Title: Semiparametric multinomial mixed-effects linear models: An expectation-maximization algorithm
Authors: Chiara Masci - Politecnico di Milano (Italy) [presenting]
Francesca Ieva - Politecnico di Milano (Italy)
Anna Maria Paganoni - MOX-Politecnico di Milano (Italy)
Abstract: An expectation-maximization algorithm is proposed for semiparametric mixed-effects linear models dealing with a multinomial response. Multinomial Linear Mixed-effects Models (MLMMs) are often treated as multivariate models, where the integration issues typical of generalised linear mixed-effects models grow in complexity. In MLMMs, 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 a 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 related to the integration and, second, to identify a latent structure at the highest level of the hierarchy, where groups are clustered into subpopulations. We show a simulation study and we apply the proposed algorithm to a real case study for predicting higher education student dropout, where students are nested within engineering degree programmes, comparing the results with the ones of a full parametric method.