I am currently conducting research with binary logistic regression of panel data. For now, I am planning to conduct the specification test with linktest, goodness of fit test (Hosmer & Lemeshows test) and multicollinearity test with collin in Stata. Is this correct?
Second, how do I check for heteroskedasticity in panel logistic regression in Stata? Once found, how do I correct them?
Best Answer
You could approach this problem using probit models, and once you've figured out if there's an issue and how it should be handle, then you could do equivalent logistics for ease of interpretation if you didn't want to stick with probit - they are essentially the same model in many ways, but there are some options with probit that relate to your question.
I believe you could fit your model with something like xtgee or oglm to get a first model. Then you can fit a heteroskedastic probit (oglm or a similar command). Once you have both models, since the probit model is nested within the het prob model, you can then do an LR test of nested models to see if there is an improvement in fit when using the heteroskedastic model.
I've read a surprising amount of "ignore it" regarding heteroscedasticity and binary outcomes. That seems like a bad idea, particularly with a lot of corrections available. Various robust options are available in Stata commands that address some related issues and are explained well in the Stata documentation.
I'd say I'm slightly past beginner status with this level of detail on advanced models - which translates to "use my advice as a good starting point." I might be able to come up with something better given more information about your data.
Here are some places where you could do some digging based on what you already know and what little bit of direction I've offered -
http://www3.nd.edu/~rwilliam/oglm/oglm_Stata.pdf - pretty in depth discussion and explains things using reference to a specific Stata command.
Allison, Paul. 1999. Comparing Logit and Probit Coefficients Across Groups. Sociological Methods and Research 28(2): 186-208.
Yatchew, Adonis and Zvi Griliches. Specification Error in Probit Models. 1985. The Review of Economics and Statistics 67(1):134-139.
Hope this helps.