Semiparametric mixture models for multivariate count data, with application

Abstract

The analysis of overdispersed counts has been the focus of a wide range of literature, with the general objective of providing reliable parameter estimates in the presence of heterogeneity or dependence among subjects. In this paper we extend the standard variance component models to the analysis of multivariate counts, defining the dependence among counts through a set of correlated random coefficients. Estimation is carried out by numerical integration through an EM algorithm without parametric assumptions upon the random coefficients distribution. The proposed model is computationally parsimonious and, when applied to a real dataset, seems to produce better results than parametric models. A simulation study has been carried out to investigate the behaviour of the proposed models in a series of empirical situation

A finite mixture model for multivariate counts under endogenous selectivity

“…Similar finite mixture models have been successfully used to model overdispersed counts and may outperform mixed models based on parametric specifications, particularly when extreme (very high or very low) intensity users are present, see e.g. Deb and Trivedi (1997), Deb and Holmes (2000), Alfò and Trovato (2004). Finite mixture models have several significant advantages over parametric mixture models; first, the discrete nature of the estimate helps to classify subjects in clusters characterized by homogeneous values of random parameters.…”

“…Estimates obtained by using a bivariate Poisson log-Normal model, see Munkin and Trivedi (1999), are shown in Table 2, while parameter estimates obtained using the semiparametric approach developed by Alfò and Trovato (2004) are displayed in Table 3; in both cases parameter estimates for the mixed logit modeling private insurance are shown. Since the effect of private insurance, assuming endogeneity can not be identified without introducing legitimate ex- It is worth noticing that the first location corresponds to low frequencies which represent people who either do not use health care services or use them very rarely, while the second and third locations correspond, respectively, to very high and high frequencies of health care utilization.…”

“…Uni-factor models have been proposed as well, for example the bivariate negative binomial of Winkelmann (2000c). Semiparametric multivariate alternatives with unspecified G(·) are discussed in Alfò and Trovato (2004). Given the model assumptions, the likelihood function conditional on the selection variable can be written as follows:…”

“…Meligkotsidou (2006, 2007), latent effect models, see e.g. Chib and Winkelmann (2001), Alfò and Trovato (2004), and copula-based models, see e.g. Harry (1997), Nikoloulopoulos and Karlis (2006), Zimmer and Trivedi (2006).…”

“…In this case, parameter distinctiveness does not hold and the likelihood can not be factorized; therefore, we need to account for potential dependence of the selection variable on the random effects in the primary outcomes equations. An additional purpose of this work is to ascertain if correlation between random effects can be consistently estimated within this framework; analyzing bivariate binary responses, Smith and Moffatt (1999) found that the correlation parameter could not be estimated with enough precision, while Alfò and Trovato (2004) show different results in the bivariate count data context.…”