Question 1: Since the Logit and Probit models are so similar, what is the deciding factor when trying to determine which model is more robust? Or at that point, is it just personal preference?
Question 2: I want to make sure I am correctly understanding the 'mfx' function in Stata and the math behind marginal effects. My understanding is that the marginal effects represents how much the dependent variable is expected to change when one independent variable increases by one unit, with other variables held constant. So is it correct to say that the marginal effect is expressed mathematically as the partial derivative of the expected value of the dependent variable with respect to the independent variable of interest?
Question 3: There are two ways to measure the fit of a LPM, probit or logit model: the fraction correctly predicted or the pseudo-R-squared. The textbook says that the pseudo-R-squared is subject to the same upward bias as the unadjusted R-squared, in that adding more regressors increases the value of the maximized likelihood. Is there an adjusted-pseudo-R-squared? Furthermore, the textbook says, "This suggests measuring the quality of fit of a probit model by comparing values of the maximized likelihood function with all the regressors to the value of the likelihood with none." I'm having trouble understanding what that means. I appreciate any insight here!