Power-Transformation for Ordered Categorical Data

We consider in this paper a model of asymmetric power-transformation of response probability explained by linear function of some covariates. This model includes logistic and complementary log-log transformation models as its specific case, so we can use the model to evaluate the appropriateness or the goodness of fit of these models. Then the performances of the asymmetric power-transformation model are evaluated and examined, based on data used in published literatures. And we discuss various issues of diagnoses which may occur in the process of applying the model. Further we consider alternative transformations, and then in comparison with them, we point out the advantages of the asymmetric power-transformation.