.8 3065.6 80.262 2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
The model comparisons show that the model with both random intercepts and random slopes is improving the model fit. The Is.Singular
message tells us that there is a chance there is a complete separation in the model.
4.4.2.3 Gettings results
4.4.2.3.1 Model’s fit
print(tab_model(mdl.glmmSlope2, file = paste0("outputs/mdl.glmmSlope2.html")))
htmltools::includeHTML("outputs/mdl.glmmSlope2.html")
Age Subject | |||
---|---|---|---|
Predictors | Odds Ratios | CI | p |
(Intercept) | 0.00 | 0.00 – 0.00 | <0.001 |
RTlexdec | 908896482053.62 | 37919398480.78 – 21785493657243.48 | <0.001 |
Random Effects | |||
σ2 | 3.29 | ||
τ00 Word | 3325.68 | ||
τ11 Word.RTlexdec | 80.01 | ||
ρ01 Word | -1.00 | ||
N Word | 2197 | ||
Observations | 4568 | ||
Marginal R2 / Conditional R2 | 0.850 / NA |
4.4.2.3.2 Fixed effects
## (Intercept) RTlexdec
## -179.9800 27.5355
## (Intercept)
## -179.98
## RTlexdec
## 27.5355
4.4.2.3.3 Random effects
## (Intercept)
## ace -183.90595
## act -194.45240
## add -188.40335
## age -187.46412
## aid -181.03498
## aide -158.07462
## ail -123.55216
## aim -190.10412
## air -200.14398
## aisle -174.27289
## ale -180.30492
## angst -165.78721
## ant -191.28908
## ape -187.24207
## arc -126.77946
## arch -184.42682
## are -182.46610
## arm -217.59079
## art -189.04805
## ash -182.98222
## ask -196.70369
## ass -183.23601
## axe -181.94945
## babe -188.70261
## back -195.42041
## badge -183.01597
## bag -199.54316
## bail -168.15031
## bait -190.95481
## bale -121.78656
## ball -187.58023
## ban -150.32498
## band -182.62445
## bang -196.73785
## bank -193.70563
## bar -200.25190
## bard -117.84681
## barge -141.73049
## bark -196.61580
## barn -200.39052
## base -192.56567
## bash -180.80003
## bat -199.64368
## batch -189.94743
## bath -193.82414
## bay -189.46414
## beach -185.19026
## bead -168.42385
## beak -133.17529
## beam -180.59026
## bean -182.07826
## bear -213.07938
## beard -196.58614
## beast -181.77338
## beat -189.71518
## beau -154.41188
## beck -91.17831
## bed -188.54685
## bee -198.73656
## beech -126.52901
## beef -211.38711
## beep -190.21974
## beer -198.75872
## beet -173.58987
## beg -200.94585
## belch -155.10295
## bell -195.09610
## belt -187.26490
## bench -200.14866
## bend -198.78981
## berth -157.88190
## bet -201.03316
## bib -167.68856
## bid -201.07979
## bide -89.33356
## bile -166.74648
## bilge -99.16026
## bill -189.36738
## bin -159.06194
## bind -150.49850
## binge -173.11797
## birch -158.44405
## bird -192.34649
## bit -197.94421
## bitch -186.76029
## bite -200.32909
## blade -194.37975
## blame -188.93561
## blanch -125.38813
## blast -186.24329
## blaze -194.63242
## bleat -157.35751
## bleed -185.28389
## bleep -132.46422
## blend -191.20351
## bless -186.61602
## blight -165.14488
## blink -180.49656
## bliss -198.34654
## blitz -171.79728
## bloat -177.86002
## blob -171.53998
## block -192.29144
## bloke -115.79912
## blood -189.62165
## bloom -196.43344
## blot -184.07466
## blouse -172.69884
## blow -194.93021
## bluff -194.80368
## blur -180.40576
## blush -200.80529
## boar -143.98104
## board -193.40373
## boast -190.16579
## boat -200.62994
## bob -143.95567
## bog -163.01172
## boil -187.41756
## bolt -201.12837
## bomb -187.14946
## bond -193.50090
## bone -199.94607
## boo -183.41255
## book -182.65019
## boom -182.31856
## boon -136.22258
## boost -180.50189
## boot -191.30092
## booth -197.22091
## booze -185.34295
## bore -184.45601
## boss -193.25145
## bough -96.02205
## bounce -200.88344
## bound -185.03389
## bout -140.82693
## bowl -185.48562
## box -181.85503
## boy -197.94152
## brace -188.09040
## brad -93.89472
## brag -188.95758
## braid -179.85518
## brain -195.29234
## brake -200.99393
## bran -84.22163
## branch -183.72879
## brand -185.22586
## brass -198.41295
## brat -182.01106
## brawl -174.25436
## brawn -82.04808
## breach -140.02971
## bread -200.46402
## break -190.42290
## breast -183.88245
## breath -188.84560
## breed -189.48454
## breeze -199.04385
## brew -192.13874
## bribe -192.44280
## brick -183.68376
## bride -193.32448
## bridge -182.66703
## brig -87.00210
## brim -156.28507
## bring -199.97938
## brink -165.33007
## broach -101.67590
## broad -184.14713
## broil -188.83625
## bronze -194.90986
## brooch -144.85308
## brood -111.85702
## brook -138.60348
## broom -200.65624
## broth -105.41151
## brow -168.12984
## bruise -184.30591
## brunt -135.10110
## brush -183.22357
## brute -178.24259
## buck -171.40398
## bud -198.25591
## budge -180.94458
## buff -178.05974
## bug -200.45605
## build -195.49858
## bulb -190.58620
## bulge -181.62074
## bulk -201.21284
## bull -192.23013
## bum -185.53351
## bump -180.65767
## bun -181.01943
## bunch -194.60410
## bunk -148.84435
## burn -187.44695
## burr -149.28861
## burst -184.95027
## bus -195.88882
## bush -187.16603
## bust -192.71988
## butt -185.85766
## buy -197.22610
## buzz -191.01298
## cab -189.31417
## cad -94.64562
## cage -196.05198
## cake -197.79403
## calf -189.19362
## call -199.38307
## cam -179.76375
## camp -186.84923
## can -194.03452
## cane -182.10094
## cant -165.08881
## cap -189.91371
## cape -185.06192
## car -199.84932
## card -187.43887
## care -187.49423
## cart -183.78951
## carve -187.96570
## case -183.55077
## cash -199.32523
## cask -150.36262
## cast -191.30005
## caste -146.56770
## cat -191.56696
## catch -200.53962
## cause -191.64142
## cave -194.45722
## cease -181.37337
## cell -186.90546
## cent -184.33531
## chafe -75.51497
## chain -181.65688
## chair -200.40360
## chaise -100.81512
## chalk -196.17669
## champ -191.66875
## chance -200.93096
## change -192.45365
## chant -185.03449
## chap -177.44022
## char -68.46758
## charge -194.79498
## charm -200.86640
## chart -197.81127
## chase -200.24428
## chat -189.45651
## cheat -190.39803
## check -198.39313
## cheek -184.48967
## cheer -200.34695
## cheese -193.36716
## chef -196.11280
## chess -188.22429
## chest -189.05613
## chew -198.32587
## chide -91.71205
## chief -192.85388
## child -195.18985
## chime -184.57578
## chin -181.01095
## chip -199.00445
## chive -123.44145
## choice -197.97147
## choir -192.00611
## choke -186.05492
## chomp -121.12000
## choose -193.94852
## chop -218.63855
## chord -171.56334
## chore -176.05109
## chow -129.50782
## chrome -172.35501
## chuck -108.07041
## chum -94.27295
## chump -146.09801
## chunk -181.15675
## church -198.07688
## churn -168.15094
## chute -135.57633
## cinch -132.48823
## cite -169.39442
## claim -183.59402
## clam -183.37829
## clamp -180.45168
## clan -150.00297
## clang -173.81100
## clap -207.24223
## clash -181.86252
## class -193.98182
## clause -133.02072
## claw -187.57446
## clay -196.65091
## cleat -83.63746
## clench -142.35170
## clerk -183.34218
## click -190.02283
## cliff -195.01136
## climb -199.07738
## clinch -122.08349
## cling -187.60080
## clip -218.89313
## cloak -184.24441
## clock -194.97956
## clod -130.05891
## clog -147.25098
## clot -180.13861
## cloth -184.46513
## cloud -187.55841
## clout -174.13907
## clove -131.16564
## clown -196.03990
## club -180.83262
## cluck -124.64114
## clump -139.14258
## clutch -185.24988
## coach -198.34058
## coal -200.14167
## coast -199.03568
## coat -184.64240
## coax -170.23923
## cock -178.45822
## cod -174.57755
## code -180.97525
## coil -181.77307
## coin -193.51356
## coke -187.51024
## colt -164.12222
## comb -194.19491
## come -191.11125
## cone -180.49718
## cook -194.54502
## coop -132.64990
## cop -187.59231
## cope -190.58582
## cord -196.17562
## core -188.10521
## cork -199.57278
## corn -192.90894
## corps -164.00446
## corpse -189.23187
## cost -195.36966
## cot -156.64107
## couch -197.45141
## cough -187.03210
## count -217.84094
## coup -130.69606
## coupe -131.78314
## course -192.21291
## court -199.68155
## cove -174.66381
## cow -207.93442
## cowl -79.16102
## cox -185.92869
## crab -187.65682
## crack -190.65623
## craft -190.62083
## crag -133.96322
## cram -171.49644
## cramp -183.33558
## crane -179.95951
## crank -181.54297
## crap -186.18661
## crash -199.75403
## crate -160.10063
## crave -180.76335
## crawl -190.86483
## craze -184.42819
## creak -180.55223
## cream -190.42549
## crease -141.98036
## creed -187.18250
## creek -182.42285
## creep -193.43469
## crepe -126.11991
## crest -182.43335
## crew -191.06476
## crime -181.11051
## croak -161.38982
## crone -165.66315
## crook -191.27335
## croon -78.44560
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## gong -136.75768
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## hitch -148.42064
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## wilt -176.39696
## win -182.73619
## wine -200.01716
## wing -201.17582
## wink -191.84227
## wipe -199.77178
## wire -200.67935
## wish -197.65220
## wisp -133.95200
## wit -182.50256
## witch -183.96758
## woe -184.55422
## wolf -199.94778
## womb -181.50125
## woo -106.62975
## wood -182.96857
## wool -178.06062
## word -192.47041
## work -196.50376
## world -198.47112
## worm -183.73084
## would -195.31638
## wow -180.40014
## wrack -180.52854
## wrap -188.24931
## wrath -178.23654
## wreak -170.33325
## wreath -175.45290
## wreck -188.39151
## wren -134.32344
## wrest -178.39661
## wretch -180.97686
## wring -93.40979
## wrist -196.10915
## writ -87.58469
## write -188.71382
## writhe -164.88819
## yacht -155.32949
## yak -69.96091
## yam -179.76095
## yang -69.95411
## yank -139.63449
## yard -186.10504
## yarn -185.51758
## yaw -117.54558
## yawl -114.62595
## yawn -185.24873
## yea -165.71545
## year -187.99051
## yearn -163.12216
## yeast -187.47526
## yell -183.94923
## yelp -142.53706
## yen -123.83434
## yes -201.01983
## yield -200.55056
## yoke -186.55671
## yolk -177.72981
## yore -125.92411
## youth -192.62613
## zeal -172.60322
## zest -171.22512
## zinc -160.04073
## zing -108.93644
## zip -188.51310
## zone -192.72950
## zoo -180.22780
## RTlexdec
## ace 28.144460
## act 29.780340
## add 28.842061
## age 28.696374
## aid 27.699138
## aide 24.137715
## ail 18.782872
## aim 29.105869
## air 30.663172
## aisle 26.650259
## ale 27.585897
## angst 25.334029
## ant 29.289671
## ape 28.661932
## arc 19.283464
## arch 28.225253
## are 27.921122
## arm 33.369377
## art 28.942060
## ash 28.001179
## ask 30.129540
## ass 28.040544
## axe 27.840985
## babe 28.888478
## back 29.930490
## badge 28.006414
## bag 30.569977
## bail 25.700574
## bait 29.237822
## bale 18.509007
## ball 28.714384
## ban 22.935654
## band 27.945684
## bang 30.134840
## bank 29.664507
## bar 30.679911
## bard 17.897905
## barge 21.602546
## bark 30.115909
## barn 30.701413
## base 29.487685
## bash 27.662695
## bat 30.585568
## batch 29.081565
## bath 29.682889
## bay 29.006601
## beach 28.343672
## bead 25.743002
## beak 20.275533
## beam 27.630158
## bean 27.860964
## bear 32.669605
## beard 30.111308
## beast 27.813674
## beat 29.045540
## beau 23.569580
## beck 13.761305
## bed 28.864318
## bee 30.444863
## beech 19.244618
## beef 32.407114
## beep 29.123803
## beer 30.448300
## beet 26.544315
## beg 30.787551
## belch 23.676774
## bell 29.880185
## belt 28.665473
## bench 30.663898
## bend 30.453124
## berth 24.107821
## bet 30.801093
## bib 25.628950
## bid 30.808326
## bide 13.475163
## bile 25.482823
## bilge 14.999400
## bill 28.991593
## bin 24.290859
## bind 22.962568
## binge 26.471116
## birch 24.195017
## bird 29.453688
## bit 30.321961
## bitch 28.587201
## bite 30.691883
## blade 29.769070
## blame 28.924620
## blanch 19.067653
## blast 28.507009
## blaze 29.808262
## bleat 24.026482
## bleed 28.358195
## bleep 20.165239
## blend 29.276398
## bless 28.564825
## blight 25.234396
## blink 27.615623
## bliss 30.384367
## blitz 26.266262
## bloat 27.206665
## blob 26.226351
## block 29.445149
## bloke 17.580283
## blood 29.031032
## bloom 30.087622
## blot 28.170629
## blouse 26.406105
## blow 29.854453
## bluff 29.834827
## blur 27.601539
## blush 30.765748
## boar 21.951633
## board 29.617679
## boast 29.115435
## boat 30.738549
## bob 21.947699
## bog 24.903518
## boil 28.689152
## bolt 30.815862
## bomb 28.647567
## bond 29.632751
## bone 30.632473
## boo 28.067927
## book 27.949677
## boom 27.898237
## boon 20.748204
## boost 27.616450
## boot 29.291508
## booth 30.209768
## booze 28.367356
## bore 28.229781
## boss 29.594058
## bough 14.512626
## bounce 30.777870
## bound 28.319417
## bout 21.462394
## bowl 28.389486
## box 27.826338
## boy 30.321544
## brace 28.793518
## brad 14.182653
## brag 28.928028
## braid 27.516137
## brain 29.910624
## brake 30.795008
## bran 12.682242
## branch 28.116981
## brand 28.349194
## brass 30.394668
## brat 27.850539
## brawl 26.647385
## brawn 12.345097
## breach 21.338736
## bread 30.712813
## break 29.155316
## breast 28.140815
## breath 28.910659
## breed 29.009765
## breeze 30.492528
## brew 29.421464
## bribe 29.468626
## brick 28.109995
## bride 29.605386
## bridge 27.952289
## brig 13.113525
## brim 23.860135
## bring 30.637640
## brink 25.263121
## broach 15.389606
## broad 28.181870
## broil 28.909208
## bronze 29.851296
## brooch 22.086897
## brood 16.968817
## brook 21.117510
## broom 30.742629
## broth 15.969042
## brow 25.697399
## bruise 28.206498
## brunt 20.574250
## brush 28.038616
## brute 27.266007
## buck 26.205256
## bud 30.370309
## budge 27.685117
## buff 27.237644
## bug 30.711577
## build 29.942615
## bulb 29.180647
## bulge 27.789997
## bulk 30.828964
## bull 29.435639
## bum 28.396914
## bump 27.640613
## bun 27.696727
## bunch 29.803869
## bunk 22.705991
## burn 28.693712
## burr 22.774900
## burst 28.306447
## bus 30.003146
## bush 28.650138
## bust 29.511605
## butt 28.447193
## buy 30.210574
## buzz 29.246845
## cab 28.983338
## cad 14.299126
## cage 30.028454
## cake 30.298666
## calf 28.964641
## call 30.545144
## cam 27.501956
## camp 28.600998
## can 29.715521
## cane 27.864482
## cant 25.225699
## cap 29.076334
## cape 28.323764
## car 30.617466
## card 28.692459
## care 28.701045
## cart 28.126399
## carve 28.774176
## case 28.089368
## cash 30.536174
## cask 22.941492
## cast 29.291373
## caste 22.352856
## cat 29.332773
## catch 30.724539
## cause 29.344324
## cave 29.781087
## cease 27.751626
## cell 28.609720
## cent 28.211059
## chafe 11.331735
## chain 27.795602
## chair 30.703441
## chaise 15.256088
## chalk 30.047796
## champ 29.348562
## chance 30.785241
## change 29.470309
## chant 28.319510
## chap 27.141549
## char 10.238601
## charge 29.833477
## charm 30.775228
## chart 30.301340
## chase 30.678729
## chat 29.005417
## cheat 29.151458
## check 30.391593
## cheek 28.235003
## cheer 30.694654
## cheese 29.612007
## chef 30.037888
## chess 28.814286
## chest 28.943314
## chew 30.381160
## chide 13.844094
## chief 29.532390
## child 29.894726
## chime 28.248359
## chin 27.695411
## chip 30.486416
## chive 18.765700
## choice 30.326188
## choir 29.400890
## choke 28.477791
## chomp 18.405616
## choose 29.702182
## chop 33.531898
## chord 26.229975
## chore 26.926078
## chow 19.706665
## chrome 26.352773
## chuck 16.381469
## chum 14.241321
## chump 22.280001
## chunk 27.718026
## church 30.342540
## churn 25.700671
## chute 20.647964
## cinch 20.168962
## cite 25.893550
## claim 28.096077
## clam 28.062614
## clamp 27.608661
## clan 22.885706
## clang 26.578613
## clap 31.764193
## clash 27.827499
## class 29.707348
## clause 20.251558
## claw 28.713489
## clay 30.121355
## cleat 12.591629
## clench 21.698904
## clerk 28.057012
## click 29.093261
## cliff 29.867041
## climb 30.497728
## clinch 18.555065
## cling 28.717575
## clip 33.571387
## cloak 28.196960
## clock 29.862107
## clod 19.792147
## clog 22.458840
## clot 27.560102
## cloth 28.231196
## cloud 28.711000
## clout 26.629501
## clove 19.963813
## clown 30.026580
## club 27.667751
## cluck 18.951786
## clump 21.201131
## clutch 28.352920
## coach 30.383442
## coal 30.662812
## coast 30.491261
## coat 28.258692
## coax 26.024590
## cock 27.299453
## cod 26.697514
## code 27.689874
## coil 27.813625
## coin 29.634715
## coke 28.703528
## colt 25.075768
## comb 29.740400
## come 29.262087
## cone 27.615720
## cook 29.794705
## coop 20.194040
## cop 28.716258
## cope 29.180586
## cord 30.047631
## core 28.795814
## cork 30.574571
## corn 29.540930
## corps 25.057503
## corpse 28.970573
## cost 29.922618
## cot 23.915354
## couch 30.245521
## cough 28.629363
## count 33.408180
## coup 19.890976
## coupe 20.059594
## course 29.432969
## court 30.591442
## cove 26.710895
## cow 31.871561
## cowl 11.897281
## cox 28.458211
## crab 28.726264
## crack 29.191508
## craft 29.186017
## crag 20.397750
## cram 26.219598
## cramp 28.055988
## crane 27.532320
## crank 27.777934
## crap 28.498218
## crash 30.602686
## crate 24.451973
## crave 27.657005
## crawl 29.223865
## craze 28.225466
## creak 27.624259
## cream 29.155719
## crease 21.641305
## creed 28.652691
## creek 27.914414
## creep 29.622480
## crepe 19.181162
## crest 27.916042
## crew 29.254876
## crime 27.710854
## croak 24.651941
## crone 25.314786
## crook 29.287231
## croon 11.786310
## crop 29.437746
## cross 28.823966
## crouch 27.578142
## crow 29.803259
## crowd 28.211797
## crown 30.026585
## crumb 30.100752
## crunch 27.669076
## crush 29.899520
## crust 30.724333
## crutch 27.494628
## crux 15.263074
## cry 28.956613
## crypt 27.307705
## cub 26.902686
## cube 30.234904
## cud 14.591752
## cue 28.643100
## cuff 23.718828
## cull 21.464687
## cult 27.254569
## cup 30.361857
## cur 27.560381
## curb 27.654123
## curd 22.399987
## cure 28.092256
## curl 30.075477
## curse 29.507712
## curve 29.753908
## cusp 22.850857
## cut 30.591028
## cyst 13.449308
## czar 13.761941
## dad 30.117269
## dale 15.987633
## dam 26.577465
## dame 24.823139
## damn 27.797336
## damp 32.178410
## dance 30.738695
## dare 30.701983
## darn 25.680645
## dash 29.244194
## date 28.127236
## daunt 20.399407
## dawn 29.111551
## deal 30.797559
## dean 25.706071
## dearth 22.638779
## debt 29.699634
## deck 30.819348
## deed 29.247229
## deem 13.753965
## deer 30.071908
## dell 12.135646
## den 27.606895
## dent 27.639861
## desk 30.801490
## dial 28.079279
## dice 28.896934
## die 28.950432
## dig 30.262467
## dike 14.289348
## dill 20.973941
## dime 27.945487
## din 27.156299
## dine 25.307547
## dint 8.460977
## dip 29.275947
## dirge 25.033000
## dirt 30.147180
## disc 27.600695
## dish 32.038440
## ditch 27.828829
## dive 28.325549
## do 29.869920
## dock 33.121278
## dodge 28.277292
## doe 24.689890
## dog 29.738669
## dole 26.292562
## doll 27.846973
## dome 27.525696
## doom 27.796931
## door 30.341516
## dope 28.092042
## dose 27.865592
## doubt 29.356234
## dough 29.091287
## douse 13.258126
## draft 28.410205
## drag 30.511415
## drain 28.610924
## drake 19.627177
## dram 9.183555
## drape 25.996087
## draught 26.919341
## draw 28.603498
## drawl 27.785543
## dread 26.959935
## dream 30.709527
## dress 29.048598
## drift 27.581090
## drill 29.991477
## drink 30.456710
## drip 30.438133
## drive 30.279579
## drone 27.291877
## droop 18.681625
## drop 29.332874
## dross 27.007927
## drought 25.620145
## drove 26.943619
## drown 27.702174
## drum 29.765694
## duck 33.229677
## duct 19.247478
## dud 19.744037
## duel 28.889774
## dug 28.512630
## duke 27.688215
## dump 29.299379
## dun 27.582102
## dune 27.125201
## dung 14.957654
## dunk 23.150562
## dusk 29.108548
## dust 30.569819
## dwarf 27.658752
## dwell 26.376095
## ear 30.157240
## earl 24.047000
## earn 28.705383
## earth 29.993446
## ease 27.691228
## east 26.160857
## eat 29.083235
## ebb 21.259724
## edge 29.789685
## eel 24.630408
## egg 30.589902
## elk 27.761634
## elm 27.942029
## end 27.785235
## err 17.834010
## eve 27.789382
## ewe 17.393020
## face 30.329635
## fact 30.565724
## fad 25.851073
## fade 28.888023
## fail 27.626605
## fair 29.442666
## faith 30.769189
## fake 28.026940
## fame 27.588722
## fan 27.762796
## fang 23.492742
## farce 19.602771
## fare 27.002914
## farm 30.708482
## fast 29.938548
## fate 30.605292
## fault 29.982833
## fawn 25.953552
## faze 24.650352
## fear 30.549964
## feast 30.454934
## feat 26.268800
## fee 27.016297
## feed 28.744808
## feel 30.758959
## feint 22.298765
## fell 33.361220
## fen 24.522095
## fence 29.595406
## fern 20.347945
## fetch 30.036753
## feud 27.110712
## fiend 15.138994
## fife 14.373496
## fig 27.239282
## fight 27.899235
## file 29.350451
## fill 26.869858
## film 29.419534
## filth 25.171510
## fin 27.090288
## find 28.974263
## fine 27.821819
## fink 19.503739
## fir 24.543839
## fire 30.620515
## firm 30.301279
## fish 30.378463
## fist 24.444996
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## flail 12.661781
## flair 25.525805
## flake 27.206654
## flame 29.822504
## flange 11.684015
## flank 25.292848
## flare 29.672911
## flask 28.475858
## flaw 28.390873
## flax 22.959595
## flea 28.592608
## fleck 17.424087
## flee 27.523039
## fleet 27.174460
## flesh 29.120219
## flex 28.533268
## flick 27.261709
## flight 27.739211
## fling 28.097827
## flint 27.432505
## flip 27.867622
## flirt 29.940445
## float 28.288833
## flock 28.718485
## floe 18.982326
## flog 26.342520
## flood 30.796840
## floor 29.855102
## flop 25.482716
## flour 30.132832
## flow 27.652433
## fluff 27.909070
## fluke 28.076973
## flush 29.072822
## flute 27.862102
## flux 25.564195
## fly 33.431790
## foal 22.414183
## foam 28.563652
## foe 28.549070
## fog 28.467571
## foil 28.539874
## fold 30.508934
## folk 29.321991
## font 19.533728
## food 29.471885
## fool 30.760335
## foot 30.362233
## force 27.811613
## ford 23.630157
## forge 24.274617
## fork 30.065444
## form 27.941614
## fort 22.658281
## found 30.447020
## fowl 30.582703
## fox 30.770533
## frame 26.970910
## fraud 25.634116
## fray 22.911815
## freak 29.166521
## freeze 28.222731
## freight 26.854431
## fret 18.017420
## friend 29.511037
## frieze 23.094414
## fright 27.677941
## frill 25.610841
## fringe 26.968103
## frock 21.246176
## frog 29.625848
## front 30.364205
## frost 28.002915
## froth 16.378138
## frown 27.609914
## fruit 30.256111
## fry 31.763274
## fuel 30.381276
## full 29.731306
## fun 29.440518
## fund 27.888040
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## fur 29.706355
## fuse 27.076174
## fuss 27.955257
## fuzz 22.841724
## gab 21.653152
## gag 23.490494
## gain 27.838922
## gait 19.537570
## gal 18.773276
## gale 23.970120
## gall 23.998249
## game 30.373916
## gang 28.340301
## gap 29.085973
## garb 17.288144
## gas 27.640341
## gash 15.932050
## gasp 27.652121
## gate 27.139679
## gauge 21.562478
## gauze 20.590525
## gay 27.823390
## gaze 27.055726
## gear 29.962306
## gel 26.920803
## gem 28.254978
## gene 24.800216
## get 29.423014
## ghost 29.522477
## ghoul 17.631276
## gibe 23.315892
## gift 30.734698
## gig 18.410097
## gill 11.706716
## gilt 21.044342
## gin 27.731263
## gird 27.528888
## girl 28.378300
## gist 19.645679
## give 30.705866
## glance 28.634456
## gland 27.771859
## glare 30.626514
## glass 30.560392
## glaze 28.547835
## gleam 22.839680
## glean 11.740680
## glee 24.555534
## glen 21.032430
## glide 27.442012
## glimpse 27.787693
## glint 24.325218
## gloat 22.553954
## globe 26.782442
## gloom 29.436008
## gloss 30.182786
## glove 27.718869
## glow 27.681590
## glue 29.190228
## gnaw 22.596092
## gnome 16.039988
## go 28.732386
## goad 26.829045
## goal 30.165494
## goat 28.688437
## gob 14.032807
## god 27.607365
## gold 27.767164
## golf 27.481475
## gong 20.831205
## goon 12.428550
## goose 27.714699
## gore 17.260054
## gouge 17.149647
## gourd 16.998064
## gout 21.626386
## gown 26.932128
## grab 27.850191
## grace 29.501049
## grade 28.565741
## graft 23.626551
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## grain 28.174168
## gram 22.294146
## grant 29.312267
## grape 29.028141
## graph 28.444395
## grasp 28.355852
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## grate 25.426265
## grave 29.256134
## graze 27.069795
## grease 27.885584
## greed 28.470043
## greet 20.085252
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## grin 26.661657
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## groom 29.638713
## groove 28.136801
## grope 22.564184
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## grove 24.778970
## grow 30.806203
## growl 27.916603
## grub 18.530423
## grudge 26.912614
## grunt 27.177399
## guard 30.648987
## guess 28.665600
## guest 28.958373
## guide 30.778625
## guild 21.968996
## guile 19.223254
## guilt 27.946752
## guise 21.918910
## gulf 25.609212
## gull 18.245496
## gulp 28.379228
## gum 27.830216
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## guy 28.200065
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## hail 30.494255
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## ham 30.781998
## hand 30.554056
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## hart 25.758190
## hash 26.950594
## haste 30.323916
## hat 28.779128
## hatch 29.615265
## hate 30.711777
## haul 30.782045
## haunt 24.125328
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## haw 26.639002
## hawk 28.454789
## hay 30.767077
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## head 30.787881
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## heart 30.527482
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## spurt 22.940853
## spy 28.828893
## squad 27.673716
## squall 22.946768
## square 28.099641
## squash 27.812703
## squat 25.754204
## squaw 20.001741
## squawk 22.630949
## squeak 27.960730
## squeal 27.694318
## squeeze 28.317509
## squint 27.998749
## squire 24.379806
## squirm 28.047407
## squirt 27.718435
## stab 27.946592
## stack 28.310513
## staff 30.130244
## stag 29.437602
## stage 28.941655
## stain 27.681838
## stair 28.418340
## stake 26.945769
## stalk 28.133749
## stall 29.940394
## stamp 28.473690
## stance 27.136144
## stanch 27.626482
## stand 29.433724
## star 29.109122
## starch 28.818343
## stare 28.372849
## start 28.549099
## starve 28.023268
## state 28.702210
## staunch 18.792773
## stave 21.795690
## stay 30.435904
## stead 23.809336
## steak 27.840241
## steal 30.207831
## steam 27.666422
## steed 22.141146
## steel 28.195634
## steer 27.712907
## stem 27.707495
## stench 22.455687
## step 30.739190
## stew 30.807811
## stick 29.392073
## still 30.196171
## stilt 20.345997
## sting 27.758631
## stink 28.007220
## stint 27.396989
## stir 30.722037
## stitch 24.358313
## stock 30.764157
## stole 30.212766
## stone 27.956732
## stool 30.736560
## stoop 22.440464
## stop 29.273810
## store 29.178395
## stork 28.142858
## storm 29.170299
## stout 27.402740
## stove 28.768516
## stow 22.777723
## strafe 22.550449
## strain 29.022454
## strand 27.181902
## strap 27.780015
## straw 30.402410
## stray 29.913365
## streak 28.349991
## stream 27.650640
## street 28.260742
## stress 30.590310
## stretch 28.238276
## stride 29.062389
## strife 25.707002
## strike 30.570858
## string 28.380800
## strip 30.181729
## stripe 28.838880
## strive 27.642038
## stroke 28.311268
## stroll 27.745224
## strut 22.995771
## stub 27.069917
## stud 28.874694
## stuff 29.260309
## stump 28.567863
## stunt 27.574271
## style 30.837178
## sub 15.341097
## suck 27.707704
## sue 26.683145
## suit 28.894653
## suite 28.321878
## sulk 23.044496
## sum 28.053665
## sun 28.228916
## sup 27.601802
## surf 27.949586
## surge 26.472449
## swamp 27.707983
## swan 27.675089
## swap 25.015765
## swarm 27.915988
## swath 20.190807
## sway 27.889674
## swear 29.469886
## sweat 29.373056
## sweep 27.938625
## swell 30.663167
## swerve 27.619311
## swig 22.890198
## swim 29.195988
## swine 28.084324
## swing 30.759216
## swipe 27.817291
## swirl 27.638622
## switch 28.376234
## swoop 23.950611
## sword 30.341993
## tab 28.366933
## tack 26.970738
## tact 29.510444
## tag 28.269307
## tail 28.271708
## taint 27.820406
## take 30.284514
## tale 29.155858
## talk 28.198585
## tamp 25.557622
## tan 28.214987
## tang 22.815085
## tank 27.638624
## tape 29.873767
## tar 29.456393
## tart 27.692758
## task 30.601490
## taste 30.280524
## taunt 27.673773
## tax 30.243498
## tea 30.606645
## teach 29.248362
## teak 27.541258
## team 30.464697
## tease 29.500549
## tech 13.239601
## tee 28.217617
## teens 27.636501
## tell 29.812361
## tempt 29.898271
## tend 27.643140
## tense 29.229459
## tent 30.577590
## test 29.636033
## text 30.368821
## thank 30.107537
## thaw 27.903328
## theft 28.199896
## theme 28.284183
## thief 28.126202
## thigh 30.347145
## thin 29.012704
## thing 28.673296
## think 30.817645
## thirst 30.711014
## thong 23.873075
## thorn 30.830651
## thought 29.028309
## thrash 27.270883
## thread 29.640659
## threat 27.919130
## thrift 28.330687
## thrill 28.276703
## thrive 28.082464
## throat 30.775421
## throne 25.167709
## throng 18.784358
## throw 28.148957
## thrush 21.497176
## thrust 27.339381
## thud 25.343482
## thug 27.566812
## thumb 30.773308
## thump 27.584587
## thwack 10.458866
## thwart 17.862892
## tick 28.555224
## tide 30.108284
## tie 30.772564
## tile 29.635351
## till 24.683677
## tilt 30.258303
## time 30.406156
## tin 27.685339
## tint 28.434225
## tip 30.185632
## tire 30.792423
## toad 30.155543
## toast 29.816807
## toe 27.822708
## toil 27.891681
## toll 27.219621
## tomb 30.770502
## tome 27.335648
## ton 27.628021
## tone 29.453357
## tongue 30.218354
## tool 30.692156
## toot 20.531006
## tooth 29.206983
## top 29.393229
## torch 27.949540
## torque 25.554943
## toss 30.002211
## tote 20.521421
## touch 30.700814
## tour 29.887402
## tout 22.924384
## town 30.312988
## toy 30.748919
## trace 29.829497
## track 29.747407
## tract 27.894949
## trade 30.512229
## trail 27.711583
## train 30.435105
## trait 27.291975
## tramp 27.184069
## trance 26.107228
## trap 29.223521
## trash 28.236594
## tray 25.361745
## tread 25.967651
## treat 29.511979
## tree 30.762980
## trench 27.777335
## trend 28.130173
## tribe 27.276298
## trick 28.105536
## trill 14.224084
## trip 29.368233
## tripe 26.259334
## troll 20.863389
## troop 25.373519
## trot 20.603109
## trough 14.149857
## trout 29.716756
## truce 25.177672
## truck 28.322353
## trump 22.668678
## trunk 30.367177
## trust 29.101622
## try 29.997345
## tryst 17.121382
## tub 29.731137
## tube 33.266355
## tuck 27.313707
## tug 30.439328
## tune 29.304853
## turf 26.229087
## turn 27.972382
## tusk 24.486810
## twain 24.797577
## tweed 28.289413
## twin 30.288620
## twinge 19.568851
## twist 29.527310
## twitch 24.830644
## type 28.007832
## urge 27.977366
## urn 20.451988
## use 30.770947
## vale 13.887541
## valve 27.549259
## vamp 19.512335
## van 27.665651
## vase 27.942474
## vault 28.802518
## veal 27.271619
## veer 17.452473
## veil 27.716579
## vein 28.094319
## vent 27.254079
## verb 28.265425
## verge 24.411044
## verse 28.031706
## verve 20.470941
## vest 25.676745
## vet 23.045417
## vex 26.926718
## vice 26.501542
## vie 17.538961
## view 28.538556
## vine 27.810188
## voice 30.478961
## volt 26.180079
## vote 27.889961
## vow 27.089811
## wad 27.380878
## wade 27.773565
## wag 27.830790
## wage 27.962121
## wail 27.349550
## waist 27.860326
## wait 29.496963
## waive 27.659949
## wake 27.931581
## walk 30.712978
## wall 28.966140
## waltz 30.162673
## wand 25.307029
## wane 22.699354
## want 28.952450
## war 30.526103
## ward 21.885323
## ware 25.965071
## warn 28.450538
## warp 27.623400
## wart 27.171713
## wash 28.460496
## wasp 28.175665
## waste 30.665015
## watch 29.503591
## watt 27.085973
## wave 27.989862
## wax 28.089526
## way 30.374770
## wealth 27.877321
## wear 28.320756
## weave 29.205571
## web 30.706883
## wed 30.257073
## wedge 27.774724
## weed 28.980521
## week 28.276358
## weep 27.817351
## weigh 28.644940
## weight 28.889303
## weld 21.611975
## well 30.690703
## welt 18.403092
## west 17.351376
## whack 27.254622
## wharf 28.398735
## wheat 28.850859
## wheel 27.635735
## whelp 13.669017
## whiff 23.952005
## while 29.463903
## whim 27.786092
## whine 27.188407
## whip 30.750833
## whirl 27.816991
## whit 20.464443
## whiz 28.999940
## whoop 21.052200
## whoosh 25.897416
## whore 27.957410
## whorl 16.451351
## wick 27.618511
## wield 25.207162
## wife 30.753663
## wig 28.011540
## will 30.691486
## wilt 26.979727
## win 27.963016
## wine 30.643499
## wing 30.823222
## wink 29.375477
## wipe 30.605438
## wire 30.746213
## wish 30.276666
## wisp 20.396010
## wit 27.926778
## witch 28.154020
## woe 28.245014
## wolf 30.632737
## womb 27.771463
## woo 16.158006
## wood 27.999062
## wool 27.237780
## word 29.472909
## work 30.098529
## world 30.403690
## worm 28.117299
## would 29.914353
## wow 27.600668
## wrack 27.620584
## wrap 28.818166
## wrath 27.265068
## wreak 26.039173
## wreath 26.833292
## wreck 28.840224
## wren 20.453625
## wrest 27.289895
## wretch 27.690123
## wring 14.107433
## wrist 30.037321
## writ 13.203892
## write 28.890218
## writhe 25.194581
## yacht 23.711913
## yak 10.470234
## yam 27.501522
## yang 10.469180
## yank 21.277432
## yard 28.485565
## yarn 28.394444
## yaw 17.851181
## yawl 17.398311
## yawn 28.352741
## yea 25.322899
## year 28.778024
## yearn 24.920648
## yeast 28.698102
## yell 28.151174
## yelp 21.727655
## yen 18.826642
## yes 30.799026
## yield 30.726236
## yoke 28.555624
## yolk 27.186467
## yore 19.150790
## youth 29.497063
## zeal 26.391272
## zest 26.177514
## zinc 24.442681
## zing 16.515801
## zip 28.859083
## zone 29.513097
## zoo 27.573936
4.4.2.3.4 Logodds to Odd ratios
Logodds can be modified to talk about the odds of an event.
## (Intercept)
## 6.849895e-79
## (Intercept)
## 6.225845e-67
4.4.2.3.5 LogOdds to proportions
If you want to talk about the percentage “accuracy” of our model, then we can transform our loggodds into proportions. This shows that the proportion of “grammatical” receiving a “yes” response increases by 99% (or 95% based on our “true” coefficients)
## (Intercept)
## 6.849895e-79
## (Intercept)
## 6.225845e-67
4.4.2.3.6 Plotting
english2 <- english2 %>%
mutate(prob2 = predict(mdl.glmmSlope2, type = "response"))
english2 %>%
ggplot(aes(x = as.numeric(AgeSubject), y = prob2)) +
geom_point() +
geom_smooth(method = "glm",
method.args = list(family = "binomial"),
se = T) + theme_bw(base_size = 20)+
labs(y = "Probability", x = "")+
coord_cartesian(ylim = c(0,1))+
scale_x_discrete(limits = c("Young", "Old"))
The plot above shows how the two groups differ using a glmm. The results point to an overall increase in the proportion of reaction time when moving from the “Young” to the “Old” group.
Let’s use z-scoring next
4.4.2.4 With z-scoring of predictor
4.4.2.4.1 Model estimation
english2 <- english2 %>%
mutate(`RTlexdec_z` = scale(RTlexdec, center = TRUE, scale = TRUE))
english2['RTlexdec_z'] <- as.data.frame(scale(english2$RTlexdec))
4.4.2.4.1.1 Random Intercepts
mdl.glmm3 <- english2 %>%
glmer(AgeSubject ~ RTlexdec_z + (1|Word), data = ., family = "binomial")
summary(mdl.glmm3)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: AgeSubject ~ RTlexdec_z + (1 | Word)
## Data: .
##
## AIC BIC logLik -2*log(L) df.resid
## 3151.8 3171.1 -1572.9 3145.8 4565
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -26.3468 -0.3058 -0.0166 0.3893 4.0750
##
## Random effects:
## Groups Name Variance Std.Dev.
## Word (Intercept) 0 0
## Number of obs: 4568, groups: Word, 2197
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.07690 0.04480 1.716 0.0861 .
## RTlexdec_z 3.08341 0.09107 33.856 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## RTlexdec_z 0.025
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
4.4.2.4.1.2 Random Slopes
mdl.glmmSlope3 <- english2 %>%
glmer(AgeSubject ~ RTlexdec_z + (RTlexdec_z|Word), data = ., family = "binomial")
summary(mdl.glmmSlope3)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: AgeSubject ~ RTlexdec_z + (RTlexdec_z | Word)
## Data: .
##
## AIC BIC logLik -2*log(L) df.resid
## 3075.6 3107.7 -1532.8 3065.6 4563
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3927 -0.2133 -0.0024 0.2512 5.8055
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Word (Intercept) 0.8508 0.9224
## RTlexdec_z 1.9696 1.4034 1.00
## Number of obs: 4568, groups: Word, 2197
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.38012 0.07664 4.96 7.05e-07 ***
## RTlexdec_z 4.32050 0.26713 16.17 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## RTlexdec_z 0.646
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00335891 (tol = 0.002, component 1)
4.4.2.4.2 Model comparison
## Data: .
## Models:
## mdl.glmm3: AgeSubject ~ RTlexdec_z + (1 | Word)
## mdl.glmmSlope3: AgeSubject ~ RTlexdec_z + (RTlexdec_z | Word)
## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)
## mdl.glmm3 3 3151.8 3171.1 -1572.9 3145.8
## mdl.glmmSlope3 5 3075.6 3107.7 -1532.8 3065.6 80.259 2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
The model comparisons show that the model with both random intercepts and random slopes is improving the model fit. The Is.Singular
message tells us that there is a chance there is a complete separation in the model.
4.4.2.4.3 Gettings results
4.4.2.4.3.1 Model’s fit
print(tab_model(mdl.glmmSlope3, file = paste0("outputs/mdl.glmmSlope3.html")))
htmltools::includeHTML("outputs/mdl.glmmSlope3.html")
Age Subject | |||
---|---|---|---|
Predictors | Odds Ratios | CI | p |
(Intercept) | 1.46 | 1.26 – 1.70 | <0.001 |
RTlexdec z | 75.23 | 44.56 – 126.99 | <0.001 |
Random Effects | |||
σ2 | 3.29 | ||
τ00 Word | 0.85 | ||
τ11 Word.RTlexdec_z | 1.97 | ||
ρ01 Word | 1.00 | ||
ICC | 0.46 | ||
N Word | 2197 | ||
Observations | 4568 | ||
Marginal R2 / Conditional R2 | 0.753 / 0.867 |
4.4.2.4.3.2 Fixed effects
## (Intercept) RTlexdec_z
## 0.3801193 4.3205029
## (Intercept)
## 0.3801193
## RTlexdec_z
## 4.320503
4.4.2.4.3.3 Random effects
## (Intercept)
## ace 0.4429212637
## act 0.6115900993
## add 0.5148513960
## age 0.4998303024
## aid 0.3969975952
## aide 0.0298149457
## ail -0.5223248920
## aim 0.5420519930
## air 0.7025897634
## aisle 0.2888583972
## ale 0.3853232087
## angst 0.1531547853
## ant 0.5610006668
## ape 0.4962788323
## arc -0.4707015084
## arch 0.4512528389
## are 0.4198901328
## arm 0.9816125475
## art 0.5251614946
## ash 0.4281455397
## ask 0.6475872009
## ass 0.4322048232
## axe 0.4116260599
## babe 0.5196373616
## back 0.6270678266
## badge 0.4286905200
## bag 0.6929868460
## bail 0.1909596118
## bait 0.5556562438
## bale -0.5505704375
## ball 0.5016870267
## ban -0.0941223592
## band 0.4224229334
## bang 0.6481332676
## bank 0.5996475267
## bar 0.7043147769
## bard -0.6135752052
## barge -0.2315978510
## bark 0.6462121316
## barn 0.7065307175
## base 0.5814176531
## bash 0.3932383080
## bat 0.6945639688
## batch 0.5395463959
## bath 0.6015430074
## bay 0.5318171846
## beach 0.4634627256
## bead 0.1953244038
## beak -0.3684048394
## beam 0.3898833217
## bean 0.4136863882
## bear 0.9094956778
## beard 0.6457097003
## beast 0.4088095955
## beat 0.5358319249
## beau -0.0287634590
## beck -1.0401672566
## bed 0.5170928203
## bee 0.6800920701
## beech -0.4747123984
## beef 0.8824327201
## beep 0.5439011712
## beer 0.6804450006
## beet 0.2779529997
## beg 0.7154007065
## belch -0.0177078249
## bell 0.6218300941
## belt 0.4966436753
## bench 0.7026657475
## bend 0.6809424799
## berth 0.0267365037
## bet 0.7167968807
## bib 0.1835735923
## bid 0.7175521351
## bide -1.0696921302
## bile 0.1685029621
## bilge -0.9124773087
## bill 0.5302685540
## bin 0.0456044002
## bind -0.0913567686
## binge 0.2704045341
## birch 0.0357240783
## bird 0.5779126783
## bit 0.6674249010
## bitch 0.4885831627
## bite 0.7055495815
## blade 0.6104278444
## blame 0.5233630982
## blanch -0.4929583589
## blast 0.4803043073
## blaze 0.6144688025
## bleat 0.0183456161
## bleed 0.4649603651
## bleep -0.3797852982
## blend 0.5596330958
## bless 0.4862663439
## blight 0.1428873962
## blink 0.3883831213
## bliss 0.6738568960
## blitz 0.2492738579
## bloat 0.3462414401
## blob 0.2451566487
## block 0.5770305003
## bloke -0.6463286354
## blood 0.5343354434
## bloom 0.6432669970
## blot 0.4456271471
## blouse 0.2636920842
## blow 0.6192294225
## bluff 0.6172042368
## blur 0.3869336735
## blush 0.7131474304
## boar -0.1955958722
## board 0.5947657521
## boast 0.5430369452
## boat 0.7103581623
## bob -0.1959878583
## bog 0.1087750715
## boil 0.4990938952
## bolt 0.7183260398
## bomb 0.4947974370
## bond 0.5963739485
## bone 0.6994280481
## boo 0.4350288449
## book 0.4228348289
## boom 0.4175301020
## boon -0.3196660622
## boost 0.3884695283
## boot 0.5611917375
## booth 0.6558586105
## booze 0.4659052452
## bore 0.4517195072
## boss 0.5923835714
## bough -0.9627047005
## bounce 0.7144017667
## bound 0.4609616571
## bout -0.2460322292
## bowl 0.4681865740
## box 0.4100776287
## boy 0.6673379100
## brace 0.5098469818
## brad -0.9966896627
## brag 0.5237158832
## braid 0.3781290908
## brain 0.6250201213
## brake 0.7161658576
## bran -1.1514660807
## branch 0.4400871815
## brand 0.4640320808
## brass 0.6749200766
## brat 0.4126113388
## brawl 0.2885613311
## brawn -1.1862039707
## breach -0.2587840272
## bread 0.7076881101
## break 0.5471484226
## breast 0.4425448250
## breath 0.5219254049
## breed 0.5321428406
## breeze 0.6850056664
## brew 0.5745906890
## bribe 0.5794532261
## brick 0.4393668579
## bride 0.5935510820
## bridge 0.4231040292
## brig -1.1069673462
## brim 0.0011982951
## bring 0.6999609443
## brink 0.1458544124
## broach -0.8722497068
## broad 0.4467782091
## broil 0.5217749464
## bronze 0.6189044123
## brooch -0.1816354895
## brood -0.7094065232
## brook -0.2816186167
## broom 0.7107733646
## broth -0.8125147519
## brow 0.1906300586
## bruise 0.4493189892
## brunt -0.3376069307
## brush 0.4320060311
## brute 0.3523559613
## buck 0.2429907001
## bud 0.6724083757
## budge 0.3955515982
## buff 0.3494155734
## bug 0.7075605668
## build 0.6283170006
## bulb 0.5497611363
## bulge 0.4063718473
## bulk 0.7196745111
## bull 0.5760512511
## bum 0.4689530236
## bump 0.3909613508
## bun 0.3967498974
## bunch 0.6140159054
## bunk -0.1178040820
## burn 0.4995560188
## burr -0.1106972838
## burst 0.4596244774
## bus 0.6345575285
## bush 0.4950627199
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## spike 0.7037231010
## spill 0.7129656689
## spin 0.7074585336
## spine 0.4847710148
## spire 0.0386015569
## spit 0.4941619703
## spite 0.1699295065
## splash 0.5570397618
## spleen -0.5924357224
## splice -0.2288975348
## split 0.5597450844
## splurge -0.1002071716
## spoil 0.5540042891
## spoke 0.6879898977
## spoof -0.2481621072
## spool 0.7051260481
## spoon 0.4285327354
## sport 0.5359462208
## spot 0.5045540044
## spouse 0.4548230229
## spout 0.3838265433
## sprawl 0.3956958988
## spray 0.3960537089
## spread 0.4197436147
## spree -0.4502054718
## sprig -0.6583895101
## spring 0.5526199153
## sprite -0.2685975183
## sprout 0.4741292781
## spur 0.3973935043
## spurt -0.0935863650
## spy 0.5134927774
## squad 0.3943750187
## squall -0.0929776735
## square 0.4383059276
## squash 0.4087199054
## squat 0.1964756936
## squaw -0.3966431899
## squawk -0.1255408571
## squeak 0.4239746220
## squeal 0.3965000322
## squeeze 0.4607647912
## squint 0.4278958404
## squire 0.0547801972
## squirm 0.4329130394
## squirt 0.3989877044
## stab 0.4225167228
## stack 0.4600439723
## staff 0.6476384168
## stag 0.5762546632
## stage 0.5251203098
## stain 0.3952127950
## stair 0.4711615776
## stake 0.3193355830
## stalk 0.4418163619
## stall 0.6280899938
## stamp 0.4768688499
## stance 0.3389588618
## stanch 0.3895027918
## stand 0.5758526478
## star 0.5423871362
## starch 0.5124065660
## stare 0.4664708767
## start 0.4846445657
## starve 0.4304239944
## state 0.5004411746
## staunch -0.5213060833
## stave -0.2116612836
## stay 0.6791303022
## stead -0.0040413015
## steak 0.4115552010
## steal 0.6556128545
## steam 0.3936229975
## steed -0.1760420031
## steel 0.4481974911
## steer 0.3984256453
## stem 0.3978616568
## stench -0.1436106630
## step 0.7104275575
## stew 0.7174967837
## stick 0.5715583688
## still 0.6544575358
## stilt -0.3611379726
## sting 0.4031331292
## stink 0.4287687215
## stint 0.3658448282
## stir 0.7086564275
## stitch 0.0525604114
## stock 0.7129862604
## stole 0.6561674545
## stone 0.4235623353
## stool 0.7101379041
## stoop -0.1451800544
## stop 0.5593653529
## store 0.5495292426
## stork 0.4427599247
## storm 0.5486938183
## stout 0.3664389276
## stove 0.5072683556
## stow -0.1104065272
## strafe -0.1338401010
## strain 0.5334517063
## strand 0.3436894971
## strap 0.4053399203
## straw 0.6757182559
## stray 0.6253042857
## streak 0.4641142402
## stream 0.3919957669
## street 0.4549115789
## stress 0.6950819796
## stretch 0.4525948797
## stride 0.5375692887
## strife 0.1916126049
## strike 0.6930475038
## string 0.4672910181
## strip 0.6529683584
## stripe 0.5145241398
## strive 0.3911115206
## stroke 0.4601214524
## stroll 0.4017575164
## strut -0.0879243153
## stub 0.3321284066
## stud 0.5182169286
## stuff 0.5579753599
## stump 0.4865810288
## stunt 0.3841311442
## style 0.7205198432
## sub -0.8772349158
## suck 0.3978809934
## sue 0.2922644261
## suit 0.5202746510
## suite 0.4612154910
## sulk -0.0829006520
## sum 0.4335581218
## sun 0.4516291488
## sup 0.3869577672
## surf 0.4228254182
## surge 0.2705418903
## swamp 0.3979094428
## swan 0.3945166391
## swap 0.1203464608
## swarm 0.4193622586
## swath -0.3771428577
## sway 0.4166484453
## swear 0.5795812043
## sweat 0.5695988086
## sweep 0.4216950785
## swell 0.7025946811
## swerve 0.3887633670
## swig -0.0988098683
## swim 0.5513417407
## swine 0.4367197074
## swing 0.7124850174
## swipe 0.4091825994
## swirl 0.3907563649
## switch 0.4668208026
## swoop 0.0105260403
## sword 0.6694880366
## tab 0.4658618850
## tack 0.3218981187
## tact 0.5837614661
## tag 0.4557941818
## tail 0.4560424400
## taint 0.4095047606
## take 0.6635654933
## tale 0.5472058439
## talk 0.4485013805
## tamp 0.1762076582
## tan 0.4501934049
## tang -0.1065540195
## tank 0.3907565890
## tape 0.6212205963
## tar 0.5781918746
## tart 0.3963598478
## task 0.6962347909
## taste 0.6631508501
## taunt 0.3943852843
## tax 0.6593343514
## tea 0.6967651300
## teach 0.5567436962
## teak 0.3807209852
## team 0.6821384944
## tease 0.5827443523
## tech -1.0939461581
## tee 0.4504653904
## teens 0.3905369142
## tell 0.6148905912
## tempt 0.6237481836
## tend 0.3912217892
## tense 0.5547946494
## tent 0.6937415733
## test 0.5967120764
## text 0.6722533681
## thank 0.6453213730
## thaw 0.4180556718
## theft 0.4486371877
## theme 0.4573282644
## thief 0.4410376567
## thigh 0.6700206132
## thin 0.5324461070
## thing 0.4974501012
## think 0.7185078061
## thirst 0.7075244854
## thong 0.0025310604
## thorn 0.7198490460
## thought 0.5340539857
## thrash 0.3528474381
## thread 0.5971888874
## threat 0.4196847127
## thrift 0.4621267940
## thrill 0.4565570624
## thrive 0.4365313832
## throat 0.7141548729
## throne 0.1360092327
## throng -0.5221724183
## throw 0.4433842637
## thrush -0.2424476075
## thrust 0.3599236343
## thud 0.1541410654
## thug 0.3833580456
## thumb 0.7139320597
## thump 0.3851926259
## thwack -1.3807722719
## thwart -0.6171944862
## tick 0.4852781922
## tide 0.6453499809
## tie 0.7138583702
## tile 0.5966393299
## till 0.0861079784
## tilt 0.6608630329
## time 0.6761022182
## tin 0.3955739452
## tint 0.4728003411
## tip 0.6533711351
## tire 0.7159129524
## toad 0.6502701167
## toast 0.6152950186
## toe 0.4097036420
## toil 0.4168540867
## toll 0.3475586511
## tomb 0.7136529851
## tome 0.3595173898
## ton 0.3896617344
## tone 0.5778778005
## tongue 0.6567431004
## tool 0.7055573143
## toot -0.3420714116
## tooth 0.5524209503
## top 0.5716231720
## torch 0.4228207262
## torque 0.1759307693
## toss 0.6344630918
## tote -0.3430924751
## touch 0.7064746225
## tour 0.6226259100
## tout -0.0952850911
## town 0.6664988971
## toy 0.7114112372
## trace 0.6166577554
## track 0.6081945934
## tract 0.4171982298
## trade 0.6870366633
## trail 0.3982816413
## train 0.6791223254
## trait 0.3550182611
## tramp 0.3439133327
## trance 0.2328757478
## trap 0.5541822915
## trash 0.4524210664
## tray 0.1560241156
## tread 0.2184965593
## treat 0.5839225472
## tree 0.7128801062
## trench 0.4050634525
## trend 0.4414485586
## tribe 0.3534116365
## trick 0.4389068337
## trill -0.9924333132
## trip 0.5691022473
## tripe 0.2485523492
## troll -0.3077973519
## troop 0.1572383363
## trot -0.3346297175
## trough -1.0001073953
## trout 0.6050270714
## truce 0.1370396140
## truck 0.4612649955
## trump -0.1216554030
## trunk 0.6720856929
## trust 0.5416143084
## try 0.6339591947
## tryst -0.6936545860
## tub 0.6065161697
## tube 0.9710066137
## tuck 0.3572735638
## tug 0.6795214012
## tune 0.5625680203
## turf 0.2454477951
## turn 0.4251762005
## tusk 0.0658116943
## twain 0.0978503683
## tweed 0.4578676651
## twin 0.6639871295
## twinge -0.4412745484
## twist 0.5855022323
## twitch 0.1012613522
## type 0.4288318014
## urge 0.4256918944
## urn -0.3502132763
## use 0.7136931203
## vale -1.0271371555
## valve 0.3815424027
## vamp -0.4471003083
## van 0.3935456240
## vase 0.4220954210
## vault 0.5107748421
## veal 0.3529227751
## veer -0.6595118309
## veil 0.3988018346
## vein 0.4377503798
## vent 0.3511095377
## verb 0.4553964383
## verge 0.0579961970
## verse 0.4312977501
## verve -0.3482590258
## vest 0.1884937222
## vet -0.0828050253
## vex 0.3173577662
## vice 0.2735327069
## vie -0.6505831705
## view 0.4835578098
## vine 0.4084499752
## voice 0.6836048121
## volt 0.2403914702
## vote 0.4166767237
## vow 0.3341724827
## wad 0.3641875326
## wade 0.4046844035
## wag 0.4105905334
## wage 0.4241180925
## wail 0.3609623915
## waist 0.4136206644
## wait 0.5823737144
## waive 0.3929558755
## wake 0.4209682721
## walk 0.7077046833
## wall 0.5276454447
## waltz 0.6509983980
## wand 0.1503714846
## wane -0.1184865954
## want 0.5262338942
## war 0.6884318348
## ward -0.2024225128
## ware 0.2182219672
## warn 0.4744821828
## warp 0.3891875241
## wart 0.3426262731
## wash 0.4755088550
## wasp 0.4461385750
## waste 0.7027578728
## watch 0.5830571015
## watt 0.3337828516
## wave 0.4269790728
## wax 0.4372562106
## way 0.6728259728
## wealth 0.4153732039
## wear 0.4610994343
## weave 0.5523302490
## web 0.7070998702
## wed 0.6607343506
## wedge 0.4047926377
## weed 0.5291270392
## week 0.4565218502
## weep 0.4091887220
## weigh 0.4945272158
## weight 0.5197220282
## weld -0.2306306286
## well 0.7054074569
## welt -0.5614888197
## west -0.6699577498
## whack 0.3511707699
## wharf 0.4691446493
## wheat 0.5157589833
## wheel 0.3904584404
## whelp -1.0496900270
## whiff 0.0106696173
## while 0.5789656600
## whim 0.4059655880
## whine 0.3443370108
## whip 0.7116281818
## whirl 0.4091523982
## whit -0.3489260686
## whiz 0.5311302684
## whoop -0.2883259957
## whoosh 0.2112390970
## whore 0.4236323130
## whorl -0.7627530485
## wick 0.3886820590
## wield 0.1400763917
## wife 0.7119029586
## wig 0.4292142124
## will 0.7054877192
## wilt 0.3228393861
## win 0.4242101484
## wine 0.7005649904
## wing 0.7190845171
## wink 0.5698492285
## wipe 0.6966418582
## wire 0.7111327937
## wish 0.6627542683
## wisp -0.3559947047
## wit 0.4204796908
## witch 0.4439064670
## woe 0.4532896728
## wolf 0.6994288317
## womb 0.4044563243
## woo -0.7929897168
## wood 0.4279273221
## wool 0.3494362172
## word 0.5798947642
## work 0.6443923195
## world 0.6758082892
## worm 0.4401197825
## would 0.6254040988
## wow 0.3868415563
## wrack 0.3888945360
## wrap 0.5123883472
## wrath 0.3522556691
## wreak 0.2258550272
## wreath 0.3077379071
## wreck 0.5146626362
## wren -0.3500511922
## wrest 0.3548004346
## wretch 0.3960672498
## wring -1.0044820911
## wrist 0.6380822668
## writ -1.0976343576
## write 0.5198170323
## writhe 0.1387777447
## yacht -0.0140847626
## yak -1.3796354650
## yam 0.3766225683
## yang -1.3796752708
## yank -0.2650992783
## yard 0.4780938936
## yarn 0.4686981657
## yaw -0.6183874180
## yawl -0.6650962496
## yawn 0.4643977766
## yea 0.1520120392
## year 0.5082492774
## yearn 0.1105385909
## yeast 0.5000092140
## yell 0.4436131516
## yelp -0.2186835663
## yen -0.5178110963
## yes 0.7165871732
## yield 0.7090935202
## yoke 0.4853180111
## yolk 0.3441380481
## yore -0.4843829130
## youth 0.5823842698
## zeal 0.2621717479
## zest 0.2401278634
## zinc 0.0612578299
## zing -0.7560967377
## zip 0.5166070163
## zone 0.5840377042
## zoo 0.3840845368
## RTlexdec_z
## ace 4.416057
## act 4.672691
## add 4.525501
## age 4.502646
## aid 4.346184
## aide 3.787507
## ail 2.947415
## aim 4.566887
## air 4.811148
## aisle 4.181648
## ale 4.328421
## angst 3.975172
## ant 4.595718
## ape 4.497242
## arc 3.025961
## arch 4.428734
## are 4.381015
## arm 5.235687
## art 4.541188
## ash 4.393576
## ask 4.727461
## ass 4.399752
## axe 4.368441
## babe 4.532783
## back 4.696240
## badge 4.394405
## bag 4.796537
## bail 4.032692
## bait 4.587586
## bale 2.904439
## ball 4.505471
## ban 3.598934
## band 4.384869
## bang 4.728292
## bank 4.654520
## bar 4.813773
## bard 2.808576
## barge 3.389762
## bark 4.725369
## barn 4.817145
## base 4.626783
## bash 4.340464
## bat 4.798937
## batch 4.563075
## bath 4.657404
## bay 4.551314
## beach 4.447312
## bead 4.039334
## beak 3.181608
## beam 4.335359
## bean 4.371576
## bear 5.125960
## beard 4.724604
## beast 4.364156
## beat 4.557423
## beau 3.698379
## beck 2.159507
## bed 4.528911
## bee 4.776918
## beech 3.019858
## beef 5.084783
## beep 4.569700
## beer 4.777455
## beet 4.165055
## beg 4.830640
## belch 3.715201
## bell 4.688271
## belt 4.497797
## bench 4.811264
## bend 4.778212
## berth 3.782824
## bet 4.832765
## bib 4.021454
## bid 4.833914
## bide 2.114584
## bile 3.998524
## bilge 2.353790
## bill 4.548958
## bin 3.811531
## bind 3.603142
## binge 4.153570
## birch 3.796498
## bird 4.621450
## bit 4.757644
## bitch 4.485533
## bite 4.815652
## blade 4.670922
## blame 4.538451
## blanch 2.992097
## blast 4.472936
## blaze 4.677071
## bleat 3.770057
## bleed 4.449590
## bleep 3.164292
## blend 4.593637
## bless 4.482008
## blight 3.959550
## blink 4.333076
## bliss 4.767431
## blitz 4.121419
## bloat 4.268957
## blob 4.115154
## block 4.620107
## bloke 2.758741
## blood 4.555146
## bloom 4.720888
## blot 4.420174
## blouse 4.143356
## blow 4.684314
## bluff 4.681233
## blur 4.330871
## blush 4.827212
## boar 3.444540
## board 4.647092
## boast 4.568385
## boat 4.822968
## bob 3.443944
## bog 3.907647
## boil 4.501525
## bolt 4.835091
## bomb 4.494988
## bond 4.649539
## bone 4.806338
## boo 4.404049
## book 4.385495
## boom 4.377424
## boon 3.255765
## boost 4.333208
## boot 4.596008
## booth 4.740046
## booze 4.451028
## bore 4.429444
## boss 4.643467
## bough 2.277368
## bounce 4.829121
## bound 4.443506
## bout 3.367800
## bowl 4.454499
## box 4.366085
## boy 4.757512
## brace 4.517886
## brad 2.225659
## brag 4.538988
## braid 4.317475
## brain 4.693125
## brake 4.831805
## bran 1.990163
## branch 4.411745
## brand 4.448178
## brass 4.769048
## brat 4.369940
## brawl 4.181196
## brawn 1.937309
## breach 3.348398
## bread 4.818906
## break 4.574641
## breast 4.415485
## breath 4.536264
## breed 4.551810
## breeze 4.784394
## brew 4.616395
## bribe 4.623794
## brick 4.410649
## bride 4.645244
## bridge 4.385905
## brig 2.057869
## brim 3.743967
## bring 4.807149
## brink 3.964064
## broach 2.414997
## broad 4.421926
## broil 4.536035
## bronze 4.683819
## brooch 3.465781
## brood 2.662766
## brook 3.313655
## broom 4.823600
## broth 2.505885
## brow 4.032191
## bruise 4.425792
## brunt 3.228467
## brush 4.399450
## brute 4.278260
## buck 4.111859
## bud 4.765227
## budge 4.343983
## buff 4.273787
## bug 4.818711
## build 4.698141
## bulb 4.578616
## bulge 4.360447
## bulk 4.837143
## bull 4.618617
## bum 4.455665
## bump 4.336999
## bun 4.345807
## bunch 4.676381
## bunk 3.562902
## burn 4.502228
## burr 3.573715
## burst 4.441472
## bus 4.707636
## bush 4.495392
## bust 4.630564
## butt 4.463562
## buy 4.740171
## buzz 4.589003
## cab 4.547664
## cad 2.243888
## cage 4.711607
## cake 4.753922
## calf 4.544732
## call 4.792643
## cam 4.315245
## camp 4.487682
## can 4.662522
## cane 4.372128
## cant 3.958181
## cap 4.562253
## cape 4.444188
## car 4.803942
## card 4.502030
## care 4.503377
## cart 4.413225
## carve 4.514852
## case 4.407415
## cash 4.791186
## cask 3.599850
## cast 4.595988
## caste 3.507504
## cat 4.602479
## catch 4.820771
## cause 4.604294
## cave 4.672808
## cease 4.354421
## cell 4.489051
## cent 4.426511
## chafe 1.778225
## chain 4.361320
## chair 4.817435
## chaise 2.394051
## chalk 4.714641
## champ 4.604983
## chance 4.830290
## change 4.624056
## chant 4.443521
## chap 4.258714
## char 1.606686
## charge 4.681023
## charm 4.828719
## chart 4.754411
## chase 4.813592
## chat 4.551129
## cheat 4.574038
## check 4.768567
## cheek 4.430269
## cheer 4.816055
## cheese 4.646284
## chef 4.713085
## chess 4.521142
## chest 4.541384
## chew 4.766926
## chide 2.172477
## chief 4.633793
## child 4.690551
## chime 4.432358
## chin 4.345599
## chip 4.783381
## chive 2.944704
## choice 4.758304
## choir 4.613167
## choke 4.468353
## chomp 2.888236
## choose 4.660427
## chop 5.261176
## chord 4.115723
## chore 4.224932
## chow 3.092332
## chrome 4.134981
## chuck 2.570554
## chum 2.234799
## chump 3.496075
## chunk 4.349149
## church 4.760869
## churn 4.032689
## chute 3.240012
## cinch 3.164876
## cite 4.062945
## claim 4.408465
## clam 4.403215
## clamp 4.332014
## clan 3.591098
## clang 4.170412
## clap 4.983942
## clash 4.366331
## class 4.661239
## clause 3.177828
## claw 4.505331
## clay 4.726177
## cleat 1.975943
## clench 3.404912
## clerk 4.402336
## click 4.564909
## cliff 4.686290
## climb 4.785212
## clinch 2.911671
## cling 4.505972
## clip 5.267364
## cloak 4.424305
## clock 4.685513
## clod 3.105757
## clog 3.524132
## clot 4.324373
## cloth 4.429665
## cloud 4.504938
## clout 4.178408
## clove 3.132701
## clown 4.711313
## club 4.341261
## cluck 2.973925
## clump 3.326821
## clutch 4.448763
## coach 4.767284
## coal 4.811095
## coast 4.784198
## coat 4.433978
## coax 4.083510
## cock 4.283487
## cod 4.189087
## code 4.344738
## coil 4.364150
## coin 4.649844
## coke 4.503766
## colt 3.934655
## comb 4.666422
## come 4.591393
## cone 4.333093
## cook 4.674941
## coop 3.168819
## cop 4.505765
## cope 4.578630
## cord 4.714616
## core 4.518246
## cork 4.797262
## corn 4.635132
## corps 3.931809
## corpse 4.545662
## cost 4.695008
## cot 3.752628
## couch 4.745654
## cough 4.492131
## count 5.241723
## coup 3.121269
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## creek 4.379963
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## yea 3.973433
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## yell 4.417110
## yelp 3.409412
## yen 2.954283
## yes 4.832446
## yield 4.821044
## yoke 4.480565
## yolk 4.265757
## yore 3.005145
## youth 4.628253
## zeal 4.141043
## zest 4.107503
## zinc 3.835348
## zing 2.591726
## zip 4.528172
## zone 4.630769
## zoo 4.326536
4.4.2.4.4 Plotting
4.4.2.4.4.1 Normal
english2 <- english2 %>%
mutate(prob3 = predict(mdl.glmmSlope3, type = "response"))
english2 %>%
ggplot(aes(x = as.numeric(AgeSubject), y = prob3)) +
geom_point() +
geom_smooth(method = "glm",
method.args = list(family = "binomial"),
se = T) + theme_bw(base_size = 20)+
labs(y = "Probability", x = "")+
coord_cartesian(ylim = c(0,1))+
scale_x_discrete(limits = c("Young", "Old"))
We obtain the exact same plots, but the model estimations are different. Let’s use another type of predictions
4.4.2.4.4.2 z-scores
z_vals <- seq(-3, 3, 0.01)
n = nrow(english2)
dfPredNew <- data.frame(RTlexdec_z = z_vals)
### store the predicted probabilities for each value of RTlexdec_z
pp <- cbind(dfPredNew, prob = predict(mdl.glmmSlope3, newdata = dfPredNew, type = "response", re.form = NA))#re.form is used to cancel random effects
pp %>%
ggplot(aes(x = RTlexdec_z, y = prob)) +
geom_point() +
theme_bw(base_size = 20) +
labs(y = "Probability", x = "") +
coord_cartesian(ylim = c(-0.1, 1.1), expand = FALSE) +
scale_y_discrete(limits = c(0,1), labels = c("Young", "Old")) +
scale_x_continuous(breaks = c(-3, -2, -1, 0, 1, 2, 3))
## Warning in scale_y_discrete(limits = c(0, 1), labels = c("Young", "Old")): Continuous limits supplied to discrete scale.
## ℹ Did you mean `limits = factor(...)` or `scale_*_continuous()`?
We obtain the exact same plots, but the model estimations are different.