A finite mixture model for multivariate counts under endogenous selectivity

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.

A two‐part mixed‐effects pattern‐mixture model to handle zero‐inflation and incompleteness in a longitudinal setting

“…While various parametric specification of similar models have been proposed in the last few years, we adopt a finite mixture specification to avoid any unverifiable assumptions upon the random effect distribution and extend the standard treatment by allowing for correlated random effects across equations. A simulation study to ascertain if correlation between random effects can be consistently estimated is provided in Alfò et al (2011). A possible drawback in correlation estimate may arise when correlation is high, i.e.…”

“…Several model specifications have been proposed for the correlation between longitudinal count responses in order to account for potential dependence structures in the data (see e.g. Alfò and Trovato, 2004; Ma et al, 2009; Nikoloulopoulos and Karlis, 2010; Alfò et al, 2011). Here, we consider a mixed‐effects hurdle model (Bago d'Uva, 2006; Alfò and Maruotti, 2010) to account for overdispersion and to account directly for excess zeros, in order to propose a model experiencing less restrictive mean–variance relationships.…”

Handling endogeneity and nonnegativity in correlated random effects models: Evidence from ambulatory expenditure

“…As expected, in small sample size schemes, increasing heterogeneity may strongly affect parameter estimates. This is particularly true for binary-model regression coefficients, as discussed in Alfó et al (2011) and as displayed in Table 6. Parameters associated with the endogenous binary variable are overestimated.…”

“…This type of self-selection is analyzed in this work. Several studies addressed the endogeneity issue related to self-selection (Munkin and Trivedi, 2008;Alfó et al, 2011), but just a few account for both the spike-at-zero and self-selection simultaneously. To the best of our knowledge, to date only Deb et al (2006), Terza et al (2008), and Bratti and Miranda (2011) have addressed both issues in a joint approach.…”

A two-state mixed hidden Markov model for risky teenage driving behavior

“…The shared random effect proposes a rather strong modeling assumption in order to take advantage of an appealing reduction in computational complexity. Using more general correlated random effects approaches is an alternative, but others have found that identification of the correlation parameter is difficult [Smith and Moffatt (1999) and Alfò, Maruotti and Trovato (2011)]. Formal testing for heterogeneity in these models is also a challenging problem [Altman (2008)].…”