A multinomial mixed-effects model with discrete random effects for modelling dependence across response categories
Wednesday 27th April 2022
Masci, C.; Ieva, F.; Paganoni, A.M.
We propose a Semi-Parametric Mixed-Effects Multinomial regression model to deal with estimation and inference issues in the case of categorical and hierarchical data. The proposed modelling assumes the probability of each response category to be identified by a set of fixed and random effects parameters, estimated by means of an Expectation-Maximization algorithm. Random effects are assumed to follow a discrete distribution with an a priori unknown number of support points. For a K-category response, this method identifies a latent structure at the highest level of grouping, where groups are clustered into (K-1)-dimensional subpopulations. This method is an extension of the multinomial semi-parametric EM algorithm proposed in the literature, in which we relax the independence assumption across random-effects relative to different response categories. Since the category-specific random effects arise from the same subjects, their independence assumption is seldom verified in real data. In this sense, the proposed method properly models the natural data structure, as emerges by the results of simulation and case studies, which highlight the importance of taking into account the data dependence structure in real data applications.