Alternative to LPM and logit regression in Stata I'm dealing currently with complex dataset that was already tested with Linear probability model and logit regression. I'd like to find an alternative for original regressions.
The sample uses a binary dependent variable explained by many regressors. Besides the sample is quite big (~50 000 observations).
Any suggestions will be welcome!
 A: All attempts at modeling should begin by thinking hard about the data generating mechanism (DGM) and how it can be represented mathematically. One often discusses, say, the assumptions of the Gauss-Markov theorem, but in many presentations the most important assumption - that the underlying model is linear in the parameters - is skipped or only adressed summarily. 
In that sense, a logit model is appropriate if you think that the log-odds of the DGM is linear in the parameters. Sometimes another model may outperform the logit model when applied to binary outcomes, but if the model with good performance does so on basis of assumptions that are clearly not representative of the underlying DGM according to domain-theory, one should consider what that really means instead of just adopting the model. 
A: If you go to "statistics => binary data" in Stata, you will see all built-in models for models with binary outcomes. 
In terms of computation speed OLS (LPM) should be faster than any ML model. So if speed is the concern you should stick with OLS. Besides that, you already tried logit, and you could also try probit, but it usually doesn't produce results very different from logit. 
These three are usually used. If you have panel data, you can use the fixed effects or random effects versions of these models.
