Model choice for regression models with a categorical response

The multinomial logit model and the cumulative logit model represent two important tools for regression modeling with a categorical response with numerous applications in various fields. First, this paper presents a systematic review of these two models including available tools for model choice (model selection). Then, numerical experiments are presented for two real datasets with an ordinal categorical response. These experiments reveal that a backward model choice procedure by means of hypothesis testing is more effective compared to a procedure based on Akaike information criterion. While the tendency of the backward selection to be superior to Akaike information criterion has recently been justified in linear regression, such a result seems not to have been presented for models with a categorical response. In addition, we report a mistake in VGAM package of R software, which has however no influence on the process of model choice.