CNTSELECT Procedure

The CNTSELECT (count regression) procedure analyzes regression models in which the dependent variable takes nonnegative integer or count values. The dependent variable is usually an event count, which refers to the number of times an event occurs. For example, an event count might represent the number of ship accidents per year for a given fleet. In count regression, the conditional mean of the dependent variable is assumed to be a function of a vector of covariates .

The models that PROC CNTSELECT supports can contain main effects that consist of both continuous and classification variables and interaction effects of these variables. The models can also include constructed effects such as splines. The procedure offers effect-selection methods along with capabilities for customizing the model selection process by using various selection and stopping criteria.

The Poisson (log-linear) regression model is the most basic model that explicitly takes into account the nonnegative integer-valued aspect of the outcome. For this model, the probability of an event count is determined by a Poisson distribution, where the conditional mean of the distribution is a function of a vector of covariates. However, the basic Poisson regression model is limited because it forces the conditional mean of the outcome to equal the conditional variance. This assumption is often violated in real-life data. Negative binomial regression is an extension of Poisson regression in which the conditional variance can exceed the conditional mean. Also, a common characteristic of count data is that the number of zeros in the sample exceeds the number of zeros that are predicted by either the Poisson or negative binomial model. Zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models explicitly model the production of zero counts to account for excess zeros and also enable the conditional variance of the outcome to differ from the conditional mean.

In zero-inflated models, additional zeros occur with probability , which is determined by a separate model, , where F is the normal or logistic distribution function that results in a probit or logistic model and is a set of covariates.