Dear all:

My name is Siyu. I am running a random-effects logit model involving many interaction terms. The model syntax is as follows:
xtlogit author c.ideodist##c.constraint_sd##i.statCase c.ideodist##c.bills_lag##i.statCase c.ideodist##c.divma_lag##i.StatCase i.cj c.saj c.newexpmx effnatct i.median##c.xmargin c.xmargin##c.ideodist c.xmargin##i.cj c.early_salience_est##i.cj c.early_salience_est##c.ideodist i.legalimp##c.ideodist i.legalimp##i.cj i.legalimp##c.newexpmx c.xdays##c.ideodist c.xdays##i.cj c.xdays##c.effnatct,re



The model output suggests that c.ideodist##c.constraint_sd##i.statCase and c.ideodist##c.divma_lag##i.StatCase are statistically significant, which supports my hypotheses.

Should I trust the p-value associated with these three-way interactions? Or should I perform separate Wald-test as some reviewers suggest. If I do need to test separately, what would be the proper syntax? Existing Q&A here do not seem to provide a satisfactory answer. What is more complicated is that "ideodist" also appears in multiple other interaction terms. But I am only interested in if the three-way interactions are statistically significant.

Appreciate your comments and answers!
Best,
Siyu