Interaction term with categorical predictors with more than one level

Question

I am looking at the interaction between education (LTHS, HS, SOME COLLEGE, COLLEGE) and race (WHITE, BLACK, HISPANIC, ASIAN, NATIVE AMERICAN). I am using SAS and am including a class statement in my proc genmod (it is a linear binomial model). I am so confused by the output. It gives me estimates for the following:

Less than high school*African American

Less than high school*Hispanic

Less than high school*Asian

Less than high school*Native American

High school*African American

High school*Hispanic

High school*Asian

High school*Native American

Some college*African American

Some college*Hispanic

Some college*Asian

Some college*Native American

So what's the reference category? I thought at first it was college-White, but that's not it because it doesn't give me estimates for any of the other races at the college level or whites at the other levels of education. In addition, I am calculating risk differences and when I subtracted mortality per 100,000 in one of the groups from mortality per 100,000 in college educated Whites, it didn't match the betas for risk differences. I think the reference group is anyone who is either white or college educated, but that doesn't seem right.

Does anyone have experience with categorical predictors with >2 levels and interaction? What is the appropriate reference group and how do you specify that in SAS?

Answer 1

The estimates for education = college and race != white and the estimates for race = white with education != college can be found from linear combinations of the variables that are output. I am guessing that the main effect estimates for education and race are also included in your output even though you did not include it in your question. The notation below might help you with that...

Notation:

$$Y = \beta_0 + \sum_{j=1} \beta_{1,j}*Education_j + \sum_{k=1} \beta_{2,k}*Race_k + \sum_{j=1,k=1} \beta_{3,j,k}*Education_j*Race_k + \epsilon$$

$$Y_{college, white} = \beta_0$$ $$Y_{LTHS, white} = \beta_0 + \beta_{1,LTHS}$$ $$Y_{college, Asian} = \beta_0 + \beta_{2,Asian}$$ $$Y_{LTHS, Asian} = \beta_0 + \beta_{1,LTHS} + \beta_{2,Asian} + \beta_{3,LTHS,Asian}$$

Answer 2

This was partially answered in the comments. The simplest solution is to add /diff to the lsmeans statement. It gives you all the subgroup differences and their CI. You can then choose whichever comparison you need.

proc genmod data=other ; class educ3 (ref="College") race2 (ref=" Non-hispanic white") age_binary (ref='0') id/param=glm; model inddea= educ3 race2 age_binary educ3race2 / link=identity dist=poisson wald type3 ; repeated subject=id / type=ind PRINTMLE; lsmeans educ3 educ3race2 /cl diff ; weight wt; ods output lsmeans=lsmeans estimates=estimates parameterestimates=betas modelanova=type3 ; run;