Semiparametric multiple inflation count model with application to a smoking cessation study.

Count data are observed by practitioners across various fields. Often, a substantially large proportion of one or some values causes extra variation and may lead to a particular case of mixed structured data. In these cases, a standard count model may lead to poor inference of the parameters involved because of its inability to account for extra variation. Furthermore, we hypothesize a possible nonlinear relationship of a continuous covariate with the logarithm of the mean count and with the probability of belonging to an inflated category. We propose a semiparametric multiple inflation Poisson (MIP) model that considers the two nonlinear link functions. We develop a sieve maximum likelihood estimator (sMLE) for the regression parameters of interest. We establish the asymptotic behavior of the sMLE. Simulations are conducted to evaluate the performance of the proposed sieve MIP (sMIP). Then, we illustrate the methodology on data from a smoking cessation study. Finally, some remarks and opportunities for future research conclude the article.