|Abstract:|| This paper proposes an EM algorithm for semiparametric mixed-effects
models dealing with a multinomial response. In multinomial mixed-effects models, in order to obtain the marginal distribution of the response, random effects need to be integrated out. In a full parametric context, where random effects follow a multivariate normal distribution, this is often computationally infeasible. We propose an alternative novel semiparametric approach in which random effects follow a multivariate discrete distribution with an a priori unknown number of support points, that is allowed to differ across categories.
The advantage of this modelling is twofold: the discrete distribution
on random effects allows, first, to express the marginal density as a weighted sum, avoiding numerical problems typical of the integration and, second, to identify a latent structure at the highest level of the hierarchy, where groups are clustered into subpopulations. The paper shows a simulation study to evaluate the method's performance and applies the proposed algorithm to a real case study for predicting higher education student dropout, comparing the results with the ones of a full parametric method.|