Is it ok to interpret the sign of an interaction term coeficiente in a logit or probit model with random effects?
being Y binary (e.g. 1 if company i has reduced the employees' monetary incentives in year t, 0 otherwise), X1 is continuous (e.g. return of company i in year t), and X2 is binary (e.g. 1 if company i is a big one).
Suppose b0<0; b1<0; b2>0; b3<0
I believe b3 can be interpreted as the incremental relation between the likelihood of reducing employees' monetary incentives and returns for big companies.
Nonetheless, I have seen some warnings regarding the interpretation of interaction terms in non-linear models. However, I am just interested in the sign and its association with a positive/negative effect in the likelihood of Y and not in marginal effects.
I would also like to ask if there is a meaningful interpretation of the intercept sign in this kind of models. For instance, if b0<0, is it likely that companies have a propensy not to reduce employees' monetary incentives (when not taking into account the rest of the regressors)? I am not sure if this makes any sense.
Thanks in advance.