A finite mixture model for multivariate counts under endogenous selectivity

Authors:
Marco Alfò;Antonello Maruotti;Giovanni Trovato
Affiliations:
Dipartimento di Statistica, Probabilità e Statistiche Applicate, "Sapienza" Università di Roma, Rome, Italy 00185;Dipartimento di Istituzioni Pubbliche, Economia e Società, Università di Roma Tre, Rome, Italy 00145;Dipartimento di Economia e Istituzioni, Università di Roma "Tor Vergata", Rome, Italy 00133
Venue:
Statistics and Computing
Year:
2011

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Abstract

We describe a selection model for multivariate counts, where association between the primary outcomes and the endogenous selection source is modeled through outcome-specific latent effects which are assumed to be dependent across equations. Parametric specifications of this model already exist in the literature; in this paper, we show how model parameters can be estimated in a finite mixture context. This approach helps us to consider overdispersed counts, while allowing for multivariate association and endogeneity of the selection variable. In this context, attention is focused both on bias in estimated effects when exogeneity of selection (treatment) variable is assumed, as well as on consistent estimation of the association between the random effects in the primary and in the treatment effect models, when the latter is assumed endogeneous. The model behavior is investigated through a large scale simulation experiment. An empirical example on health care utilization data is provided.