Evaluation of goodness of fit test for the proportional odds logistic regression model via simulation

Ordinal logistic regression model is used when the effect of ordered categorical response variables and explanatory variables is modeled. Proportional odds logistic regression model is the most commonly used model among the ordinal logistic regression models. In all logistic regression models, it is necessary to assess whether the model is adequate for data fit. Various goodness of fit tests can be used for this purpose. The goodness of fit tests developed in proportional odds logistic regression models are Lipsitz test statistics, Pulkstenis&Robinson test statistics and Fagerland&Hosmer test statistics. This thesis aims to compare the performance of the goodness of fit tests developed in proportional odds logistic regression models with the simulation study. For this purpose, models have been established under various scenarios. The performance of the models, which was created by R software, was evaluated in terms of type I error, power and adjusted power. The goodness of fit tests generally have low adjusted power values, except for the model containing interaction term. Pulkstenis&Robinson tests and Lipsitz tests are better to performance detect lack of fit than Hosmer&Fagerland test. As the sample size increases, the performance of each goodness of fit test to detect lack of fit is increased.