A mixed effects model for longitudinal designs considering multiple covariates

Abstract This article discusses a mixed effects logit model that can be viewed as an extension of the so-called linear logistic model (LLTM) by considering additional covariates assumed to have a linear effect on the logits of response probabilities of the persons. Specifically, it gives up the parameter invariance assumption of the original LLTM. The focus of the discussion is on repeated measurement and longitudinal experimental designs. It includes estimation procedures based on a conditional maximum likelihood (CML) approach and statistical tests of various hypotheses derived from asymptotic theory that represent different scenarios on effects of items, time points, and covariates. To illustrate the application of the model, inference on parameters, and interpretation of results, a real-data example from the field of developmental psychology is used. The results of the data example reveal considerable time point effects, but not depending on the covariates considered.