SUMM: QMLE, Logit, Poisson with continuous data

[josef-pkt]

I have problems finding various pieces for fractional data analysis with Logit/Probit/Binomial and related Poisson with continuous data.
question on stackoverflow in connection with penalization
http://stackoverflow.com/questions/33845539/modelling-probabilities-in-a-regularized-logistic-regression-model-in-python/33850446#33850446

main point: It works but I don't find examples or recipes, and I don't think there are explicit unit tests. There should be enough unit tests for the robust covariance HC0.
#2074 FAQ for LEF robustness
#2642 FAQ overview models by type of response, endog data

fractional/proportion data

• enh: fractional Logit, Probit #2040 main issue, GEE example for Papke/Wooldridge, closed ENH: Allow unit interval for binary models. Closes #2040. #2044 (enable continuous data)
• EX/DOC: movie ratings as a Binomial or proportion regression #2538 almost duplicate, request for examples/docs
• ENH: fractional data, treatment effect in paired proportions (not potential) #2661 more towards stats, treatment effects for proportions

Stata 14 has explicit method fracreg, but I didn't read enough to understand what it adds to just using the regular models, with cov_type HC

Poisson positive continuous data

• ENH: Poisson for continuous regression #1151 older main issue, not updated since I started to look at QMLE,
  we should get more references, pages on internet and articles with discussion
  (??? I looked at several papers in economics, applied econometrics)

general issues

• SUMM: score tests and similar #2041 score tests, including robust and conditional moment tests
• GLM with "foreign" variance function #1777 GLM with foreign variance function
• everything GMM, GLMGMM #1790 GMM version of GLM models, also other related GMM issues
• combination with penalization, I never checked, see above stackoverflow question