I've faced an interesting situation, which is out of my area of expertise, so I need an advice here from someone more experienced in the field.

The problem is following. Suppose, we have a binary logit model. Let's call it

**old model**. The model is estimated over a set of co-variates and observations. Then, we use the model for log-odds prediction for new observations. The predicted log-odds are saved together with new observations.

Now, we do the following. We take new observations and use them to develop a

**new model**, which is also binary logit, and we use log-odds, predicted by

**old model**as one of the co-variates for the new model, plus some other variables. However, the observations are completely different.

This is the part I cannot completely understand. It looks like we use predicted value to predict another value. I wonder, which shortcomings/advantages it has. I mean, we can do that, but then, we must be careful with confidence intervals and model interpretation, must we not?

I read a bit about 2-stage regression models and instrumental variables, and they do have some similarities to the issue. But, as far as I understand, they run over the same set of observations, or am I wrong?

My area of expertise in statistics is a bit different, so I do not know if I'm correct or not. Does this situation has a name? How do we call such models?

Is there any academical work about similar matters so I can use it as a reference? Or, maybe some nice examples with explanation? Something, like 2-stage logit-logit with different data-sets, but connected to each other in a way I described.

I tried to Google the matter, but it is hard to do when I do not know exactly what to search.

I would appreciate any guideline about the problem.