# model fit in logistic regression

I have developed a model for simple logistic regression with 1 independent ordinal variable and 4 binary independent variables. The model gives 64% correctly predicted cases, a Nagelkerke r2 of 12% and Hosmer-Lemeshow 0.125. I used forward stepwise LR where all variables were included in the equation, but if I leave out one of the variables I get 68% correctly predicted cases, nagelkerke 25% and Hosmer Lemeshow 0.450. Would you stick to the first model or in this circumstance leave out the variable for a better fit of the model...?

• Did you do any cross-validation or the like to account for your model building? Otherwise the fit statistics you get are probably quite meaningless and any seemingly better fit may just be overfitting. – Björn Mar 14 '16 at 10:46
• Yes I did, using crosstabs. Please see comment below from prof. Harrell; what about the nagelkerke..? – schvost Mar 14 '16 at 13:42

Formulate a model, pre-specified using subject matter considerations. Otherwise you need to use data reduction (masked to $Y$) or penalization. You didn't state the frequency of levels of $Y$.