Modeles mixtes
Jerome Silva
02 avril, 2021
Délai de Succès au MM
description
Chose que l’on n’avait pas vu tant que l’on travaillait sur des moyennes de temps de réponses aggrégées par individu et non au niveau expérience : le délai de succès au multimorphe à un « pic » énorme sur la modalité 40 qui correspond si j’ai bien compris, à ceux qui répondent seulement à la fin , c’est à dire au bout de 20 secondes ou après. Modéliser ce temps de réponse de façon linéaire va nous poser problème : les données ne sont pas normales, on voit bien qu’on a une rupture de cohérence dans le processus qui amène des valeurs <40, et les valeurs égales à 40.
Ici on a l’histrogramme pour nos 89 individus x 36 expériences (6 visages x 6 emotions) (8966=3204 observations)
Histogramme du Délai de succès chez BL et Témoins.
Histogrammes par emotion chez BL
Histogrammes par emotion chez T
Modélisation
Délai de succès
Graphes “splines” des relations entre les Dimensions Abandon et Intrusion et le Délai de Succès.
library(ggstance)
library(ggformula)
plot3 <- ggplot(data = DBMODEL_delai,aes(Dim.Abandon,DEL_SUCC, color=factor(borderline))) + geom_point() +
geom_spline(aes(Dim.Abandon,DEL_SUCC, colour=factor(borderline)), df= 3 )
plot3
plot3 <- ggplot(data = DBMODEL_delai,aes(Dim.Intrusion,DEL_SUCC, color=factor(borderline))) + geom_point() +
geom_spline(aes(Dim.Abandon,DEL_SUCC, colour=factor(borderline)), df= 3 )
plot3
Modèle linéaire mixte. On a introduit les effet linéaires et quadratiques (polynomes orthogonaux) de Dim.Abandon et Dim.Intrusion, ainsi que l’interaction de ces effets avec le fait d’être borderline.
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2 + traitement
+ poly_abandon_1 * borderline
+ poly_abandon_2 * borderline
+ poly_intrusion_1 * borderline
+ poly_intrusion_2 * borderline
, random = ~ 1 | z1,
data = DBMODEL_delai)
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai
## AIC BIC logLik
## 13878.58 13968.14 -6923.289
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.198124 7.518288
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + traitement + poly_abandon_1 * borderline + poly_abandon_2 * borderline + poly_intrusion_1 * borderline + poly_intrusion_2 * borderline
## Value Std.Error DF t-value p-value
## (Intercept) 40.5821 8.87938 1932 4.570373 0.0000
## age -0.7082 0.56779 61 -1.247255 0.2171
## sexe -1.3232 1.74263 61 -0.759296 0.4506
## CSP_bin2 5.0410 1.45298 61 3.469406 0.0010
## traitement 3.9263 2.01906 61 1.944603 0.0564
## poly_abandon_1 195.4783 85.64567 1932 2.282407 0.0226
## borderline 3.8800 2.40000 61 1.616686 0.1111
## poly_abandon_2 40.5277 64.28532 1932 0.630434 0.5285
## poly_intrusion_1 -225.0702 91.62972 1932 -2.456301 0.0141
## poly_intrusion_2 -161.2001 101.37916 1932 -1.590071 0.1120
## poly_abandon_1:borderline -383.6991 112.19613 1932 -3.419896 0.0006
## borderline:poly_abandon_2 108.2878 85.14600 1932 1.271790 0.2036
## borderline:poly_intrusion_1 196.2441 103.82272 1932 1.890184 0.0589
## borderline:poly_intrusion_2 224.9047 107.59080 1932 2.090371 0.0367
## Correlation:
## (Intr) age sexe CSP_b2 trtmnt ply_b_1 brdrln ply_b_2 ply_n_1 ply_n_2 pl__1: brdrln:ply_b_2 br:__1
## age -0.986
## sexe 0.130 -0.258
## CSP_bin2 0.235 -0.263 0.040
## traitement -0.004 0.001 0.052 -0.152
## poly_abandon_1 0.097 -0.088 0.232 0.227 -0.022
## borderline 0.207 -0.223 -0.141 0.179 -0.455 -0.165
## poly_abandon_2 0.068 -0.068 0.188 0.250 -0.029 0.768 -0.109
## poly_intrusion_1 0.080 -0.065 -0.121 -0.120 0.015 -0.603 0.050 -0.494
## poly_intrusion_2 0.129 -0.106 -0.191 0.021 -0.010 -0.285 0.085 -0.377 0.789
## poly_abandon_1:borderline -0.171 0.168 -0.221 -0.204 0.020 -0.777 -0.240 -0.597 0.457 0.211
## borderline:poly_abandon_2 0.075 -0.078 -0.103 -0.156 0.190 -0.567 0.352 -0.746 0.381 0.297 0.119
## borderline:poly_intrusion_1 -0.128 0.118 0.088 0.020 -0.083 0.510 -0.200 0.413 -0.875 -0.701 -0.380 -0.358
## borderline:poly_intrusion_2 -0.069 0.044 0.189 0.063 0.018 0.287 0.052 0.375 -0.749 -0.936 -0.234 -0.249 0.538
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.64029926 -0.64881584 0.08122169 0.67533409 2.40472219
##
## Number of Observations: 2007
## Number of Groups: 67 Plot des résidus et question à propos de celui-ci
plot(lmm2)
On retrouve la même structure “pyramide” des résidus quelle que soit la spécification du modèle (même uniquement un intercept). En gros le modèle ne prédit jamais au dessus de 40. on revient à notre problème de données “censurées”. Est-ce grave pour l’estimation ?
Interprétation du modèle :
Effet linéaire positif de Abandon. Effet linéaire negatif de Intrusion. Effet positif de Borderline en moyenne par rapport aux témoins.
Moins facilement interprétable :
Si on est borderline, sur-effet linéaire négatif de la Dim.Abandon. Si on est borderline, sur-effet linéaire positif de la Dim.Intrusion Si on est borderline, sur-effet quadratique positif de la Dim.Intrusion (courbe en U)
Autres Modèles testés :
ECHANTILLON TOTAL : effets linéaires uniquement
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2 + traitement
+ Dim.Abandon
+ Dim.Intrusion
, random = ~ 1 | z1,
data = DBMODEL_delai)
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai
## AIC BIC logLik
## 13964.03 14014.44 -6973.015
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.691951 7.518255
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + traitement + Dim.Abandon + Dim.Intrusion
## Value Std.Error DF t-value p-value
## (Intercept) 35.88603 9.346324 1940 3.839587 0.0001
## age -0.38885 0.598314 60 -0.649910 0.5182
## sexe -2.50440 1.780057 60 -1.406918 0.1646
## CSP_bin2 4.16816 1.478600 60 2.818991 0.0065
## traitement 3.68200 1.578522 60 2.332564 0.0230
## Dim.Abandon 0.22638 0.454973 60 0.497558 0.6206
## Dim.Intrusion 0.10077 0.467940 60 0.215340 0.8302
## Correlation:
## (Intr) age sexe CSP_b2 trtmnt Dm.Abn
## age -0.986
## sexe 0.151 -0.297
## CSP_bin2 0.175 -0.207 0.049
## traitement 0.046 -0.062 -0.119 -0.069
## Dim.Abandon 0.118 -0.113 0.012 0.059 -0.093
## Dim.Intrusion 0.023 -0.018 0.067 -0.066 -0.334 -0.405
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.67831798 -0.64824176 0.09671342 0.66127955 2.39158349
##
## Number of Observations: 2007
## Number of Groups: 67ECHANTILLON TOTAL : effets quadratiques (polynomes orthogonaux)
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2 + traitement
+ poly_abandon_1
+ poly_abandon_2
+ poly_intrusion_1
+ poly_intrusion_2
, random = ~ 1 | z1,
data = DBMODEL_delai)
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai
## AIC BIC logLik
## 13932.21 13993.81 -6955.107
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.6897 7.518248
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + traitement + poly_abandon_1 + poly_abandon_2 + poly_intrusion_1 + poly_intrusion_2
## Value Std.Error DF t-value p-value
## (Intercept) 36.03466 9.38769 1936 3.838501 0.0001
## age -0.39198 0.60084 62 -0.652374 0.5166
## sexe -2.64533 1.79210 62 -1.476103 0.1450
## CSP_bin2 4.44829 1.52022 62 2.926091 0.0048
## traitement 3.46049 1.65086 62 2.096180 0.0402
## poly_abandon_1 35.85362 34.22989 1936 1.047436 0.2950
## poly_abandon_2 -23.87573 28.99438 1936 -0.823461 0.4103
## poly_intrusion_1 -12.08667 32.88340 1936 -0.367561 0.7132
## poly_intrusion_2 33.21350 27.19820 1936 1.221165 0.2222
## Correlation:
## (Intr) age sexe CSP_b2 trtmnt ply_b_1 ply_b_2 ply_n_1
## age -0.986
## sexe 0.138 -0.283
## CSP_bin2 0.190 -0.219 0.019
## traitement 0.071 -0.085 -0.137 -0.021
## poly_abandon_1 0.124 -0.116 -0.027 0.132 -0.081
## poly_abandon_2 0.074 -0.077 -0.055 0.086 0.282 -0.129
## poly_intrusion_1 0.003 -0.003 0.095 -0.133 -0.288 -0.513 0.125
## poly_intrusion_2 0.061 -0.054 -0.102 0.212 0.067 0.428 -0.060 -0.399
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.67143356 -0.64993215 0.08266817 0.66861487 2.39329838
##
## Number of Observations: 2007
## Number of Groups: 67ECHANTILLON TOTAL : effets quadratiques avec interaction BORDERLINE (MODELE RETENU)
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2 + traitement
+ poly_abandon_1 *borderline
+ poly_abandon_2 *borderline
+ poly_intrusion_1 *borderline
+ poly_intrusion_2 *borderline
, random = ~ 1 | z1,
data = DBMODEL_delai)
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai
## AIC BIC logLik
## 13878.58 13968.14 -6923.289
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.198124 7.518288
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + traitement + poly_abandon_1 * borderline + poly_abandon_2 * borderline + poly_intrusion_1 * borderline + poly_intrusion_2 * borderline
## Value Std.Error DF t-value p-value
## (Intercept) 40.5821 8.87938 1932 4.570373 0.0000
## age -0.7082 0.56779 61 -1.247255 0.2171
## sexe -1.3232 1.74263 61 -0.759296 0.4506
## CSP_bin2 5.0410 1.45298 61 3.469406 0.0010
## traitement 3.9263 2.01906 61 1.944603 0.0564
## poly_abandon_1 195.4783 85.64567 1932 2.282407 0.0226
## borderline 3.8800 2.40000 61 1.616686 0.1111
## poly_abandon_2 40.5277 64.28532 1932 0.630434 0.5285
## poly_intrusion_1 -225.0702 91.62972 1932 -2.456301 0.0141
## poly_intrusion_2 -161.2001 101.37916 1932 -1.590071 0.1120
## poly_abandon_1:borderline -383.6991 112.19613 1932 -3.419896 0.0006
## borderline:poly_abandon_2 108.2878 85.14600 1932 1.271790 0.2036
## borderline:poly_intrusion_1 196.2441 103.82272 1932 1.890184 0.0589
## borderline:poly_intrusion_2 224.9047 107.59080 1932 2.090371 0.0367
## Correlation:
## (Intr) age sexe CSP_b2 trtmnt ply_b_1 brdrln ply_b_2 ply_n_1 ply_n_2 pl__1: brdrln:ply_b_2 br:__1
## age -0.986
## sexe 0.130 -0.258
## CSP_bin2 0.235 -0.263 0.040
## traitement -0.004 0.001 0.052 -0.152
## poly_abandon_1 0.097 -0.088 0.232 0.227 -0.022
## borderline 0.207 -0.223 -0.141 0.179 -0.455 -0.165
## poly_abandon_2 0.068 -0.068 0.188 0.250 -0.029 0.768 -0.109
## poly_intrusion_1 0.080 -0.065 -0.121 -0.120 0.015 -0.603 0.050 -0.494
## poly_intrusion_2 0.129 -0.106 -0.191 0.021 -0.010 -0.285 0.085 -0.377 0.789
## poly_abandon_1:borderline -0.171 0.168 -0.221 -0.204 0.020 -0.777 -0.240 -0.597 0.457 0.211
## borderline:poly_abandon_2 0.075 -0.078 -0.103 -0.156 0.190 -0.567 0.352 -0.746 0.381 0.297 0.119
## borderline:poly_intrusion_1 -0.128 0.118 0.088 0.020 -0.083 0.510 -0.200 0.413 -0.875 -0.701 -0.380 -0.358
## borderline:poly_intrusion_2 -0.069 0.044 0.189 0.063 0.018 0.287 0.052 0.375 -0.749 -0.936 -0.234 -0.249 0.538
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.64029926 -0.64881584 0.08122169 0.67533409 2.40472219
##
## Number of Observations: 2007
## Number of Groups: 67 abandon (+) et intrusion (-) linéaires
abandon*borderline (-) lineaire
intrusion*borderline (+) lineaire ET QuadratiqueCHEZ BORDERLINES : effets linéaires uniquement
rien de significatif
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2 + traitement
+ Dim.Abandon
+ Dim.Intrusion
, random = ~ 1 | z1,
data = DBMODEL_delai[which(DBMODEL_delai$borderline==1),])
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai[which(DBMODEL_delai$borderline == 1), ]
## AIC BIC logLik
## 5278.264 5319.987 -2630.132
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 5.250472 7.17253
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + traitement + Dim.Abandon + Dim.Intrusion
## Value Std.Error DF t-value p-value
## (Intercept) 39.16488 18.049597 743 2.1698478 0.0303
## age -0.35317 0.932627 19 -0.3786871 0.7091
## sexe -5.09337 6.176838 19 -0.8245914 0.4198
## CSP_bin2 2.82102 2.779094 19 1.0150850 0.3228
## traitement 2.83789 2.439131 19 1.1634863 0.2590
## Dim.Abandon -0.67020 0.819356 19 -0.8179645 0.4235
## Dim.Intrusion 0.53105 0.629983 19 0.8429598 0.4097
## Correlation:
## (Intr) age sexe CSP_b2 trtmnt Dm.Abn
## age -0.936
## sexe -0.524 0.217
## CSP_bin2 -0.109 -0.016 0.337
## traitement -0.163 0.067 0.062 -0.212
## Dim.Abandon -0.028 -0.006 -0.117 -0.093 0.321
## Dim.Intrusion 0.023 -0.007 -0.084 -0.028 -0.209 -0.062
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.8044082 -0.6398352 0.1149749 0.6301366 2.4657282
##
## Number of Observations: 769
## Number of Groups: 26CHEZ BORDERLINES : effets quadratiques (polynomes orthogonaux)
Abandon² presque sign.
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2 + traitement
+ poly_abandon_1
+ poly_abandon_2
+ poly_intrusion_1
+ poly_intrusion_2
, random = ~ 1 | z1,
data = DBMODEL_delai[which(DBMODEL_delai$borderline==1),])
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai[which(DBMODEL_delai$borderline == 1), ]
## AIC BIC logLik
## 5239.877 5290.844 -2608.939
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.661887 7.172654
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + traitement + poly_abandon_1 + poly_abandon_2 + poly_intrusion_1 + poly_intrusion_2
## Value Std.Error DF t-value p-value
## (Intercept) 53.05833 17.03239 739 3.1151431 0.0019
## age -0.99309 0.87114 21 -1.1399956 0.2671
## sexe -5.17703 5.54278 21 -0.9340130 0.3609
## CSP_bin2 3.75285 2.63579 21 1.4238032 0.1692
## traitement 4.01812 2.25509 21 1.7817979 0.0893
## poly_abandon_1 -188.09806 78.16514 739 -2.4064188 0.0164
## poly_abandon_2 153.18401 63.23849 739 2.4223225 0.0157
## poly_intrusion_1 -22.39643 56.40078 739 -0.3970944 0.6914
## poly_intrusion_2 59.47347 42.94661 739 1.3848232 0.1665
## Correlation:
## (Intr) age sexe CSP_b2 trtmnt ply_b_1 ply_b_2 ply_n_1
## age -0.942
## sexe -0.497 0.207
## CSP_bin2 -0.050 -0.060 0.336
## traitement -0.087 0.008 0.049 -0.211
## poly_abandon_1 -0.236 0.190 -0.049 -0.056 0.006
## poly_abandon_2 0.291 -0.258 -0.029 0.022 0.243 -0.772
## poly_intrusion_1 -0.117 0.119 -0.095 -0.270 -0.108 0.036 -0.127
## poly_intrusion_2 0.180 -0.170 0.053 0.328 -0.019 -0.109 0.203 -0.766
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.7902189 -0.6434046 0.1374795 0.6350782 2.4659157
##
## Number of Observations: 769
## Number of Groups: 26CHEZ TEMOINS : effets linéaires uniquement
Abandon et Intrusion significatifs
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2
+ Dim.Abandon
+ Dim.Intrusion
, random = ~ 1 | z1,
data = DBMODEL_delai[which(DBMODEL_delai$borderline==0),])
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai[which(DBMODEL_delai$borderline == 0), ]
## AIC BIC logLik
## 8667.784 8708.715 -4325.892
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.147555 7.725046
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + Dim.Abandon + Dim.Intrusion
## Value Std.Error DF t-value p-value
## (Intercept) 42.00502 12.866072 1197 3.264789 0.0011
## age -0.79858 0.841957 35 -0.948485 0.3494
## sexe -1.65328 1.982276 35 -0.834032 0.4099
## CSP_bin2 5.51011 1.777304 35 3.100264 0.0038
## Dim.Abandon 2.31621 0.809420 35 2.861573 0.0071
## Dim.Intrusion -1.73680 0.826455 35 -2.101508 0.0429
## Correlation:
## (Intr) age sexe CSP_b2 Dm.Abn
## age -0.993
## sexe 0.381 -0.464
## CSP_bin2 0.257 -0.274 -0.029
## Dim.Abandon 0.109 -0.102 0.166 0.066
## Dim.Intrusion 0.031 -0.031 0.132 -0.180 -0.602
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.58487614 -0.66052447 0.06249996 0.72305560 2.32834850
##
## Number of Observations: 1238
## Number of Groups: 41CHEZ TEMOINS : effets quadratiques (polynomes orthogonaux)
abandon (+) et intrusion (-) linéaires
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2
+ poly_abandon_1
+ poly_abandon_2
+ poly_intrusion_1
+ poly_intrusion_2
, random = ~ 1 | z1,
data = DBMODEL_delai[which(DBMODEL_delai$borderline==0),])
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai[which(DBMODEL_delai$borderline == 0), ]
## AIC BIC logLik
## 8631.158 8682.306 -4305.579
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.095516 7.725035
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + poly_abandon_1 + poly_abandon_2 + poly_intrusion_1 + poly_intrusion_2
## Value Std.Error DF t-value p-value
## (Intercept) 39.18754 13.12489 1197 2.9857417 0.0029
## age -0.63592 0.85565 33 -0.7432040 0.4626
## sexe -1.08528 2.00650 33 -0.5408845 0.5922
## CSP_bin2 5.41670 1.88267 33 2.8771320 0.0070
## poly_abandon_1 203.51929 85.84562 33 2.3707590 0.0237
## poly_abandon_2 46.81697 64.41797 33 0.7267687 0.4725
## poly_intrusion_1 -232.24736 90.40097 33 -2.5690803 0.0149
## poly_intrusion_2 -167.01823 100.11750 33 -1.6682221 0.1047
## Correlation:
## (Intr) age sexe CSP_b2 ply_b_1 ply_b_2 ply_n_1
## age -0.994
## sexe 0.365 -0.449
## CSP_bin2 0.312 -0.324 0.016
## poly_abandon_1 0.171 -0.167 0.250 0.281
## poly_abandon_2 0.131 -0.132 0.191 0.309 0.777
## poly_intrusion_1 0.087 -0.076 -0.082 -0.131 -0.594 -0.492
## poly_intrusion_2 0.149 -0.130 -0.157 0.060 -0.265 -0.355 0.782
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.56719787 -0.66130432 0.05848505 0.70920234 2.33556815
##
## Number of Observations: 1238
## Number of Groups: 41QUESTIONS
- Le délai de succès au Multimorphe, avec son pic à 40 (expliqué au début du doc) me tracasse : comment modéliser ce phenomène (donnée censurée ?) ? Notre régression linéaire est-elle justifiable, sachant qu’on ne prend pas en compte cet aspect ?
Jusque ici , nous avons considéré la structure de variance suivante : les expériences sont groupées uniquement par individus. Or, chaque individu passe l’expérience pour les mêmes 6 émotions, avec les mêmes 6 visages (36 expériences par individu )
- Peut-on / doit-on aussi introduire des effets aléatoires par émotion et par visage ? (crossed random factors)
- quelles conséquences ?
- Comment interpréter les coefficients des polynomes orthogonaux dans les modèles ? Il parait difficile (mes recherches sont infructueuses et apparemment je ne suis pas le seul à avoir essayé) de “revenir” aux polynomes standards pour avoir les coefficients du type ax+bx² qui nous permettraient d’avoir une interprétation plus directe de nos résultats.
- Nous avons modélisé jusqu’ici le délai de réponse au multimorphe, mais nous avons aussi le “succès” à chaque expérience. Nous aimerions modéliser la probabilité de succèe de la même façon. Or, j’ai tenté des modèles mixtes logistiques mais souvent l’estimation plante pour cause de matrice de var-covar singulière. Que faire ?
Modèles supplémentaires
visage et émotion comme effets fixes
Modèle où l’on introduit le visage et l’émotion comme effets fixes.
lmm2 <- lme(DEL_SUCC ~ age + sexe + CSP_bin2
+ stats::poly(Dim.Abandon,2) *borderline
+ stats::poly(Dim.Intrusion,2) *borderline
+ traitement
+ emotion.f
+ face.f
, random = ~ 1 | z1,
data = DBMODEL_delai)
summary(lmm2)## Linear mixed-effects model fit by REML
## Data: DBMODEL_delai
## AIC BIC logLik
## 13410.4 13555.8 -6679.2
##
## Random effects:
## Formula: ~1 | z1
## (Intercept) Residual
## StdDev: 4.326075 6.646568
##
## Fixed effects: DEL_SUCC ~ age + sexe + CSP_bin2 + stats::poly(Dim.Abandon, 2) * borderline + stats::poly(Dim.Intrusion, 2) * borderline + traitement + emotion.f + face.f
## Value Std.Error DF t-value p-value
## (Intercept) 43.4034 9.04449 1922 4.798879 0.0000
## age -0.7539 0.57729 61 -1.305874 0.1965
## sexe -1.4716 1.77179 61 -0.830566 0.4095
## CSP_bin2 5.0650 1.47797 61 3.426972 0.0011
## stats::poly(Dim.Abandon, 2)1 194.4855 87.12353 1922 2.232296 0.0257
## stats::poly(Dim.Abandon, 2)2 41.5611 65.38832 1922 0.635604 0.5251
## borderline 3.8109 2.44274 61 1.560107 0.1239
## stats::poly(Dim.Intrusion, 2)1 -222.4133 93.21722 1922 -2.385968 0.0171
## stats::poly(Dim.Intrusion, 2)2 -158.4803 103.15279 1922 -1.536364 0.1246
## traitement 3.9374 2.05435 61 1.916622 0.0600
## emotion.fDisgust 0.0190 0.53978 1922 0.035118 0.9720
## emotion.fFear 0.9215 0.52785 1922 1.745831 0.0810
## emotion.fHappiness -8.5438 0.50929 1922 -16.775813 0.0000
## emotion.fSadness 0.0614 0.53498 1922 0.114771 0.9086
## emotion.fSurprise -2.2459 0.53412 1922 -4.204786 0.0000
## face.f2 -1.0219 0.52436 1922 -1.948819 0.0515
## face.f4 -0.1047 0.52518 1922 -0.199389 0.8420
## face.f5 -0.5428 0.51754 1922 -1.048776 0.2944
## face.f6 0.7292 0.52303 1922 1.394120 0.1634
## face.f7 0.5182 0.53062 1922 0.976637 0.3289
## stats::poly(Dim.Abandon, 2)1:borderline -380.8371 114.15452 1922 -3.336154 0.0009
## stats::poly(Dim.Abandon, 2)2:borderline 106.2910 86.62552 1922 1.227018 0.2200
## borderline:stats::poly(Dim.Intrusion, 2)1 195.8977 105.61772 1922 1.854781 0.0638
## borderline:stats::poly(Dim.Intrusion, 2)2 218.4036 109.44670 1922 1.995524 0.0461
## Correlation:
## (Intr) age sexe CSP_b2 st::(D.A,2)1 st::(D.A,2)2 brdrln s::(D.I,2)1 s::(D.I,2)2 trtmnt emtn.D emtn.F emtn.H emtn.fSd emtn.fSr fac.f2 fac.f4 fac.f5 fac.f6 fac.f7 s::(D.A,2)1: s::(D.A,2)2: b:::(D.I,2)1
## age -0.985
## sexe 0.130 -0.258
## CSP_bin2 0.235 -0.263 0.040
## stats::poly(Dim.Abandon, 2)1 0.097 -0.088 0.233 0.226
## stats::poly(Dim.Abandon, 2)2 0.068 -0.068 0.188 0.249 0.768
## borderline 0.207 -0.223 -0.141 0.179 -0.164 -0.108
## stats::poly(Dim.Intrusion, 2)1 0.080 -0.065 -0.121 -0.120 -0.603 -0.494 0.050
## stats::poly(Dim.Intrusion, 2)2 0.130 -0.106 -0.191 0.020 -0.285 -0.377 0.085 0.789
## traitement -0.004 0.001 0.052 -0.152 -0.022 -0.029 -0.455 0.015 -0.010
## emotion.fDisgust -0.033 -0.001 0.008 -0.004 0.003 0.003 -0.001 -0.001 -0.003 -0.001
## emotion.fFear -0.035 0.000 0.003 -0.002 0.004 0.001 -0.002 -0.002 -0.002 0.000 0.523
## emotion.fHappiness -0.038 0.002 0.007 -0.004 0.002 0.000 -0.001 -0.001 -0.002 0.000 0.538 0.553
## emotion.fSadness -0.033 -0.002 0.005 -0.005 -0.001 -0.003 -0.001 0.001 -0.001 0.000 0.514 0.529 0.546
## emotion.fSurprise -0.034 0.000 0.005 -0.004 0.003 0.000 0.001 -0.004 -0.004 -0.002 0.510 0.524 0.542 0.517
## face.f2 -0.036 0.004 -0.003 0.001 0.002 0.003 0.001 -0.005 -0.004 0.000 0.025 0.041 0.043 0.048 0.066
## face.f4 -0.036 0.002 0.002 0.001 0.004 0.005 -0.002 -0.003 -0.005 0.003 0.092 0.097 0.074 0.083 0.052 0.514
## face.f5 -0.038 0.004 0.000 -0.001 0.003 0.003 0.000 -0.002 -0.003 0.002 0.051 0.068 0.072 0.097 0.052 0.524 0.526
## face.f6 -0.040 0.005 0.000 -0.003 0.002 0.001 -0.001 -0.003 -0.003 0.002 0.060 0.097 0.082 0.106 0.069 0.518 0.522 0.531
## face.f7 -0.038 0.004 0.000 -0.001 0.004 0.003 -0.002 -0.003 -0.003 0.000 0.088 0.094 0.075 0.092 0.075 0.511 0.516 0.521 0.518
## stats::poly(Dim.Abandon, 2)1:borderline -0.170 0.168 -0.221 -0.204 -0.777 -0.597 -0.240 0.457 0.211 0.021 -0.003 -0.004 -0.003 0.001 -0.003 -0.002 -0.004 -0.004 -0.003 -0.002
## stats::poly(Dim.Abandon, 2)2:borderline 0.075 -0.078 -0.103 -0.156 -0.567 -0.745 0.352 0.380 0.297 0.189 -0.001 -0.001 0.001 0.002 0.001 -0.001 -0.001 -0.001 0.000 -0.002 0.118
## borderline:stats::poly(Dim.Intrusion, 2)1 -0.128 0.118 0.088 0.020 0.510 0.413 -0.200 -0.875 -0.701 -0.083 0.002 0.002 0.001 -0.001 0.004 0.003 0.002 0.002 0.003 0.002 -0.380 -0.358
## borderline:stats::poly(Dim.Intrusion, 2)2 -0.069 0.044 0.190 0.063 0.287 0.375 0.052 -0.749 -0.936 0.018 0.003 0.001 0.003 0.000 0.004 0.005 0.004 0.003 0.003 0.003 -0.234 -0.249 0.538
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.81962668 -0.71299277 -0.04695377 0.67133253 2.93269453
##
## Number of Observations: 2007
## Number of Groups: 67plot(fitted.values(lmm2),residuals(lmm2))
qqnorm(residuals(lmm2))
visage et émotion comme effets aléatoires
Modèle où l’on introduit le visage et l’émotion comme effets aléatoires. (crossed random effects)
############### TEST AVEC LME4 : ON RAJOUTE EMOTION ET FACE COMME NIVEAUX (crossed)
# on créé les variables polynomes orthogonaux
DBMODEL_delai$poly_abandon_1 <- stats::poly(DBMODEL_delai$Dim.Abandon,2)[,1]
DBMODEL_delai$poly_abandon_2 <- stats::poly(DBMODEL_delai$Dim.Abandon,2)[,2]
DBMODEL_delai$poly_intrusion_1 <- stats::poly(DBMODEL_delai$Dim.Intrusion,2)[,1]
DBMODEL_delai$poly_intrusion_2 <- stats::poly(DBMODEL_delai$Dim.Intrusion,2)[,2]
DBMODEL_succes$poly_abandon_1 <- stats::poly(DBMODEL_succes$Dim.Abandon,2)[,1]
DBMODEL_succes$poly_abandon_2 <- stats::poly(DBMODEL_succes$Dim.Abandon,2)[,2]
DBMODEL_succes$poly_intrusion_1 <- stats::poly(DBMODEL_succes$Dim.Intrusion,2)[,1]
DBMODEL_succes$poly_intrusion_2 <- stats::poly(DBMODEL_succes$Dim.Intrusion,2)[,2]
lmm2 <- lmer(DEL_SUCC ~ age + sexe + CSP_bin2
+ poly_abandon_1 *borderline
+ poly_abandon_2 *borderline
+ poly_intrusion_1 *borderline
+ poly_intrusion_2 *borderline
+ (1 | z1)
+ (1 | emotion.f)
+ (1 | face.f)
,
data = DBMODEL_delai)
summary(lmm2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DEL_SUCC ~ age + sexe + CSP_bin2 + poly_abandon_1 * borderline + poly_abandon_2 * borderline + poly_intrusion_1 * borderline + poly_intrusion_2 * borderline + (1 | z1) + (1 | emotion.f) + (1 | face.f)
## Data: DBMODEL_delai
##
## REML criterion at convergence: 13405.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.81281 -0.71657 -0.04859 0.66307 2.96014
##
## Random effects:
## Groups Name Variance Std.Dev.
## z1 (Intercept) 19.6770 4.4359
## emotion.f (Intercept) 12.4633 3.5303
## face.f (Intercept) 0.2922 0.5405
## Residual 44.1788 6.6467
## Number of obs: 2007, groups: z1, 67; emotion.f, 6; face.f, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 41.7715 9.3536 4.466
## age -0.7559 0.5908 -1.279
## sexe -1.6500 1.8109 -0.911
## CSP_bin2 5.5019 1.4951 3.680
## poly_abandon_1 198.1630 89.1527 2.223
## borderline 5.9472 2.2269 2.671
## poly_abandon_2 45.2973 66.8990 0.677
## poly_intrusion_1 -225.2621 95.4019 -2.361
## poly_intrusion_2 -156.7295 105.5795 -1.484
## poly_abandon_1:borderline -385.4446 116.8206 -3.299
## borderline:poly_abandon_2 74.9334 87.0626 0.861
## borderline:poly_intrusion_1 212.6911 107.7328 1.974
## borderline:poly_intrusion_2 214.8693 112.0052 1.918library(car)
Anova(lmm2)## Analysis of Deviance Table (Type II Wald chisquare tests)
##
## Response: DEL_SUCC
## Chisq Df Pr(>Chisq)
## age 1.6367 1 0.2007840
## sexe 0.8302 1 0.3622249
## CSP_bin2 13.5413 1 0.0002334 ***
## poly_abandon_1 0.2940 1 0.5876618
## borderline 2.5482 1 0.1104180
## poly_abandon_2 4.0709 1 0.0436292 *
## poly_intrusion_1 1.7185 1 0.1898809
## poly_intrusion_2 0.7907 1 0.3738803
## poly_abandon_1:borderline 10.8864 1 0.0009687 ***
## borderline:poly_abandon_2 0.7408 1 0.3894119
## borderline:poly_intrusion_1 3.8977 1 0.0483537 *
## borderline:poly_intrusion_2 3.6802 1 0.0550619 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(fitted.values(lmm2),residuals(lmm2))
qqnorm(residuals(lmm2))
# abandon
p <- ggplot(DBMODEL_delai, aes(Dim.Abandon, DEL_SUCC, color=factor(borderline))) +
geom_jitter() +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE) +
geom_smooth(method = "lm", formula = y ~ poly(x, 1), se = TRUE)
p
# intrusion
p <- ggplot(DBMODEL_delai, aes(Dim.Intrusion, DEL_SUCC, color=factor(borderline))) +
geom_jitter() +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE)+
geom_smooth(method = "lm", formula = y ~ poly(x, 1), se = TRUE)
p
# intrusion sans l'outlier
p <- ggplot(DBMODEL_delai[which(DBMODEL_delai$Dim.Intrusion <6),], aes(Dim.Intrusion, DEL_SUCC, color=factor(borderline))) +
geom_jitter() +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = TRUE)+
geom_smooth(method = "lm", formula = y ~ poly(x, 1), se = TRUE)
p
Modèle de probabilité de succès
En enlevant age et CSP, on réussit à avoir des estimations qui convergent. Le modèle ne révèle aucune influence significative d’Abandon et Intrusion sur la probabilité de Succès. (on teste des effets linéaires et quadratiques)
lmm <- glmer(SUC_FIN ~ sexe
+ poly(Dim.Intrusion,2) * borderline
+ poly(Dim.Abandon,2) * borderline
+ traitement
+ emotion.f
+ face.f
+ (1 | z1 ) ,
data = DBMODEL_succes,
family = binomial(link = "probit"))
summary(lmm)## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
## Family: binomial ( probit )
## Formula: SUC_FIN ~ sexe + poly(Dim.Intrusion, 2) * borderline + poly(Dim.Abandon, 2) * borderline + traitement + emotion.f + face.f + (1 | z1)
## Data: DBMODEL_succes
##
## AIC BIC logLik deviance df.resid
## 2025.3 2158.4 -989.6 1979.3 2389
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -12.5277 0.0924 0.4060 0.5034 1.3867
##
## Random effects:
## Groups Name Variance Std.Dev.
## z1 (Intercept) 0.002449 0.04949
## Number of obs: 2412, groups: z1, 67
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.344168 0.123030 2.797 0.005151 **
## sexe 0.340251 0.097424 3.492 0.000479 ***
## poly(Dim.Intrusion, 2)1 -0.794918 7.993168 -0.099 0.920781
## poly(Dim.Intrusion, 2)2 0.437354 7.711870 0.057 0.954775
## borderline 0.066590 0.145259 0.458 0.646646
## poly(Dim.Abandon, 2)1 3.396440 5.546128 0.612 0.540274
## poly(Dim.Abandon, 2)2 -1.899436 4.117253 -0.461 0.644558
## traitement -0.003583 0.122053 -0.029 0.976583
## emotion.fDisgust 0.045717 0.099709 0.459 0.646592
## emotion.fFear 0.352912 0.105351 3.350 0.000809 ***
## emotion.fHappiness 1.630351 0.199979 8.153 3.56e-16 ***
## emotion.fSadness 0.154300 0.101017 1.527 0.126645
## emotion.fSurprise 0.134051 0.100975 1.328 0.184319
## face.f2 0.175588 0.108135 1.624 0.104423
## face.f4 0.189166 0.108260 1.747 0.080579 .
## face.f5 0.431078 0.114112 3.778 0.000158 ***
## face.f6 0.254502 0.109475 2.325 0.020085 *
## face.f7 0.043656 0.105683 0.413 0.679542
## poly(Dim.Intrusion, 2)1:borderline -11.794143 8.584224 -1.374 0.169463
## poly(Dim.Intrusion, 2)2:borderline 1.316854 8.138171 0.162 0.871454
## borderline:poly(Dim.Abandon, 2)1 -6.687963 7.370201 -0.907 0.364178
## borderline:poly(Dim.Abandon, 2)2 4.528851 5.585898 0.811 0.417501
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1