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When count data exhibit excess zero, that is more zero counts than a simpler parametric distribution
can model, the zero-inflated Poisson (ZIP) or zero-inflated negative binomial (ZINB)
models are often used. Variable selection for these models is even more challenging than other
regression situations because the availability of p covariates implies 4p possible models. We
adapt to zero-inflated models an approach for variable selection that avoids the screening of all
possible models.
As an additional novelty, we propose a new way of extracting information from a rich chain
of covariates, this approach is based on a stochastic search through all regression models with
all available covariates. We fit a binary indicator of the inflation, which generates a first subset
of covariates for the zero part. Poisson and Negative Binomial models are fitted to generate a
second chain of covariates for the count part. Finally, a backward elimination algorithm is used
to fit a zero-inflated model. an application on automobile insurance data is described. Finally,
A simulation study is conducted to assess finite-sample behaviour, where we also compare our
approach with regularization (penalized) techniques available in the literature.
