Poisson and negative binomial regression models

In recent years, regression analysis, which is one of the fundamental fields that includes advanced estimation models needed as with the increasing data sizeas a result of the information era, is used more extensively in many disciplines. Although regression analysis is mostly used to estimate a continuous response variable, poisson and negative binomial regression models are increasingly used when the response variable takes discrete and countable values. In this study, study, in addition to poisson and negative binomial regression models with their corresponding models for zero inflated data, which are commonly used in count data, models based on biased estimators such as ridge and Liu estimator, have been examined. In addition to the theoretical properties of the mentioned models, performance comparisons on a real data set have been also performed. A total of 10 different models have been studied within the scope of the study. The performance comparisons of these models have been made with criteria such as Akaike information criterion, log likelihood value, mean squared residuals, and mean absolute residuals. According to the results, zero inflated negative binomial regression model has been found as the most suitable model and coefficient estimation of this model has been obtained. Apart from the coefficient estimations, comments have been given in detail.