9.3 Correlation tests

Above, we did a correlation test on two predictors. What if we want to obtain a nice plot of all numeric predictors and add significance levels? We use the package corrplot

9.3.1 Correlation plots

9.3.1.1 Correlation plots 1

corr <- 
  dfPharV2 %>% 
  select(where(is.numeric)) %>% 
  cor() %>% 
  print()

##                  CPP      Energy        H1A1c       H1A2c        H1A3c
## CPP      1.000000000 -0.03399038  0.404706765 -0.26455286 -0.113482532
## Energy  -0.033990377  1.00000000 -0.186476670  0.09170318 -0.122377040
## H1A1c    0.404706765 -0.18647667  1.000000000  0.05465872  0.007167585
## H1A2c   -0.264552856  0.09170318  0.054658717  1.00000000 -0.233216979
## H1A3c   -0.113482532 -0.12237704  0.007167585 -0.23321698  1.000000000
## H1H2c    0.251810189 -0.44444137  0.648990000  0.11615684 -0.164917390
## H2H4c   -0.005458994  0.20371885 -0.220955156  0.04292950  0.210063534
## H2KH5Kc -0.336168212 -0.12504346 -0.431991841  0.51057160 -0.334656923
## H42Kc    0.019225753  0.19493845 -0.090631471 -0.59694938  0.514544301
## HNR05    0.666184301 -0.37052021  0.758327365 -0.06157287 -0.108056123
## HNR15    0.603409742 -0.67352331  0.433216471 -0.30096436 -0.075490785
## HNR25    0.504781686 -0.65091028  0.451043577 -0.06083878 -0.231125560
## HNR35    0.453677497 -0.63296467  0.470614004  0.05539693 -0.216734533
## SHR     -0.284829618  0.38017553 -0.395846797  0.25865972  0.209623680
## soe      0.386759609 -0.52487995  0.609437744 -0.11463910 -0.153217238
## Z1mnZ0   0.014248500  0.67114927  0.213674458  0.33815761  0.109502228
## Z2mnZ1   0.121821865 -0.28394211 -0.197144132 -0.84586885  0.307462932
## Z3mnZ2  -0.236018438  0.11604624 -0.014226757  0.84163102 -0.496911115
## Z4mnZ3  -0.009359468 -0.06257675  0.173172293  0.07552205  0.630948791
## F0Bark   0.417866035 -0.46400144  0.742753093 -0.06972759 -0.162186194
## A1mnA2  -0.462940266  0.18810560 -0.552669620  0.80194637 -0.198942082
## A1mnA3  -0.355892004  0.03344952 -0.664469548 -0.21090543  0.742533502
## A2mnA3   0.122501972 -0.13362699 -0.034489484 -0.83635261  0.728126945
##               H1H2c        H2H4c     H2KH5Kc       H42Kc       HNR05
## CPP      0.25181019 -0.005458994 -0.33616821  0.01922575  0.66618430
## Energy  -0.44444137  0.203718846 -0.12504346  0.19493845 -0.37052021
## H1A1c    0.64899000 -0.220955156 -0.43199184 -0.09063147  0.75832736
## H1A2c    0.11615684  0.042929498  0.51057160 -0.59694938 -0.06157287
## H1A3c   -0.16491739  0.210063534 -0.33465692  0.51454430 -0.10805612
## H1H2c    1.00000000 -0.713751116 -0.07796057 -0.41916885  0.77141984
## H2H4c   -0.71375112  1.000000000 -0.09596636  0.16166922 -0.36847378
## H2KH5Kc -0.07796057 -0.095966364  1.00000000 -0.68312931 -0.29753363
## H42Kc   -0.41916885  0.161669220 -0.68312931  1.00000000 -0.26285288
## HNR05    0.77141984 -0.368473783 -0.29753363 -0.26285288  1.00000000
## HNR15    0.65474601 -0.344119338 -0.11535020 -0.22732173  0.81480902
## HNR25    0.74616221 -0.451131758  0.10665010 -0.48042235  0.82316561
## HNR35    0.77808181 -0.471273417  0.15703813 -0.55230135  0.82336788
## SHR     -0.44306719  0.283034424  0.16958475  0.07533203 -0.50080260
## soe      0.84462374 -0.497528429 -0.12742022 -0.38269875  0.82808974
## Z1mnZ0  -0.25783681  0.314095793 -0.35109828  0.22859438 -0.10404198
## Z2mnZ1  -0.16754562  0.052215339 -0.43864642  0.65068250 -0.10884383
## Z3mnZ2   0.16165571 -0.150529963  0.71841244 -0.80426718 -0.01280049
## Z4mnZ3   0.10977975  0.003456879 -0.13027105  0.06309325  0.19394214
## F0Bark   0.89121654 -0.522808166 -0.23993155 -0.33335794  0.90374524
## A1mnA2  -0.29133499  0.168027465  0.68460673 -0.44401978 -0.50509144
## A1mnA3  -0.55795935  0.304989227  0.03925946  0.44524464 -0.58870128
## A2mnA3  -0.17484791  0.088160327 -0.54854966  0.71084573 -0.01751585
##               HNR15        HNR25       HNR35         SHR          soe
## CPP      0.60340974  0.504781686  0.45367750 -0.28482962  0.386759609
## Energy  -0.67352331 -0.650910279 -0.63296467  0.38017553 -0.524879953
## H1A1c    0.43321647  0.451043577  0.47061400 -0.39584680  0.609437744
## H1A2c   -0.30096436 -0.060838775  0.05539693  0.25865972 -0.114639103
## H1A3c   -0.07549078 -0.231125560 -0.21673453  0.20962368 -0.153217238
## H1H2c    0.65474601  0.746162213  0.77808181 -0.44306719  0.844623735
## H2H4c   -0.34411934 -0.451131758 -0.47127342  0.28303442 -0.497528429
## H2KH5Kc -0.11535020  0.106650103  0.15703813  0.16958475 -0.127420222
## H42Kc   -0.22732173 -0.480422351 -0.55230135  0.07533203 -0.382698752
## HNR05    0.81480902  0.823165610  0.82336788 -0.50080260  0.828089735
## HNR15    1.00000000  0.938770768  0.88727082 -0.55580661  0.792886846
## HNR25    0.93877077  1.000000000  0.98644454 -0.52810263  0.837725385
## HNR35    0.88727082  0.986444536  1.00000000 -0.49891921  0.839675263
## SHR     -0.55580661 -0.528102632 -0.49891921  1.00000000 -0.555384532
## soe      0.79288685  0.837725385  0.83967526 -0.55538453  1.000000000
## Z1mnZ0  -0.59593537 -0.589202134 -0.53287118  0.35389648 -0.403168468
## Z2mnZ1   0.28433812  0.009867765 -0.11639529 -0.18153788 -0.004677426
## Z3mnZ2  -0.20572721  0.109264859  0.21831675  0.13689371  0.007849427
## Z4mnZ3   0.04324078  0.035922107  0.11146279  0.08718854  0.117966357
## F0Bark   0.76082881  0.812555958  0.82810219 -0.58077659  0.934247247
## A1mnA2  -0.51038750 -0.320632658 -0.23532567  0.45272098 -0.460304226
## A1mnA3  -0.34659555 -0.474847635 -0.47720189  0.42180815 -0.522721261
## A2mnA3   0.16958474 -0.087411661 -0.16123104 -0.06414896 -0.005568759
##              Z1mnZ0       Z2mnZ1       Z3mnZ2       Z4mnZ3      F0Bark
## CPP      0.01424850  0.121821865 -0.236018438 -0.009359468  0.41786604
## Energy   0.67114927 -0.283942110  0.116046236 -0.062576748 -0.46400144
## H1A1c    0.21367446 -0.197144132 -0.014226757  0.173172293  0.74275309
## H1A2c    0.33815761 -0.845868849  0.841631017  0.075522047 -0.06972759
## H1A3c    0.10950223  0.307462932 -0.496911115  0.630948791 -0.16218619
## H1H2c   -0.25783681 -0.167545617  0.161655712  0.109779752  0.89121654
## H2H4c    0.31409579  0.052215339 -0.150529963  0.003456879 -0.52280817
## H2KH5Kc -0.35109828 -0.438646418  0.718412444 -0.130271054 -0.23993155
## H42Kc    0.22859438  0.650682503 -0.804267177  0.063093254 -0.33335794
## HNR05   -0.10404198 -0.108843828 -0.012800492  0.193942142  0.90374524
## HNR15   -0.59593537  0.284338125 -0.205727207  0.043240778  0.76082881
## HNR25   -0.58920213  0.009867765  0.109264859  0.035922107  0.81255596
## HNR35   -0.53287118 -0.116395288  0.218316751  0.111462787  0.82810219
## SHR      0.35389648 -0.181537883  0.136893713  0.087188543 -0.58077659
## soe     -0.40316847 -0.004677426  0.007849427  0.117966357  0.93424725
## Z1mnZ0   1.00000000 -0.479471463  0.132402681  0.143899368 -0.25634372
## Z2mnZ1  -0.47947146  1.000000000 -0.901393170 -0.176529973 -0.08020731
## Z3mnZ2   0.13240268 -0.901393170  1.000000000 -0.050618065  0.01898548
## Z4mnZ3   0.14389937 -0.176529973 -0.050618065  1.000000000  0.15981826
## F0Bark  -0.25634372 -0.080207311  0.018985484  0.159818261  1.00000000
## A1mnA2   0.15440193 -0.588053094  0.710977937 -0.040573920 -0.50258069
## A1mnA3  -0.06129172  0.361831277 -0.361830045  0.355533137 -0.61872264
## A2mnA3  -0.17662983  0.769563482 -0.873375083  0.302455298 -0.04228227
##              A1mnA2      A1mnA3       A2mnA3
## CPP     -0.46294027 -0.35589200  0.122501972
## Energy   0.18810560  0.03344952 -0.133626988
## H1A1c   -0.55266962 -0.66446955 -0.034489484
## H1A2c    0.80194637 -0.21090543 -0.836352608
## H1A3c   -0.19894208  0.74253350  0.728126945
## H1H2c   -0.29133499 -0.55795935 -0.174847909
## H2H4c    0.16802747  0.30498923  0.088160327
## H2KH5Kc  0.68460673  0.03925946 -0.548549664
## H42Kc   -0.44401978  0.44524464  0.710845732
## HNR05   -0.50509144 -0.58870128 -0.017515845
## HNR15   -0.51038750 -0.34659555  0.169584736
## HNR25   -0.32063266 -0.47484763 -0.087411661
## HNR35   -0.23532567 -0.47720189 -0.161231042
## SHR      0.45272098  0.42180815 -0.064148964
## soe     -0.46030423 -0.52272126 -0.005568759
## Z1mnZ0   0.15440193 -0.06129172 -0.176629833
## Z2mnZ1  -0.58805309  0.36183128  0.769563482
## Z3mnZ2   0.71097794 -0.36183005 -0.873375083
## Z4mnZ3  -0.04057392  0.35553314  0.302455298
## F0Bark  -0.50258069 -0.61872264 -0.042282270
## A1mnA2   1.00000000  0.22151418 -0.677425247
## A1mnA3   0.22151418  1.00000000  0.567258129
## A2mnA3  -0.67742525  0.56725813  1.000000000

print(corr)

##                  CPP      Energy        H1A1c       H1A2c        H1A3c
## CPP      1.000000000 -0.03399038  0.404706765 -0.26455286 -0.113482532
## Energy  -0.033990377  1.00000000 -0.186476670  0.09170318 -0.122377040
## H1A1c    0.404706765 -0.18647667  1.000000000  0.05465872  0.007167585
## H1A2c   -0.264552856  0.09170318  0.054658717  1.00000000 -0.233216979
## H1A3c   -0.113482532 -0.12237704  0.007167585 -0.23321698  1.000000000
## H1H2c    0.251810189 -0.44444137  0.648990000  0.11615684 -0.164917390
## H2H4c   -0.005458994  0.20371885 -0.220955156  0.04292950  0.210063534
## H2KH5Kc -0.336168212 -0.12504346 -0.431991841  0.51057160 -0.334656923
## H42Kc    0.019225753  0.19493845 -0.090631471 -0.59694938  0.514544301
## HNR05    0.666184301 -0.37052021  0.758327365 -0.06157287 -0.108056123
## HNR15    0.603409742 -0.67352331  0.433216471 -0.30096436 -0.075490785
## HNR25    0.504781686 -0.65091028  0.451043577 -0.06083878 -0.231125560
## HNR35    0.453677497 -0.63296467  0.470614004  0.05539693 -0.216734533
## SHR     -0.284829618  0.38017553 -0.395846797  0.25865972  0.209623680
## soe      0.386759609 -0.52487995  0.609437744 -0.11463910 -0.153217238
## Z1mnZ0   0.014248500  0.67114927  0.213674458  0.33815761  0.109502228
## Z2mnZ1   0.121821865 -0.28394211 -0.197144132 -0.84586885  0.307462932
## Z3mnZ2  -0.236018438  0.11604624 -0.014226757  0.84163102 -0.496911115
## Z4mnZ3  -0.009359468 -0.06257675  0.173172293  0.07552205  0.630948791
## F0Bark   0.417866035 -0.46400144  0.742753093 -0.06972759 -0.162186194
## A1mnA2  -0.462940266  0.18810560 -0.552669620  0.80194637 -0.198942082
## A1mnA3  -0.355892004  0.03344952 -0.664469548 -0.21090543  0.742533502
## A2mnA3   0.122501972 -0.13362699 -0.034489484 -0.83635261  0.728126945
##               H1H2c        H2H4c     H2KH5Kc       H42Kc       HNR05
## CPP      0.25181019 -0.005458994 -0.33616821  0.01922575  0.66618430
## Energy  -0.44444137  0.203718846 -0.12504346  0.19493845 -0.37052021
## H1A1c    0.64899000 -0.220955156 -0.43199184 -0.09063147  0.75832736
## H1A2c    0.11615684  0.042929498  0.51057160 -0.59694938 -0.06157287
## H1A3c   -0.16491739  0.210063534 -0.33465692  0.51454430 -0.10805612
## H1H2c    1.00000000 -0.713751116 -0.07796057 -0.41916885  0.77141984
## H2H4c   -0.71375112  1.000000000 -0.09596636  0.16166922 -0.36847378
## H2KH5Kc -0.07796057 -0.095966364  1.00000000 -0.68312931 -0.29753363
## H42Kc   -0.41916885  0.161669220 -0.68312931  1.00000000 -0.26285288
## HNR05    0.77141984 -0.368473783 -0.29753363 -0.26285288  1.00000000
## HNR15    0.65474601 -0.344119338 -0.11535020 -0.22732173  0.81480902
## HNR25    0.74616221 -0.451131758  0.10665010 -0.48042235  0.82316561
## HNR35    0.77808181 -0.471273417  0.15703813 -0.55230135  0.82336788
## SHR     -0.44306719  0.283034424  0.16958475  0.07533203 -0.50080260
## soe      0.84462374 -0.497528429 -0.12742022 -0.38269875  0.82808974
## Z1mnZ0  -0.25783681  0.314095793 -0.35109828  0.22859438 -0.10404198
## Z2mnZ1  -0.16754562  0.052215339 -0.43864642  0.65068250 -0.10884383
## Z3mnZ2   0.16165571 -0.150529963  0.71841244 -0.80426718 -0.01280049
## Z4mnZ3   0.10977975  0.003456879 -0.13027105  0.06309325  0.19394214
## F0Bark   0.89121654 -0.522808166 -0.23993155 -0.33335794  0.90374524
## A1mnA2  -0.29133499  0.168027465  0.68460673 -0.44401978 -0.50509144
## A1mnA3  -0.55795935  0.304989227  0.03925946  0.44524464 -0.58870128
## A2mnA3  -0.17484791  0.088160327 -0.54854966  0.71084573 -0.01751585
##               HNR15        HNR25       HNR35         SHR          soe
## CPP      0.60340974  0.504781686  0.45367750 -0.28482962  0.386759609
## Energy  -0.67352331 -0.650910279 -0.63296467  0.38017553 -0.524879953
## H1A1c    0.43321647  0.451043577  0.47061400 -0.39584680  0.609437744
## H1A2c   -0.30096436 -0.060838775  0.05539693  0.25865972 -0.114639103
## H1A3c   -0.07549078 -0.231125560 -0.21673453  0.20962368 -0.153217238
## H1H2c    0.65474601  0.746162213  0.77808181 -0.44306719  0.844623735
## H2H4c   -0.34411934 -0.451131758 -0.47127342  0.28303442 -0.497528429
## H2KH5Kc -0.11535020  0.106650103  0.15703813  0.16958475 -0.127420222
## H42Kc   -0.22732173 -0.480422351 -0.55230135  0.07533203 -0.382698752
## HNR05    0.81480902  0.823165610  0.82336788 -0.50080260  0.828089735
## HNR15    1.00000000  0.938770768  0.88727082 -0.55580661  0.792886846
## HNR25    0.93877077  1.000000000  0.98644454 -0.52810263  0.837725385
## HNR35    0.88727082  0.986444536  1.00000000 -0.49891921  0.839675263
## SHR     -0.55580661 -0.528102632 -0.49891921  1.00000000 -0.555384532
## soe      0.79288685  0.837725385  0.83967526 -0.55538453  1.000000000
## Z1mnZ0  -0.59593537 -0.589202134 -0.53287118  0.35389648 -0.403168468
## Z2mnZ1   0.28433812  0.009867765 -0.11639529 -0.18153788 -0.004677426
## Z3mnZ2  -0.20572721  0.109264859  0.21831675  0.13689371  0.007849427
## Z4mnZ3   0.04324078  0.035922107  0.11146279  0.08718854  0.117966357
## F0Bark   0.76082881  0.812555958  0.82810219 -0.58077659  0.934247247
## A1mnA2  -0.51038750 -0.320632658 -0.23532567  0.45272098 -0.460304226
## A1mnA3  -0.34659555 -0.474847635 -0.47720189  0.42180815 -0.522721261
## A2mnA3   0.16958474 -0.087411661 -0.16123104 -0.06414896 -0.005568759
##              Z1mnZ0       Z2mnZ1       Z3mnZ2       Z4mnZ3      F0Bark
## CPP      0.01424850  0.121821865 -0.236018438 -0.009359468  0.41786604
## Energy   0.67114927 -0.283942110  0.116046236 -0.062576748 -0.46400144
## H1A1c    0.21367446 -0.197144132 -0.014226757  0.173172293  0.74275309
## H1A2c    0.33815761 -0.845868849  0.841631017  0.075522047 -0.06972759
## H1A3c    0.10950223  0.307462932 -0.496911115  0.630948791 -0.16218619
## H1H2c   -0.25783681 -0.167545617  0.161655712  0.109779752  0.89121654
## H2H4c    0.31409579  0.052215339 -0.150529963  0.003456879 -0.52280817
## H2KH5Kc -0.35109828 -0.438646418  0.718412444 -0.130271054 -0.23993155
## H42Kc    0.22859438  0.650682503 -0.804267177  0.063093254 -0.33335794
## HNR05   -0.10404198 -0.108843828 -0.012800492  0.193942142  0.90374524
## HNR15   -0.59593537  0.284338125 -0.205727207  0.043240778  0.76082881
## HNR25   -0.58920213  0.009867765  0.109264859  0.035922107  0.81255596
## HNR35   -0.53287118 -0.116395288  0.218316751  0.111462787  0.82810219
## SHR      0.35389648 -0.181537883  0.136893713  0.087188543 -0.58077659
## soe     -0.40316847 -0.004677426  0.007849427  0.117966357  0.93424725
## Z1mnZ0   1.00000000 -0.479471463  0.132402681  0.143899368 -0.25634372
## Z2mnZ1  -0.47947146  1.000000000 -0.901393170 -0.176529973 -0.08020731
## Z3mnZ2   0.13240268 -0.901393170  1.000000000 -0.050618065  0.01898548
## Z4mnZ3   0.14389937 -0.176529973 -0.050618065  1.000000000  0.15981826
## F0Bark  -0.25634372 -0.080207311  0.018985484  0.159818261  1.00000000
## A1mnA2   0.15440193 -0.588053094  0.710977937 -0.040573920 -0.50258069
## A1mnA3  -0.06129172  0.361831277 -0.361830045  0.355533137 -0.61872264
## A2mnA3  -0.17662983  0.769563482 -0.873375083  0.302455298 -0.04228227
##              A1mnA2      A1mnA3       A2mnA3
## CPP     -0.46294027 -0.35589200  0.122501972
## Energy   0.18810560  0.03344952 -0.133626988
## H1A1c   -0.55266962 -0.66446955 -0.034489484
## H1A2c    0.80194637 -0.21090543 -0.836352608
## H1A3c   -0.19894208  0.74253350  0.728126945
## H1H2c   -0.29133499 -0.55795935 -0.174847909
## H2H4c    0.16802747  0.30498923  0.088160327
## H2KH5Kc  0.68460673  0.03925946 -0.548549664
## H42Kc   -0.44401978  0.44524464  0.710845732
## HNR05   -0.50509144 -0.58870128 -0.017515845
## HNR15   -0.51038750 -0.34659555  0.169584736
## HNR25   -0.32063266 -0.47484763 -0.087411661
## HNR35   -0.23532567 -0.47720189 -0.161231042
## SHR      0.45272098  0.42180815 -0.064148964
## soe     -0.46030423 -0.52272126 -0.005568759
## Z1mnZ0   0.15440193 -0.06129172 -0.176629833
## Z2mnZ1  -0.58805309  0.36183128  0.769563482
## Z3mnZ2   0.71097794 -0.36183005 -0.873375083
## Z4mnZ3  -0.04057392  0.35553314  0.302455298
## F0Bark  -0.50258069 -0.61872264 -0.042282270
## A1mnA2   1.00000000  0.22151418 -0.677425247
## A1mnA3   0.22151418  1.00000000  0.567258129
## A2mnA3  -0.67742525  0.56725813  1.000000000

corrplot(corr, method = 'ellipse', type = 'upper')

9.3.1.2 Correlation plots 2

Let’s first compute the correlations between all numeric variables and plot these with the p values

### correlation using "corrplot"
### based on the function `rcorr' from the `Hmisc` package
### Need to change dataframe into a matrix
corr <- 
  dfPharV2 %>% 
  select(where(is.numeric)) %>% 
  data.matrix(dfPharV2) %>% 
  rcorr(type = "pearson")
print(corr)

##           CPP Energy H1A1c H1A2c H1A3c H1H2c H2H4c H2KH5Kc H42Kc HNR05 HNR15
## CPP      1.00  -0.03  0.40 -0.26 -0.11  0.25 -0.01   -0.34  0.02  0.67  0.60
## Energy  -0.03   1.00 -0.19  0.09 -0.12 -0.44  0.20   -0.13  0.19 -0.37 -0.67
## H1A1c    0.40  -0.19  1.00  0.05  0.01  0.65 -0.22   -0.43 -0.09  0.76  0.43
## H1A2c   -0.26   0.09  0.05  1.00 -0.23  0.12  0.04    0.51 -0.60 -0.06 -0.30
## H1A3c   -0.11  -0.12  0.01 -0.23  1.00 -0.16  0.21   -0.33  0.51 -0.11 -0.08
## H1H2c    0.25  -0.44  0.65  0.12 -0.16  1.00 -0.71   -0.08 -0.42  0.77  0.65
## H2H4c   -0.01   0.20 -0.22  0.04  0.21 -0.71  1.00   -0.10  0.16 -0.37 -0.34
## H2KH5Kc -0.34  -0.13 -0.43  0.51 -0.33 -0.08 -0.10    1.00 -0.68 -0.30 -0.12
## H42Kc    0.02   0.19 -0.09 -0.60  0.51 -0.42  0.16   -0.68  1.00 -0.26 -0.23
## HNR05    0.67  -0.37  0.76 -0.06 -0.11  0.77 -0.37   -0.30 -0.26  1.00  0.81
## HNR15    0.60  -0.67  0.43 -0.30 -0.08  0.65 -0.34   -0.12 -0.23  0.81  1.00
## HNR25    0.50  -0.65  0.45 -0.06 -0.23  0.75 -0.45    0.11 -0.48  0.82  0.94
## HNR35    0.45  -0.63  0.47  0.06 -0.22  0.78 -0.47    0.16 -0.55  0.82  0.89
## SHR     -0.28   0.38 -0.40  0.26  0.21 -0.44  0.28    0.17  0.08 -0.50 -0.56
## soe      0.39  -0.52  0.61 -0.11 -0.15  0.84 -0.50   -0.13 -0.38  0.83  0.79
## Z1mnZ0   0.01   0.67  0.21  0.34  0.11 -0.26  0.31   -0.35  0.23 -0.10 -0.60
## Z2mnZ1   0.12  -0.28 -0.20 -0.85  0.31 -0.17  0.05   -0.44  0.65 -0.11  0.28
## Z3mnZ2  -0.24   0.12 -0.01  0.84 -0.50  0.16 -0.15    0.72 -0.80 -0.01 -0.21
## Z4mnZ3  -0.01  -0.06  0.17  0.08  0.63  0.11  0.00   -0.13  0.06  0.19  0.04
## F0Bark   0.42  -0.46  0.74 -0.07 -0.16  0.89 -0.52   -0.24 -0.33  0.90  0.76
## A1mnA2  -0.46   0.19 -0.55  0.80 -0.20 -0.29  0.17    0.68 -0.44 -0.51 -0.51
## A1mnA3  -0.36   0.03 -0.66 -0.21  0.74 -0.56  0.30    0.04  0.45 -0.59 -0.35
## A2mnA3   0.12  -0.13 -0.03 -0.84  0.73 -0.17  0.09   -0.55  0.71 -0.02  0.17
##         HNR25 HNR35   SHR   soe Z1mnZ0 Z2mnZ1 Z3mnZ2 Z4mnZ3 F0Bark A1mnA2
## CPP      0.50  0.45 -0.28  0.39   0.01   0.12  -0.24  -0.01   0.42  -0.46
## Energy  -0.65 -0.63  0.38 -0.52   0.67  -0.28   0.12  -0.06  -0.46   0.19
## H1A1c    0.45  0.47 -0.40  0.61   0.21  -0.20  -0.01   0.17   0.74  -0.55
## H1A2c   -0.06  0.06  0.26 -0.11   0.34  -0.85   0.84   0.08  -0.07   0.80
## H1A3c   -0.23 -0.22  0.21 -0.15   0.11   0.31  -0.50   0.63  -0.16  -0.20
## H1H2c    0.75  0.78 -0.44  0.84  -0.26  -0.17   0.16   0.11   0.89  -0.29
## H2H4c   -0.45 -0.47  0.28 -0.50   0.31   0.05  -0.15   0.00  -0.52   0.17
## H2KH5Kc  0.11  0.16  0.17 -0.13  -0.35  -0.44   0.72  -0.13  -0.24   0.68
## H42Kc   -0.48 -0.55  0.08 -0.38   0.23   0.65  -0.80   0.06  -0.33  -0.44
## HNR05    0.82  0.82 -0.50  0.83  -0.10  -0.11  -0.01   0.19   0.90  -0.51
## HNR15    0.94  0.89 -0.56  0.79  -0.60   0.28  -0.21   0.04   0.76  -0.51
## HNR25    1.00  0.99 -0.53  0.84  -0.59   0.01   0.11   0.04   0.81  -0.32
## HNR35    0.99  1.00 -0.50  0.84  -0.53  -0.12   0.22   0.11   0.83  -0.24
## SHR     -0.53 -0.50  1.00 -0.56   0.35  -0.18   0.14   0.09  -0.58   0.45
## soe      0.84  0.84 -0.56  1.00  -0.40   0.00   0.01   0.12   0.93  -0.46
## Z1mnZ0  -0.59 -0.53  0.35 -0.40   1.00  -0.48   0.13   0.14  -0.26   0.15
## Z2mnZ1   0.01 -0.12 -0.18  0.00  -0.48   1.00  -0.90  -0.18  -0.08  -0.59
## Z3mnZ2   0.11  0.22  0.14  0.01   0.13  -0.90   1.00  -0.05   0.02   0.71
## Z4mnZ3   0.04  0.11  0.09  0.12   0.14  -0.18  -0.05   1.00   0.16  -0.04
## F0Bark   0.81  0.83 -0.58  0.93  -0.26  -0.08   0.02   0.16   1.00  -0.50
## A1mnA2  -0.32 -0.24  0.45 -0.46   0.15  -0.59   0.71  -0.04  -0.50   1.00
## A1mnA3  -0.47 -0.48  0.42 -0.52  -0.06   0.36  -0.36   0.36  -0.62   0.22
## A2mnA3  -0.09 -0.16 -0.06 -0.01  -0.18   0.77  -0.87   0.30  -0.04  -0.68
##         A1mnA3 A2mnA3
## CPP      -0.36   0.12
## Energy    0.03  -0.13
## H1A1c    -0.66  -0.03
## H1A2c    -0.21  -0.84
## H1A3c     0.74   0.73
## H1H2c    -0.56  -0.17
## H2H4c     0.30   0.09
## H2KH5Kc   0.04  -0.55
## H42Kc     0.45   0.71
## HNR05    -0.59  -0.02
## HNR15    -0.35   0.17
## HNR25    -0.47  -0.09
## HNR35    -0.48  -0.16
## SHR       0.42  -0.06
## soe      -0.52  -0.01
## Z1mnZ0   -0.06  -0.18
## Z2mnZ1    0.36   0.77
## Z3mnZ2   -0.36  -0.87
## Z4mnZ3    0.36   0.30
## F0Bark   -0.62  -0.04
## A1mnA2    0.22  -0.68
## A1mnA3    1.00   0.57
## A2mnA3    0.57   1.00
## 
## n= 402 
## 
## 
## P
##         CPP    Energy H1A1c  H1A2c  H1A3c  H1H2c  H2H4c  H2KH5Kc H42Kc  HNR05 
## CPP            0.4968 0.0000 0.0000 0.0229 0.0000 0.9131 0.0000  0.7007 0.0000
## Energy  0.4968        0.0002 0.0662 0.0141 0.0000 0.0000 0.0121  0.0000 0.0000
## H1A1c   0.0000 0.0002        0.2743 0.8861 0.0000 0.0000 0.0000  0.0695 0.0000
## H1A2c   0.0000 0.0662 0.2743        0.0000 0.0198 0.3906 0.0000  0.0000 0.2180
## H1A3c   0.0229 0.0141 0.8861 0.0000        0.0009 0.0000 0.0000  0.0000 0.0303
## H1H2c   0.0000 0.0000 0.0000 0.0198 0.0009        0.0000 0.1186  0.0000 0.0000
## H2H4c   0.9131 0.0000 0.0000 0.3906 0.0000 0.0000        0.0545  0.0011 0.0000
## H2KH5Kc 0.0000 0.0121 0.0000 0.0000 0.0000 0.1186 0.0545         0.0000 0.0000
## H42Kc   0.7007 0.0000 0.0695 0.0000 0.0000 0.0000 0.0011 0.0000         0.0000
## HNR05   0.0000 0.0000 0.0000 0.2180 0.0303 0.0000 0.0000 0.0000  0.0000       
## HNR15   0.0000 0.0000 0.0000 0.0000 0.1308 0.0000 0.0000 0.0207  0.0000 0.0000
## HNR25   0.0000 0.0000 0.0000 0.2235 0.0000 0.0000 0.0000 0.0325  0.0000 0.0000
## HNR35   0.0000 0.0000 0.0000 0.2678 0.0000 0.0000 0.0000 0.0016  0.0000 0.0000
## SHR     0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006  0.1316 0.0000
## soe     0.0000 0.0000 0.0000 0.0215 0.0021 0.0000 0.0000 0.0106  0.0000 0.0000
## Z1mnZ0  0.7758 0.0000 0.0000 0.0000 0.0281 0.0000 0.0000 0.0000  0.0000 0.0371
## Z2mnZ1  0.0145 0.0000 0.0000 0.0000 0.0000 0.0007 0.2963 0.0000  0.0000 0.0291
## Z3mnZ2  0.0000 0.0199 0.7761 0.0000 0.0000 0.0011 0.0025 0.0000  0.0000 0.7981
## Z4mnZ3  0.8516 0.2106 0.0005 0.1306 0.0000 0.0277 0.9449 0.0089  0.2068 0.0000
## F0Bark  0.0000 0.0000 0.0000 0.1629 0.0011 0.0000 0.0000 0.0000  0.0000 0.0000
## A1mnA2  0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0007 0.0000  0.0000 0.0000
## A1mnA3  0.0000 0.5036 0.0000 0.0000 0.0000 0.0000 0.0000 0.4325  0.0000 0.0000
## A2mnA3  0.0140 0.0073 0.4905 0.0000 0.0000 0.0004 0.0775 0.0000  0.0000 0.7262
##         HNR15  HNR25  HNR35  SHR    soe    Z1mnZ0 Z2mnZ1 Z3mnZ2 Z4mnZ3 F0Bark
## CPP     0.0000 0.0000 0.0000 0.0000 0.0000 0.7758 0.0145 0.0000 0.8516 0.0000
## Energy  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0199 0.2106 0.0000
## H1A1c   0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7761 0.0005 0.0000
## H1A2c   0.0000 0.2235 0.2678 0.0000 0.0215 0.0000 0.0000 0.0000 0.1306 0.1629
## H1A3c   0.1308 0.0000 0.0000 0.0000 0.0021 0.0281 0.0000 0.0000 0.0000 0.0011
## H1H2c   0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0011 0.0277 0.0000
## H2H4c   0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2963 0.0025 0.9449 0.0000
## H2KH5Kc 0.0207 0.0325 0.0016 0.0006 0.0106 0.0000 0.0000 0.0000 0.0089 0.0000
## H42Kc   0.0000 0.0000 0.0000 0.1316 0.0000 0.0000 0.0000 0.0000 0.2068 0.0000
## HNR05   0.0000 0.0000 0.0000 0.0000 0.0000 0.0371 0.0291 0.7981 0.0000 0.0000
## HNR15          0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3872 0.0000
## HNR25   0.0000        0.0000 0.0000 0.0000 0.0000 0.8436 0.0285 0.4726 0.0000
## HNR35   0.0000 0.0000        0.0000 0.0000 0.0000 0.0196 0.0000 0.0254 0.0000
## SHR     0.0000 0.0000 0.0000        0.0000 0.0000 0.0003 0.0060 0.0808 0.0000
## soe     0.0000 0.0000 0.0000 0.0000        0.0000 0.9255 0.8753 0.0180 0.0000
## Z1mnZ0  0.0000 0.0000 0.0000 0.0000 0.0000        0.0000 0.0079 0.0038 0.0000
## Z2mnZ1  0.0000 0.8436 0.0196 0.0003 0.9255 0.0000        0.0000 0.0004 0.1083
## Z3mnZ2  0.0000 0.0285 0.0000 0.0060 0.8753 0.0079 0.0000        0.3114 0.7043
## Z4mnZ3  0.3872 0.4726 0.0254 0.0808 0.0180 0.0038 0.0004 0.3114        0.0013
## F0Bark  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1083 0.7043 0.0013       
## A1mnA2  0.0000 0.0000 0.0000 0.0000 0.0000 0.0019 0.0000 0.0000 0.4172 0.0000
## A1mnA3  0.0000 0.0000 0.0000 0.0000 0.0000 0.2201 0.0000 0.0000 0.0000 0.0000
## A2mnA3  0.0006 0.0800 0.0012 0.1993 0.9114 0.0004 0.0000 0.0000 0.0000 0.3978
##         A1mnA2 A1mnA3 A2mnA3
## CPP     0.0000 0.0000 0.0140
## Energy  0.0001 0.5036 0.0073
## H1A1c   0.0000 0.0000 0.4905
## H1A2c   0.0000 0.0000 0.0000
## H1A3c   0.0000 0.0000 0.0000
## H1H2c   0.0000 0.0000 0.0004
## H2H4c   0.0007 0.0000 0.0775
## H2KH5Kc 0.0000 0.4325 0.0000
## H42Kc   0.0000 0.0000 0.0000
## HNR05   0.0000 0.0000 0.7262
## HNR15   0.0000 0.0000 0.0006
## HNR25   0.0000 0.0000 0.0800
## HNR35   0.0000 0.0000 0.0012
## SHR     0.0000 0.0000 0.1993
## soe     0.0000 0.0000 0.9114
## Z1mnZ0  0.0019 0.2201 0.0004
## Z2mnZ1  0.0000 0.0000 0.0000
## Z3mnZ2  0.0000 0.0000 0.0000
## Z4mnZ3  0.4172 0.0000 0.0000
## F0Bark  0.0000 0.0000 0.3978
## A1mnA2         0.0000 0.0000
## A1mnA3  0.0000        0.0000
## A2mnA3  0.0000 0.0000

## use corrplot to obtain a nice correlation plot!
corrplot(corr$r, p.mat = corr$P,
         addCoef.col = "black", diag = FALSE, type = "upper", tl.srt = 55)

9.3.2 Reduce dimensionality by selecting uncorrelated predictors

We can use the package recipes to allow us to only select uncorrelated predictors at a particular level. For this to work, we need to create a recipe with our outcome. Let’s say we want to use context as our outcome to be predicted from all available predictors in the dataset dfPharV2. We select all variables. Let us test various R² values between all numeric predictors, at 0.9, 0.75, 0.5, 0.25 and 0.1. Any comments?

9.3.2.1 R² = 0.9

dim(dfPharV2)[2]-1

## [1] 24

rec <- dfPharV2 %>% 
  recipe(context ~ .) %>%
  step_corr(all_numeric_predictors(), threshold = 0.9) %>% 
  prep()
bake(rec, new_data = dfPharV2)

## # A tibble: 402 × 21
##    contextN   CPP Energy H1A1c H1A2c   H1A3c   H1H2c H2H4c H2KH5Kc  H42Kc HNR05
##    <fct>    <dbl>  <dbl> <dbl> <dbl>   <dbl>   <dbl> <dbl>   <dbl>  <dbl> <dbl>
##  1 G_01      23.5  22.8   15.2  16.0 -3.30   -1.18    2.65    23.2 -0.793 15.1 
##  2 G_02      25.7  22.8   13.2  11.6 -5.92   -0.739   1.65    16.5  3.22  27.6 
##  3 G_03      19.6   9.16  16.5  18.5  0.604  -0.928   4.50    18.5  3.88   8.08
##  4 G_04      23.6  17.2   16.0  20.1 -7.63    0.782   2.42    28.2  1.85  18.4 
##  5 G_05      26.0  15.6   14.5  14.6 -6.73    0.0442  3.13    27.6  3.15  25.3 
##  6 G_06      24.5  14.4   16.6  16.6 -5.46    1.34    4.51    21.6  2.89  15.2 
##  7 G_07      23.1  18.6   15.0  15.8 -5.94   -0.211   2.11    26.3  2.23  18.7 
##  8 G_08      22.2   9.04  17.1  18.4  2.10   -0.742   3.41    19.1  6.57  19.0 
##  9 G_09      28.4  25.5   12.5  15.1 -3.33   -1.59    3.80    25.6 -2.15  25.1 
## 10 G_10      28.2  15.8   14.7  16.3 -0.0528  0.108   3.50    22.5  1.01  29.4 
## # ℹ 392 more rows
## # ℹ 10 more variables: HNR25 <dbl>, SHR <dbl>, soe <dbl>, Z1mnZ0 <dbl>,
## #   Z2mnZ1 <dbl>, Z4mnZ3 <dbl>, A1mnA2 <dbl>, A1mnA3 <dbl>, A2mnA3 <dbl>,
## #   context <fct>

9.3.2.2 R² = 0.75

dim(dfPharV2)[2]-1

## [1] 24

rec <- dfPharV2 %>% 
  recipe(context ~ .) %>%
  step_corr(all_numeric_predictors(), threshold = 0.75) %>% 
  prep()
bake(rec, new_data = dfPharV2)

## # A tibble: 402 × 14
##    contextN   CPP Energy H1A1c H1A2c   H1A3c   H1H2c H2H4c H2KH5Kc   SHR Z1mnZ0
##    <fct>    <dbl>  <dbl> <dbl> <dbl>   <dbl>   <dbl> <dbl>   <dbl> <dbl>  <dbl>
##  1 G_01      23.5  22.8   15.2  16.0 -3.30   -1.18    2.65    23.2 0.425   5.08
##  2 G_02      25.7  22.8   13.2  11.6 -5.92   -0.739   1.65    16.5 0.358   5.16
##  3 G_03      19.6   9.16  16.5  18.5  0.604  -0.928   4.50    18.5 0.393   4.83
##  4 G_04      23.6  17.2   16.0  20.1 -7.63    0.782   2.42    28.2 0.384   4.81
##  5 G_05      26.0  15.6   14.5  14.6 -6.73    0.0442  3.13    27.6 0.42    4.71
##  6 G_06      24.5  14.4   16.6  16.6 -5.46    1.34    4.51    21.6 0.310   4.85
##  7 G_07      23.1  18.6   15.0  15.8 -5.94   -0.211   2.11    26.3 0.595   5.17
##  8 G_08      22.2   9.04  17.1  18.4  2.10   -0.742   3.41    19.1 0.478   5.15
##  9 G_09      28.4  25.5   12.5  15.1 -3.33   -1.59    3.80    25.6 0.405   4.83
## 10 G_10      28.2  15.8   14.7  16.3 -0.0528  0.108   3.50    22.5 0.497   4.75
## # ℹ 392 more rows
## # ℹ 3 more variables: Z4mnZ3 <dbl>, A1mnA3 <dbl>, context <fct>

9.3.2.3 R² = 0.5

dim(dfPharV2)[2]-1

## [1] 24

rec <- dfPharV2 %>% 
  recipe(context ~ .) %>%
  step_corr(all_numeric_predictors(), threshold = 0.5) %>% 
  prep()
bake(rec, new_data = dfPharV2)

## # A tibble: 402 × 9
##    contextN   CPP H1A1c H2H4c H2KH5Kc   SHR Z1mnZ0 Z4mnZ3 context 
##    <fct>    <dbl> <dbl> <dbl>   <dbl> <dbl>  <dbl>  <dbl> <fct>   
##  1 G_01      23.5  15.2  2.65    23.2 0.425   5.08  0.974 Guttural
##  2 G_02      25.7  13.2  1.65    16.5 0.358   5.16  1.27  Guttural
##  3 G_03      19.6  16.5  4.50    18.5 0.393   4.83  1.81  Guttural
##  4 G_04      23.6  16.0  2.42    28.2 0.384   4.81  0.789 Guttural
##  5 G_05      26.0  14.5  3.13    27.6 0.42    4.71  0.962 Guttural
##  6 G_06      24.5  16.6  4.51    21.6 0.310   4.85  0.591 Guttural
##  7 G_07      23.1  15.0  2.11    26.3 0.595   5.17  1.19  Guttural
##  8 G_08      22.2  17.1  3.41    19.1 0.478   5.15  1.41  Guttural
##  9 G_09      28.4  12.5  3.80    25.6 0.405   4.83  1.47  Guttural
## 10 G_10      28.2  14.7  3.50    22.5 0.497   4.75  1.51  Guttural
## # ℹ 392 more rows

9.3.2.4 R² = 0.25

dim(dfPharV2)[2]-1

## [1] 24

rec <- dfPharV2 %>% 
  recipe(context ~ .) %>%
  step_corr(all_numeric_predictors(), threshold = 0.25) %>% 
  prep()
bake(rec, new_data = dfPharV2)

## # A tibble: 402 × 5
##    contextN   CPP H2H4c Z4mnZ3 context 
##    <fct>    <dbl> <dbl>  <dbl> <fct>   
##  1 G_01      23.5  2.65  0.974 Guttural
##  2 G_02      25.7  1.65  1.27  Guttural
##  3 G_03      19.6  4.50  1.81  Guttural
##  4 G_04      23.6  2.42  0.789 Guttural
##  5 G_05      26.0  3.13  0.962 Guttural
##  6 G_06      24.5  4.51  0.591 Guttural
##  7 G_07      23.1  2.11  1.19  Guttural
##  8 G_08      22.2  3.41  1.41  Guttural
##  9 G_09      28.4  3.80  1.47  Guttural
## 10 G_10      28.2  3.50  1.51  Guttural
## # ℹ 392 more rows

9.3.2.5 R² = 0.1

dim(dfPharV2)[2]-1

## [1] 24

rec <- dfPharV2 %>% 
  recipe(context ~ .) %>%
  step_corr(all_numeric_predictors(), threshold = 0.1) %>% 
  prep()
bake(rec, new_data = dfPharV2)

## # A tibble: 402 × 5
##    contextN   CPP H2H4c Z4mnZ3 context 
##    <fct>    <dbl> <dbl>  <dbl> <fct>   
##  1 G_01      23.5  2.65  0.974 Guttural
##  2 G_02      25.7  1.65  1.27  Guttural
##  3 G_03      19.6  4.50  1.81  Guttural
##  4 G_04      23.6  2.42  0.789 Guttural
##  5 G_05      26.0  3.13  0.962 Guttural
##  6 G_06      24.5  4.51  0.591 Guttural
##  7 G_07      23.1  2.11  1.19  Guttural
##  8 G_08      22.2  3.41  1.41  Guttural
##  9 G_09      28.4  3.80  1.47  Guttural
## 10 G_10      28.2  3.50  1.51  Guttural
## # ℹ 392 more rows

This first solution allowed us to reduce the number of predictors from 23 (removing word and the outcome context) to a maximum of 4 predictors (+context).

The problem with this approach is that it depends on the decision of what to consider as an optimal value for R²! The second solution is to use PCA to reduce dimensionality. This is a more robust approach as it allows us to reduce the number of predictors without having to make arbitrary decisions on what R² value to use.