Abstract
A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.
Highlights
In many applications the response variable of interest is a nonnegative integer or count which one wants to relate to a set of covariates
Before giving details of the fitting procedure we demonstrate the flexibility of the proposed transition model by a small benchmark experiment that was based on 100 replications
Maximum likelihood (ML) estimators tend to fail because model (5) contains many parameters, in particular the number of intercepts becomes large unless the counts are restricted to very small numbers
Summary
In many applications the response variable of interest is a nonnegative integer or count which one wants to relate to a set of covariates. Various methods have been proposed to estimate the parametric effect of covariates on the counts (Cameron and Trivedi 2013). The effect of covariates on the response is modeled by a linear term This enables an easy interpretation of the regression coefficients in terms of multiplicative increases or decreases of the counts. The proposed models are semiparametric in nature, because the distribution of the response is modeled in a flexible way adapted to the data while the effect of covariates is modeled parametrically. A main advantage of the proposed model class is that it can be embedded into the framework of binary regression This implies that standard software for maximum likelihood estimation of generalized additive models (Wood 2006) can be used for model fitting.
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