Hi, I’m working on a model based off a latent utility framework where Pr[d=1] = Pr[xb > -e] with e is distributed logistically, x is some independent variable, b is its coefficient, and d is an indicator for if the option is chosen. This is a simple binomial choice scenario.

Now, I understand the typical assumption is that e has a standard logistic distribution with a mean of 0, but what if it actually has a mean greater than 0? Can you still write the choice probabilities as the CDF of the logistic distribution? It seems to me that you should be able to, however when I run a simple simulation in a statistical package the predicted choice probabilities only match the value of the CDF when I designate the error to have mean 0.

Could someone explain what I am missing here? I greatly appreciate any help.

submitted by Nevin Manimala Nevin Manimala /u/Gustatsor

[link] [comments]