R-square and interactions (multiple regression)

[williaml]

Hi,

I am doing a GLM regression analysis and have a question about interactions and model fit.

My dependent variable is 'salary', and I have the independent variable as 'years in the workforce'. However, there are data from male and female subjects which could be important. I have included 'gender' as a dummy variable in the analysis, as well as the "gender*years worked" interaction.

I understand how to interpret the beta regression coefficients, but have a question on the model fit (R-square). Let's assume the interaction is statistically significant: my thought is that it would be appropriate to rerun the analysis with male and female separately to obtain 2 different R-squared values. But is the incremental increase in R-squared that accompanies the (significant) interaction useful, and how is it interpreted?

Thanks
William

[Dragan]

Hi,

I am doing a GLM regression analysis and have a question about interactions and model fit.

My dependent variable is 'salary', and I have the independent variable as 'years in the workforce'. However, there are data from male and female subjects which could be important. I have included 'gender' as a dummy variable in the analysis, as well as the "gender*years worked" interaction.

I understand how to interpret the beta regression coefficients, but have a question on the model fit (R-square). Let's assume the interaction is statistically significant: my thought is that it would be appropriate to rerun the analysis with male and female separately to obtain 2 different R-squared values. But is the incremental increase in R-squared that accompanies the (significant) interaction useful, and how is it interpreted?

Thanks
William

Your GLM is an ANCOVA (analysis of covariance). That is, you're regressing a dependent variable on a continuous independent variable and a categorical variable (gender).

Now, one of the assumptions underlying ANCOVA is that the within group regression slopes are equal (i.e. for both men and women).
What the significant interaction term is indicating to you is that there is a slope/treatment interaction i.e. the regression slopes are different for men and women, and thus, you’re violating the assumption of homogeneity of regression slopes.

Your approach of conducting separate analyses is appropriate, however, if needed there are other options such as the Johnson-Neyman procedure.