Finite mixtures of regression models for longitudinal data

Individual-specific, time-constant, random effects are often introduced in model specification to account for dependence and/or omitted covariates in regression models for longitudinal data. This approach has been frequently criticized as it would not be robust to the presence of correlation between the observed and the unobserved covariates. Often, this is felt as a reason to chooose the fixed effect estimator instead. Starting from the so-called correlated effect approach, we argue that the conditional random effect distribution may be estimated non-parametrically by using a discrete distribution, leading to a general solution to the problem. The effectivenes of the proposed approach is shown via a large scale simulation study.