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.

  • $\begingroup$ When looking for relationships in the data is it important to take into account multiple variables? All my independent variables are binary so to explain one is "odds of (dependent variable) increases if a person has (independent variable)" that explanation doesn't take into account all of the other variables. Would not taking into account other variables be statistically inferior? $\endgroup$ – Mike May 23 '17 at 17:15

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.

  • $\begingroup$ That makes sense. I guess I'm just confused on how to explain "control" of the other variables. Can you further explain it, please? $\endgroup$ – Mike May 23 '17 at 16:17
  • $\begingroup$ That is such a big topic topic that it requires a book, so no I cannot do it on a forum like this. Fortunately many introductory stats books discuss this topic. Just pick your favorite stats book. $\endgroup$ – Maarten Buis May 24 '17 at 10:54
  • $\begingroup$ Would it be fair to say that adding multiple independent variables in a regression model instead of looking at them independently is more accurate since you should take into account multiple variables when explaining an outcome? $\endgroup$ – Mike May 25 '17 at 17:51
  • $\begingroup$ If the answer was that easy, then it would not require a book... $\endgroup$ – Maarten Buis May 26 '17 at 7:46

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