First of all, if this question is a dup, please let me know before voting it down. I spent a good half hour reading all Q&As and I don't think I have found my answer.

I have been running logit regressions on large samples in order of hundreds of thousands in a preliminary study that will eventually end up in non-parametric tests. Both my dependent variable and my independent variable of interest are binary for now. I started with a very underspecified model containing only my IV of interest in a single logit regression. Since the dataset is quite large, I haven't been putting much trust into the significance level of my coefficients which seem to be almost always perfect. Instead, I have been calculating odds ratios that can give me some kind of indication of the predictive power of the model. While I was running my underspecified regression (`glm(dv ~ iv, family = binomial(link = logit)`) on preliminary noisy data the odds ratios seemed to be at an acceptable level, so I decided to proceed to the next step, clean the data and import the control variables, etc...

Now the issue is: since I have started using the full clean data with real control variables, the odds ratios of my variable of interest have started exploding.

Consider this:

    glm(clean_dv ~ clean_iv, family = binomial(link = logit))

> clean_iv coefficient: 4.619625

> clean_iv stderr: 0.267083

> clean_iv odds: 101.45602

    glm(clean_dv ~ clean_iv+noisy_cv1+noisy_cv2, family = binomial(link = logit))

> clean_iv coefficient: 6.233e+00

> clean_iv stderr: 2.727e-01

> clean_iv odds: 509.3612309

    glm(clean_dv ~ clean_iv+clean_cv1+clean_cv2, family = binomial(link = logit))

> clean_iv coefficient: 5.582e+00

> clean_iv stderr: 2.369e-01

> clean_iv odds: 265.6611359

The control variables behave just normally. They are significant and have acceptable odds ratios.

Better odds ratios should supposedly be good news, but at this level I don't know how to interpret them anymore. Any help is appreciated.

P.S. On the last model with very large odds ratio STATA won't converge anymore, and only R's logit model works. For the first two models STATA produces roughly the same odds ratios and coefficients as R.