Question

How to check for robustness in logit and probit models?

Answer 1

Logit and probit models are non linear probability models where the slope coefficients change inversely with the variance of the disturbances. The dilemna is when a relevant regressor is omitted then the coefficient of other regressors tends to zero and leads to heterogeneity.

Robustness check is simple in case of linear regression but not for non linear models. Misspecifications are common in non probability models, thus heterogeneity check on the estimates is essential to evaluate the robustness of the model. If the errors are hetereoskedastic, the maximum likelihood estimates of the coefficients would be biased and inconsistent.

So, an ideal method is to augment the model and adhere to heteroskedasticity before the parameters of the regressors are estimated then find heteroskedasticity consistent standard errors using appropriate econometrics package then estimate a linear probability model.

Specifically for probit model, one can use hetprobit to test heteroskedasticity and generally an augmented version of LM test can be used for both models.