# What statistical approach to use for this kind of analysis?

I have 1 dependent (continuous) variable, 3 explanatory (continuous) variables and a bunch of control variables. The explanatory variables are my interest variables.I want to do a categorical analysis.

So far, I've conducted a simple categorical analysis through multiple linear regression, where I include my 3 explanatory variables along with 3 additional interaction terms, i.e. I interact my category variable (0 for group 1, 1 for group 2) with my 3 explanatory interest variables to test for a statistically significant difference between the two groups along my 3 interest variables.

Now, however, I want to take into account control variables, i.e. my observed results could equally well be due to an omitted control variable. I could make a regression where I also include the control variables along with the interactions described above. But then, the two groups are only allowed to differ on the explanatory interest variables and none of the control variables, which is not a good solution, unless the two groups are not expected to differ on the control variables. Alternatively, I could include the control variables along with the interactions described above, plus interactions between the categorical variable and all the control variables. In this way, the two groups are allowed to differ on all the control variables, and I can "isolate" the effect of the explanator interest variable that is unique to each group. Yet there are also problems with this method, i.e. artificial multicollinearity. So both method (1) and method (2) could result in inappropriate results. As a third alternative, I've also considered ANCOVA. As far as I can tell from the Internet, however, this test is best suited for analysis of categorical variables alone, whereas I am interested in the interaction between the categorical variable and the explanatory interest variable. But could it work?

I hope anyone can help me resolve this issue! Thanks a lot guys

• Have you thought about utilizing a factorial design for this analysis? Are your three explanatory variables factors or just continuous numerical data? There is also difference-in-differences, which would treat your group variable as a binary variable in your model. – small_data88 Jul 21 '15 at 12:33
• Thanks for your answer, small_data88! You mention "factorial design", do you then mean some kind of ANOVA (i.e. one-way ANOVA)? But I don't think ANOVA would do the trick here, because I have 1 "factor" (my 0-1 category) and I am not interested in how this factor - in and of itself - differ with respect to DV. Rather, I am interested in how the factor (the two groups) interacts with the 3 explanatory interest variables to determine the level of the dependent variable. To answer your question, my 3 explanatory interest variables are continuous (ratio). – Daniel Jul 21 '15 at 13:19
• You're welcome! Yes, I was talking about some kind of ANOVA when I mentioned 'factorial design'. Have you looked into difference in differences? I haven't used it in a while, but I believe you would set up your model as: y=intercept + var1 + var2 + var3 + var1*group + var2*group + var3*group, where group is a 'dummy' variable taking 1 or 0. Then run the regression with this model. So, you would end up with the long form of the model for treatment and a shorter model for control . It sounds like you might have done this already, but I'm not sure. – small_data88 Jul 21 '15 at 14:17
• That's exactly what I've done (DD). But I would like to add control variables to the model, controlling for effects of other variables simultaneously. But if I ignore interactions between my category and control variables in the model, the groups not allowed to differ on the control variables, which could bias the results. That is, I might observe a significant interaction effect between the category and the 3 interest variables, but the effect is due to omitted variable bias, i.e. the same effect would not be observed if an interaction between the category and a control variable was allowed. – Daniel Jul 21 '15 at 15:01
• (continued...) The possible solution could be to let all parameters float freely, i.e. you allow the two groups to differ on (that is, interact with) the entire list of control variables. This is basically the same as performing two individual regressions and compare the coefficients. But as I mentioned in my post, this can lead to other problems as well (multicollinearity). Furthermore, I wonder if my solution would be a scientifically correct way of dealing with my research goal. – Daniel Jul 21 '15 at 15:02