A Fast Algorithm for Using Semi-Parametric Random Effects Model for Analyzing Longitudinal Data

Mixed effects models are frequently used for analyzing longitudinal data. Normality assumption of random effects distrbution is a routine assumption for these models, violation of which leads to model misspecification and misleading parameter estimates. We propose a semi-parametric approach using gradient function for random effect estimation. In the approach, we relax the normality assumption for random effects by estimating the random effects distribution over a pre-specified grid. Unknown parameters of the marginal model are estimated using maximum likelihood method. Some simulation studies and analyzing of a real data set are performed for illustration of the proposed semi-parametric method.