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# st: Interpreting 3-way binary interactions in svy:logit regression with margins command

 From Lauren Beresford To Statalist Subject st: Interpreting 3-way binary interactions in svy:logit regression with margins command Date Fri, 3 Feb 2012 21:00:55 +0000

```Dear statlisters,
I am estimating logistic regression models (with svy command) with three way interactions between binary ivs.
My final model without controls (for simplicity...) is:
svy:logit mgr i.female i.baplus i.firm1024 i.firm2599 i.firm100499 i.firm500999 i.firm1000 female##firm1024##baplus female##firm2599##baplus female##firm100499##baplus female##firm500999 ##baplus female##firm1000##baplus
To interpret the 3-way interaction I want to calculate the predicted probability of mgr for men and women, treating men as men and women as women (female=0 and1), with and without degrees higher than a BA (baplus=1 and 0) for each category of firm size (e.g., firm1024 - as indicated by the series of binary predictors for firm size).  I then want to calculate the difference that going from baplus=0 to baplus=1 makes for men and then for women respectively for each category of firm size.  I also want to calculate the difference that going from female=0 to female=1 makes across educational categories (baplus=0 and baplus=1).  Finally I want to test that these differences are statistically significant.

I use the margins command as follows:
margins baplus, over(female) at(firm1024==1) vce(unconditional) post
I then calculate the difference that education makes for men as a group and then women as a group using lincom commands, and test the differences in these effects using a lincom command. I do this for each firm size category.

My problem is that I have sifted through extensive documentation and I am confused about which margins command to use.
If I follow the logic put forth in Maarten Buis' Stata tip 87 "Interpretation of interactions in non-linear models" my margins command would look like this:
margins, over(female firm1024 baplus) expression(exp(xb())) vce(unconditional) post
I assume if I wanted predicted probabilities I would just omit expression(exp(xb())).
If I try to emulate the suggestions put forth by ATS UCLA in "How can I understand categorical by categorical interaction in logistic regression? (Stata 11) this leads me to the following commands:
margins baplus, at(female=(0 1) firm1024==1) vce(unconditional) postmargins female, dydx(baplus) at(firm1024==1) vce(unconditional) postmargins baplus,  dydx(female) at(firm1024==1) vce(unconditional) post
Then again, looking at ATS UCLA "How can I use margins to understand categorical by categorical interactions" I am lead to believe I want something like this:
margins female#firm1024, dydx(baplus) vce(unconditional) post
Finally, from the statslist archive I found the following command (msg01503):
margins, over(female firm1024) dydx(baplus) at female=(0 1) firm1024=(0 1)) vce(unconditional) post

Therefore, I am looking for direction as to which margins command is the most accurate to decompose my three way interaction terms.  I appreciate any help.
Kind regards,Lauren Beresford

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