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.