logit models

[Patrick Mason]

I am looking for a stata program capable of estimating a h-family logit model (Stukel 1988) and also a program that will estimate a logit model with a box-cox transformation of the explanatory variables (Siqueira and Taylor, 1999). Thanks.

[Joseph Coveney]

You might want to have a look at Faq et al. (2018)

[Nick Cox]

We Coxes like our upper case C. I am not a relative of Sir David Cox, but it's Box-Cox please.

On the real question:

I have no idea on a Stata program h-family logit model. If you Googled, searched in Stata and searched this forum, and found nothing, odds are that no one has written that.

I don't know that having a logit model for a response makes much difference to what transformations make sense for your predictors, but I don't recognise that reference. 90% of the time I find a transformation helpful it's one of reciprocal, logarithm, cube root or square root and the sign(s) of the data (existence of negative or zero values) and substantive considerations weigh heavily. I would never automate choice of transformation.

[Joseph Coveney]

Official glm does allow for simple user-written (custom) link functions, but not as far as I'm aware for parameterized link functions where the link-function parameters are estimated along with the regression coefficients. Including link-function parameters in the vector of parameters (coefficients) to be estimated requires that you set up the model using ml in Stata, or equivalent in Mata. There are user-written estimation commands that fit models with auxiliary parameters, but I'm not aware of anyone's going down that path for a generalized logistic regression command.

You might want to explore some of the built-in link functions that glm comes with, such as log-log, log-complement and complementary log-log, and see whether the fit is satisfactory.

As Nick mentions, transformation of the predictors is usually driven by substantive considerations. Depending upon the context, you could consider splines, where there are both official (help mkspline) and user-written (search bspline) commands available.