respectively. As a remark, the over-dispersion parameters are in general not comparable as they relate to different
dispersion forms.
The zero-inflated models can be extended to accommodate covariates in a regression setting. The estimation of
the proportion of zeros and the parameters can be divided into two parts. A logit part can be used to model the odds
of structural zeros proportion and a Poisson part to model the counts that follow the Poisson distribution. Covariates
could enter both the logit part and the Poisson part (Lambert, 1992). For ease of interpretation in current setting