from my knowledge, there are two approaches to evaluating whether the model fits the data in logistic regression. First is the predictive power. Second is from using goodness-of-fit tests.
My question is that if the results from Pearson's chi-square and Hosmer-Lemeshow test are in conflict (one significant, the other insignificant), what should I do next? Try to fit in interactions & non-linearities?
I know these two tests have their limitations. Pearson requires sufficient expected number of events/non-events for each profile or covariate pattern. Conclusion from HL test depend on the number of groups chosen, and there is no established theory to guide the choice of that number. I think the other alternative tests are not implemented in Stata yet.
On a side note, I noticed that many papers actually do not report any tests to assess their models. Why is that so?