Imputation by PLS regression for linear mixed models

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.