Please help for interaction terms multiple regression for panel data

[Arindam Pal]

Hi all,
I am doing a multiple regression using two independent variable (x1, continuous variable and x2, binary variable) and an interaction term of x1*x2. I also have a host of other control variables too. So in the 1st case I am using model as (Y=x1+ controls) (Y=x2+ controls) and (Y=x1*x2+ controls) I am getting perfect results. But when I am using model (y=x1+x2+x1*x2+ controls) , I am not getting expected results. The results are quiet different from earlier models and multi-colinearity is also high. How to reduce that and get results similar to the individual models? Plz help me out.

[Maarten Buis]

The model (Y=x1*x2+ controls) is very problematic as it assumes that the main effects are zero, which is clearly not the case (otherwise, you would not see a difference in the model (y=x1+x2+x1*x2+ controls) ). So you should forget you ever estimated that model.

It is hard to comment on your last model as you did not go into details as to how the pattern you observed differed from the pattern you expected, nor on the exact content of your explanatory variables. As so often in such cases, the devil is in the detail. However, I suspect that there is nothing wrong with your last model, except for your interpretation of the results. Multi-colinearity is not a problem in such model, it correctly indicates the amount of information present in your data to estimate that model (which may be less than you would have liked, but such is life). Notice that such models are often easier to understand when you first center the x1 and x2 variables, such that they have the value 0 at a meaningful value within or near the range of the data.

[Arindam Pal]

Like in the first case--- x1> negative and significant; x2> positive and significant; x1*x2 > positive and significant;

But when I am using (y=x1+x2+x1*x2+ controls) model----- x1> negative and not significant; x2> positive and significant; x1*x2 > negative and not significant. So what should I do ?

[Maarten Buis]

Did you center your explantory variables before creating the interaction term (or better yet, before using the factor variable notation to include the interaction term)?

[Arindam Pal]

No, I haven't done yet.

[Maarten Buis]

Also look at http://www.ats.ucla.edu/stat/stata/faq/catcon.htm