Effects of time-invariant covariates on the estimation of longitudinal trends for transition mixed models

In this paper, we investigate the impact of time-invariant covariates when fitting transition mixed models. This is carried out by emphasizing on the role of baseline responses on the estimation process. Transition models are allowed for two cases of exogenous and endogenous baseline responses. We illustrate these concepts in the special case of transition linear mixed models with centered time-varying covariates. Results of our simulation studies show that the omission, or the inclusion, of time-invariant covariates is not important in models with exogenous baseline responses, while it has an essential effect on fitting models with the endogenous baseline responses. It is also emphasized that the effect becomes minor when the endogeneity issue is handled. The practical consequences are illustrated in the analysis of a real data set taken from medical sciences.