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Two‐part regression models for longitudinal zero‐inflated count data

Two‐part models are quite well established in the economic literature, since they resemble accurately a principal‐agent type model, where homogeneous, observable, counted outcomes are subject to a (prior, exogenous) selection choice. The first decision can be represented by a binary choice model, modeled using a probit or a logit link; the second can be analyzed through a truncated discrete distribution such as a truncated Poisson, negative binomial, and so on. Only recently, a particular attention has been devoted to the extension of two‐part models to handle longitudinal data. The authors discuss a semi‐parametric estimation method for dynamic two‐part models and propose a comparison with other, well‐established alternatives. Heterogeneity sources that influence the first level decision process, that is, the decision to use a certain service, are assumed to influence also the (truncated) distribution of the positive outcomes. Estimation is carried out through an EM algorithm without parametric assumptions on the random effects distribution. Furthermore, the authors investigate the extension of the finite mixture representation to allow for unobservable transition between components in each of these parts. The proposed models are discussed using empirical as well as simulated data. The Canadian Journal of Statistics 38: 197–216; 2010 © 2010 Statistical Society of Canada