Identifying the Most Appropriate Order for Categorical Responses

Categorical responses arise naturally from various scientific disciplines. Under many circumstances, there is no predetermined order for the response categories and the response has to be modeled as nominal. In this paper we regard the order of response categories as part of the statistical model and show that the true order when it exists can be selected using likelihood-based model selection criteria. For predictive purposes, a statistical model with a chosen order may perform better than models based on nominal responses even if a true order does not exist. For multinomial logistic models widely used for categorical responses, we show the existence of theoretically equivalent orders that are indistinguishable based on likelihood criteria and discover the connections between their maximum likelihood estimators. We use simulation studies and real data analysis to confirm the needs and benefits of choosing the most appropriate order for categorical responses.