Inferences in Multinomial Dynamic Mixed Logit Models

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In this paper we propose a general multinomial dynamic mixed logits model which explains how a multinomial/categorical response at a given time can be affected by (1) an individual’s categorical fixed covariates, (2) certain category prone random effects, and (3) an individual’s past multinomial responses. This model may be considered as a generalization of the (a) existing multinomial dynamic fixed models to the mixed model setup with category prone random effects; or (b) existing standard random effects based multinomial dynamic mixed models involving past binary responses to the complete multinomial dynamic (depending on past multinomial) setup, or (c) existing multinomial mixed models to the multinomial longitudinal mixed model setup. We use a conditional fixed effects based likelihood approach for estimation of the parameters. An intensive simulation study is carried out to examine the finite sample performance of the estimators under the general dynamic mixed models, as well as under various specialized models. The proposed model and estimation methodology is also illustrated with a real life longitudinal survey data on health, ageing and retirement in Europe. Asymptotic properties such as consistency of the conditional fixed effects based likelihood estimators of the main fixed effects based regression parameters are studied in details.