Interaction terms, (un)wise to always include them if they lead to a higher R squared

[Victoria Rogers]

Dear readers,

I'm wondering if it's either wise or unwise to always include interaction terms if they lead to a higher R-squared and always exclude them when they don't give you a higher R-squared.

Can someone clarify that?

[Sebastian Kripfganz]

As a matter of fact, the R-squared always increases by adding ANY regressor with non-zero coefficient. Better look at the adjusted R-squared that compensates for the number of additional regressors.

First of all, however, you should ask yourself if there is any economic reasoning for including interaction terms. Economic theory should guide you in selecting appropriate econometric models.

[Victoria Rogers]

I also expected that the R-squared would always increase by adding more variables, however, after I ran the regression with the interaction term, the overall R-squared didn't increase,,,maybe it did increase from 0.510204 to 0.510213 so the rounded R-squared remained the same (0.5102)

In some cases it's clear if there's economic reasoning or not, in my case it's not clear at all unfortunately.

I also know that adjusted R-squared is better, however, the xtreg-commands do not show the adj. R2. I've searched a few hours how to get the adj. R2 after xtreg but I couldn't find it. Only ways to calculate it manually. For xtreg RE everyone should use the overall R-squared, but for xtreg FE some people claim that everyone must use the within R-squared and some say you need to use areg for that.

[Carlo Lazzaro]

Victoria:
I second Sebastian's advice.
Besides, it is difficult to say anything about your query without further details.
For what I can get from your message:
-you added an interaction term among the predictors of your linear panel data analysis (fe or re? Did you perform an Hausman test on which one is the best for your research goal?);
- the overall R-squared did not change substantively (but you do not provide any detail about the significance of the interaction term; it may well be the the interaction term is redundant).

Things would be easier if you report exactly what you typed and what Stata gave you back (as per FAQ).

Kind regards,
Carlo

[Victoria Rogers]

Thank you for the help.

I did perform Hausman tests to check which model I needed to use. It turned out to be re, which I expected due to the time-invariant variable gender I'm interested in. However, after adding many different dummies to control for a lot of fixed effects (i.firm i..industry i.month i.year) the -xttest0- indicates that there's no random effect anymore (due to the dummies the fraction of variance due to u_i becomes 0) and that I should use OLS instead of -xtreg re-

Please give your opinion on: http://www.statalist.org/forums/foru...i-month-i-year

The lowest p-value of the 4 interaction variables I used is 0.132. There's no economic reasoning behind the use of these interactions in my case. I just assumed that it would be statistically better but now I think they're indeed redundant. (I combined gender with things like market risk premium)

[Carlo Lazzaro]

Victoria:
- thanks for providing further details (reporting Stata code and output would have been preferable, though);,
- I am not clear about your approach of performing Hausman's specification test first, then add other predictors and eventually skip Hausman's test on the new model and rely on -xttest0-
- I have just given my opinion on: http://www.statalist.org/forums/foru...i-month-i-year;
-I am not clear about the meaning of

statistically better

. It seems like you were hunting for other predictors for window-dressing the right hand side of your panel data regression.
- I second your opinion of getting rid of interaction terms.

Kind regards,
Carlo

[Victoria Rogers]

I didn't skip the Hausman test on the model with all the different dummy types (i.industry etc.). The result of the new model is the same as the result of the old model, to use -xtreg re-. However after the Hausman test I used -xttest0- and that indicated that I shouldn't use the random effect model because the random effect 'disappears' after adding the dummies.

Yes by statistically better I meant that I was hunting for more predictors.

I think it's better to continue in my other thread/topic because this problem corresponds a lot less with this topic (title) compared with my other topic.

[Carlo Lazzaro]

Victoria:
see my reply at http://www.statalist.org/forums/foru...i-month-i-year.

As recommended, please post what you typed and what Stata gave you back. Thanks.

Kind regards,
Carlo

[Victoria Rogers]

Carlo,

Please see my reply at http://www.statalist.org/forums/foru...i-month-i-year.

Kind regards,

Victoria

[Richard Williams]

If the interaction terms are statistically insignificant and if there was no clear reason for including them in the first place, I would just drop them.

[Victoria Rogers]

Ok thank you Richard. Could you also give your opinion on my other topics please.