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RE: RE: st: Gologit, ologit and Akaike's Information Criterion
Prob>LR in -fitstat- is the result of a likelihood ratio test comparing your model with a model with only the intercept, i.e. it is a test whether the parameters of ALL explanatory variables are SIMULTANEOUSLY zero. This is comparable to the F statistic reported for a `normal' (OLS) regression. A significant result only means that the parameter of at least one explanatory variable is different from zero. So I would not use it as a goodness-of-fit statistic.
More generally, I am sceptical about using a single measure of goodness-of-fit (including R^2 and the various pseudo R^2's), and I am not alone in that respect. To quote from the Long and Freese book I recommended earlier (p.88): ``[T]here is no convincing evidence that selecting a model that maximizes the value of a given measure results in a model that is optimal in any sense other than the model having a larger (or, in some instances, smaller) value of that measure.'' Apparently, the authors think this is a very important point since this sentence is printed in italics.
More specifically, Agresti (2002, p. 177) warns that the Hosmer-Lemeshow statistic you mentioned does not have good power for detecting particular types of lack of fit, i.e. you accept models as having a good fit (or more precisely you do not reject the hypothesis that the fit is bad), which should not be accepted.
When assessing model fit, I would do three things: 1) See if your model makes theoretical sense. 2) Test assumptions of your model. For instance, ordered logit assumes proportional odds, which can be tested with the -omodel- command (findit omodel). 3) Estimate more general models, and test restrictions, like gologit instead of ologit (this also is a test for the proportional odds assumption) or a model with more explanatory variables.
This may not be the answer you were looking for, but I hope it still helps,
Agresti, Alan, (2002) Categorical Data Analysis, 2nd edition, Wiley (More comprehensive than the Long and Freese book, but also more terse)
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