I am running a logistic regression with multiple variables. When I add variables to my model the odds ratio estimates decrease. When looking at colinearlity there are some variables that have .3 or .2. All independent variables are binary so this seems like it is bound to happen. Since some odds ratios on their own are for example 2.8 but then when put into the model with other variables they shrink to 1.1 should the odds ratio in the model be used or should I simply pull up cross tabs and do the odds ratio for the independent variables all separately? My other question is that when adding more variables the odds ratio decreaes a bit but the model c statistic increases which seems to be very important.
I assume you added those other variables to your model because you wanted to control for them. If that is the case, then those smaller odds ratios are the odds ratios you want. There is no guarantee that effects will get bigger if you control for other variables; they could very well get smaller, as happened in your case. If you don't want to control for those other variables, then you can just look at the two dimensional cross tabulation. In fact the odds ratio you get out of that will be the same as the odds ratio in logistic regression without other control variables.