EM algorithm for semiparametric multinomial mixed-effects models


Statistical learning
EM algorithm for semiparametric multinomial mixed-effects models
Tuesday 21st July 2020
Masci, C.; Ieva, F.; Paganoni A.M.
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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.
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Masci, C., Ieva, F. and Paganoni, A.M. (2021). ‘Semiparametric multinomial mixed-effects models: a university students profiling tool.’ The Annals of Applied Statistics - in press