A novel method for testing goodness of fit of a proportional odds model: An application to an AIDS study

Abstract

Ordinal categorical responses occur commonly in real world situations and many authors discuss the advantages of this type of response. Generalized logit models are popular for analyzing ordinal categorical responses. Of these models, the proportional odds model is the simplest to interpret. However, Lipsitz et al. illustrate that the goodness of fit statistics provided by standard statistical packages for this model may not be reliable in justifying the fit of the model. There is no freely available software for computing and analyzing residuals or expected counts for these models. In their paper, Lipsitz et al. propose several goodness of fit statistics and residual analysis that are suitable for ordinal response regression models. However, the new methods are applied to a small artificial set of data. In this paper, the methods of Lipsitz et al. are examined, programmes developed in SAS and S-plus softwares and the methods applied to a large scale real-life data set on HIV/AIDS/STD. A proportional odds model was fitted to this data and goodness of fit and residual analysis were carried out using the methods of Lipsitz et al. The methods examined suggest that the goodness of the fitted model is satisfactory. According to the methodology, the expected counts, residuals and approximated (standardized) residuals were calculated and the overall goodness of fit of our model and the reliability of the chi-square approximation of the goodness of fit statistics were confirmed.