# Logistic regression with poor goodness of fit (hosmer lemeshow)?

I built a model with 9 categorical predictor variables. Using SPSS, my omnibus test was significant ($\chi^2$=220.01), my -2loglikelihood was 1335.2 (Nagelkerke $R^2$ 0.231), but my Hosmer and Lemeshow Test was significant (chi-sqr=16.2, p=0.042). My sample size is n=1199.

Is it problematic to proceed with this model, despite lack of fit?

I tried removing one of my binary predictor variables, and noticed that in the new model my Hosmer Lemeshow Test was significant (p=0.198), but my -2loglikelihood increased to 1442.2. Is there a trade off between Hosmer Lemeshow and -2loglikelihood?

How do I decide which model is appropriate?

My method for building this model was originally entering in all my predictor variables of interest, and examining the adjusted ORs of my variable of interest. Is my model a poor fit?

Additionally, how does one go about testing for multicollinearity when your predictor variables are all categorical (in other orders, calculating VIF is not possible). I was told in class that as long as the standard errors of Beta coefficients are less than 2 there is no reason to suspect multicollinearity, but I am not sure if this is sufficient?

To check co-linearities I suggest variable clustering, e.g., the R Hmisc package varclus function.