The problem of handling missing data in linear mixed models with correlated covariates is considered when the missing mechanism concerns both the dependent variable and the design matrix. We propose an imputation algorithm combining multiple imputation and Partial Least Squares (PLS) regression. The method relies on two steps: removing random effects, fixed effects are first imputed and PLS components are constructed on the corresponding complete case. The dependent variable is then imputed inside the linear mixed model obtained by adding the random effects to PLS components. The method is applied on simulations and on real data.
Nous considérons le problème du traitement des données manquantes dans le cadre d’un modèle linéaire mixte, en présence de dépendance linéaire entre les covariables. Le mécanisme de valeurs manquantes concerne à la fois la variable dépendante et les covariables. Nous proposons un algorithme d’imputation combinant l’imputation multiple et la régression PLS. Notre méthode se décompose en différentes étapes. Tout d’abord en omettant les effets aléatoires, les effets fixes sont imputés et les composantes PLS sont construites sur le modèle complet correspondant. On réintroduit alors les effets aléatoires du modèle et la variable dépendante est imputée à l’intérieur du modèle linéaire mixte avec composantes PLS. La méthode est appliquée sur des simulations et sur des données réelles.
@article{JSFS_2011__152_4_30_0, author = {Guyon, Emilie and Pommeret, Denys}, title = {Imputation by {PLS} regression for linear mixed models}, journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique}, pages = {30--46}, publisher = {Soci\'et\'e fran\c{c}aise de statistique}, volume = {152}, number = {4}, year = {2011}, zbl = {1316.62108}, language = {en}, url = {http://www.numdam.org/item/JSFS_2011__152_4_30_0/} }
TY - JOUR AU - Guyon, Emilie AU - Pommeret, Denys TI - Imputation by PLS regression for linear mixed models JO - Journal de la société française de statistique PY - 2011 SP - 30 EP - 46 VL - 152 IS - 4 PB - Société française de statistique UR - http://www.numdam.org/item/JSFS_2011__152_4_30_0/ LA - en ID - JSFS_2011__152_4_30_0 ER -
%0 Journal Article %A Guyon, Emilie %A Pommeret, Denys %T Imputation by PLS regression for linear mixed models %J Journal de la société française de statistique %D 2011 %P 30-46 %V 152 %N 4 %I Société française de statistique %U http://www.numdam.org/item/JSFS_2011__152_4_30_0/ %G en %F JSFS_2011__152_4_30_0
Guyon, Emilie; Pommeret, Denys. Imputation by PLS regression for linear mixed models. Journal de la société française de statistique, Volume 152 (2011) no. 4, pp. 30-46. http://www.numdam.org/item/JSFS_2011__152_4_30_0/
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