Poisson regression model and an application to divorce statistics in Turkey

ABSTRACTThe aim of this study is to apply Poisson regression models to the data of divorce statistics inTurkey between the years of 1989 and 1998. Firstly, the basic theory underlying regressionanalysis has been given. Basically there are two types of regression models: Linear modelsand nonlinear models. Poisson regression can be accepted as a specific type of nonlinearregression model. Poisson regression analysis is a regression technique available for modelingdependent variables that describe count data. For Poisson distribution, the mean and thevariance are equal. However, usually in this kind of applications the problem ofoverdispersion is faced, namely, the variance is larger than the mean. When overdispersionoccurs, there are two strategies to overcome this problem: The first way is to estimate a scaleparameter, and with the scale parameter adjusting the test statistics and residuals. The secondway is to refer to negative binomial regression models.The parameter estimators related to Poisson regression model are calculated by iterativelyreweighted least squares and the maximum likelihood methods. To find out the best statisticalmodel that fits data well, goodness of fit measures and residuals analysis techniques areemployed. In Poisson regression models, typically, the model with the least deviance is thecandidate to be chosen as the best model.S-PLUS 2000 programme is used while calculating residuals, goodness of fit measures andparameter estimations for the application of divorce data. In the part of application, divorcedata are tried to be modeled by the Poisson regression.Keywords: Poisson Regression, Divorce, Linear Regression, Nonlinear regression, NegativeBinomial Regressionxiii