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.
