Zero truncated regression models and their application

In this study; some crime data of Turkish Statistic Institute between 2009 and 2013 were used and regression methods were compared by using two different dependent variables. These crimes were reorganized into seven geographical regions. The crime rates of the regions were compared with reference to the Mediterranean Region, and the years were compared with reference to 2009. In this study, the performance of classical methods (Poisson, negative binomial) and zero truncated methods were compared. When the dependent variable was considered as "sexual crimes", the best model was found to be zero truncated negative binomial . When the dependent variable is taken as "bad treatment", it is concluded that zero truncated Poisson regression is the best method. In the modeling of the dependent variable which is obtained from positive count data with an average of more than 5, it has been shown that the methods with zero truncated produce similar results with classical methods. Regarding the dependent variable modeling with a mean of less than 5, it is determined that zero truncated regression methods give the best results. If there is overdispersion in the dependent variable, negative binomial regression methods are obtained as the most appropriate methods. The relationship between the parameter estimates and the crimes was examined and the change of these crimes by years and regions was interpreted. AIC and BIC values were used to determine the best model.