Multivariate linear mixed-effects model: consistent estimate and fixed-effects variables selection
lundi 11 mars 2019, 11h00 - 12h00
In this talk, we present the ML (Maximum Likelihood) and the REML (REstricted ML) criteria for consistently estimating multivariate linear mixed-effect models with arbitrary correlation structure between the random effects across dimensions, but independent (and possibly heteroscedastic) residuals. By factorizing the random effects covariance matrix, we provide an explicit expression of the profiled deviance through a reparameterization of the model. Beside its robustness regarding the starting points, the approach enables a numerically consistent estimate of the random effects covariance matrix while classical alternatives such as the EM algorithm are usually non consistent. We also introduce a selection procedure based on an adaptive ridge (AR) penalty of the profiled likelihood. This selection procedure is intended to approximate the performance obtained from L0 penalties. Through extensive simulation studies, the procedure is compared to the LASSO and appears to enjoy the model selection consistency.