I'm computing a multinomial logit model with Biogeme. Looking at the final results, it seems that some variables are not statistically significant when standard errors are considered. However, with robust standard errors, they are all significant. Does anyone know if it make sense in this kind of model consider only the robust standard errors? I don't know if in multinomial logit, as it is different from a linear regression, the use of robust standard errors leads to a different interpretation. Sorry for this silly question
When a model is nonlinear in parameters (like your multinomial logit), the MLE of the parameter vector is both biased and inconsistent if the errors are heteroskedastic, unless you modify the likelihood function to correctly take into account the precise form of heteroskedasticity. This is very different from the linear case. Similarly, the MLE of the asymptotic covariance matrix of the parameters will also be inconsistent. The terms "correctly" and "precise" are key, since it is hard to know exactly what sort of heteroskedasticity you have going on. To make things worse, the bias is also in an unknown direction.
I don't know about Biogeme, but other stats packages have commands that allow you to parameterize the heteroskedasticity.