Bayesian ridge estimators based on a vine copula-based prior in zero-inflated Poisson and zero-inflated negative binomial regression models

Zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models account for excess zero observations in count data. However, a challenge when using ZIP and ZINB is multicollinearity, which occurs when explanatory variables are highly correlated. In the presence of multicollinearity, ridge regression is an effective approach in which ridge estimators are also interpreted as the Bayesian posterior mean (or median) under a multivariate normal prior. However, the traditional multivariate normal prior may not effectively provide the posterior for the regression coefficients, especially in the presence of interaction terms. This study proposes vine copula-based priors that lead to novel Bayesian ridge estimators for ZIP and ZINB regression models. The simulation shows that the proposed estimator is more accurate than the existing frequentist estimators for the ZIP and ZINB regression models. We also observe that the Clayton and Gumbel copula priors provide more efficient estimates than the multivariate normal or Gaussian copula prior.