What does the * in Proc Logistic: Model signify?

[SASy_andIknowit]

If the model is:

model outcome = race  income  black_perc  race*income; <--- what does the "  *  " between the two variables signify exactly?

Ideally I would like to control for income, so is this being achieved?

Also, is there meaning to the odds ratio for a continuous variable like black_perc or income i.e. how exactly would I interpret the parameters coming from the aforementioned model?

(note: black_perc signifies percentage of population in the neighborhood that's Black or African American)

[Reeza · Accepted solution]

It's an interaction term, race x income.

You would not report the parameters specifically, you would report oddsratios, you can get oddratios from an oddsratio statement, especially with interaction terms.

https://stats.idre.ucla.edu/sas/output/proc-logistic/

[SASy_andIknowit]

From the link:

We can interpret the odds ratio as follows: for a one unit change in the predictor variable, the odds ratio for a positive outcome is expected to change by the respective coefficient, given the other variables in the model are held constant

So that means for a continuous predictor variable like income, increasing income by one unit corresponds to a change in the Odds Ratio equal to the coefficient (parameter) ? Is that an incorrect interpretation (sorry for turning this into a stats question)

[Reeza]

Yes, which is there is also a UNITS statement within PROC LOGISTIC. So you can calculate the change for 10K or whatever increment makes sense for your data.

Check the docs here:
https://documentation.sas.com/?docsetId=statug&docsetTarget=statug_logistic_syntax36.htm&docsetVersi...

[SASy_andIknowit]

Ok, I'm looking at the link and found the appropriate sub section, but it will take time to digest, so while I still have you (and I promise to throw you an accepted solution), it seems that it would be best to co-vary race and income, and keep race and black_perc as binary and continuous predictor, respectively. Now when I run the logistic regression by neighborhoods, it seems to pick an income specific to that neighborhood through which to compare the odds ratios of binary variables (e.g. black1 vs white1 at Income1, black2 vs white2 at Income2, black3 vs white3 at Income3, etc). My last question is, would you happen to know how that neighborhood specific income is determined?

[Reeza]

Your categorical variables belong in a CLASS statement. You need to also specify the parameterization (REF is the general recommendation) and the reference level.
There's a couple of fully worked examples here and in the documentation under Examples. There's specifically one with categorical variables that you may want to review.

https://stats.idre.ucla.edu/unlinked/sas-logistic/proc-logistic-and-logistic-regression-models/

Additionally, I recommend actually running some of those examples (full data and code is available) and ensure you get the same output and know how to interpret the odds ratio's correctly.
You specify what levels you want for odds ratio within the odds ratio statements. And recall you will always have N-1 parameters for a categorical variable.


*PS I don't really care about getting an accepted solutions and such, but thanks for the offer :).

[SASy_andIknowit]

Thank you so, so much. I do have class race (ref='White')/param=ref;  because my professor quickly typed up the procedure and left me to my own devices to report the result (before I've taken a formal class on regression analysis). I was just hoping for a quick answer to interpret the results so I can finalize for my project, but I guess I need to take the time to dig deeper into the procedure. Thanks for your help, remote professor 😉