Goodness-of-fit Test in Parametric Mixed-Effects Models based on the Estimation of the Error Distribution

We address the problem of checking the adequacy of a parametric functional form for the fixed effects function in mixed effects models. We propose a test based on the distance between the empirical distribution of the parametric residuals calculated under the null hypothesis and those calculated under the alternative. The proposed method is an extension of the one introduced by Van Keilegom, Gonzalez-Manteiga and Sanchez-Sellero (2008) for cross-sectional independent data i.e. when no random effects are present in the regression model. This formal test is combined for exploratory data analysis purposes with the graphical tool SiZer Map, and applied to longitudinal data analysis.