I have a question about binary logistic regression. I have been trying see which IV are the independent predictors of an outcome of a categorical variable in a sample of 680 cases, where 30% of cases are having the outcome of interest (total of ~200 cases). No missing variables.
I have about 50 IV. On univariate analysis, 20 of them are statistically significant (p<0.05). However I have 7 IV that have clinical significance (from previous studies), but did not turn significant in the univariate analyses (p>0.25 in all).
If I do logistic regression on all 27 IV at once, I get 11 variables with p <0.05. Nagelkerke R square value is 0.39, Hosmer and Lemeshow Test is 0.64. None of the SE values are (at least to me) obviously high/different from the rest.
Also, I did the automated forward LR (SPSS), which resulted basically with same eleven variables (with the rest of them removed from the model).
My question is, how can I know if the model is overfitted? In theory, I should have put maximum 20 variables to start with, however it is really hard figuring which ones to remove?
How can I know if a model can sustain testing 27 variables at once?