Logistic models as variables in a logistic model I have a binomial logistic model I'm working on, with roughly 6 significant variables.  I'd like one of those variables to be how likely something else is to happen.  Lets say that I'm primarily interested in the probability that cars get sold from a dealers lots, with sub-interest in whether the dealers are golfers.  The fact that they are/aren't golfers could affect whether they're there when the right buyer comes along, and thus it could significantly affect the probability of the car being sold.
In its own right, the sub-model might be interesting, but more important is that if I can get it to predict being a golfer well enough, and add it in the main model, it can significantly improve the prediction power of the main model.
Can something like this be done, or are there problems with using probabilities as a variables?  Should I use the logit from the sub-model instead?  One other question is what would happen if I used variables in the sub-model, and then again in the main model?  Perhaps what I'm trying to do has a specific name and I'm just not searching for it correctly.
 A: You might want to check out the literature on so-called 'double hurdle' models (Cragg, 1971). One example application of this is in Chalupka's econometric model (c.f. Chaloupka, 1999) of rational addiction (i.e. how do microeconomic actors make valuation decisions around cigarettes, when these goods are addictive). Depending on your application, zero-inflated models may also present some attractions.

References
Cragg, J. G. (1971). Some Statistical Models for Limited Dependent Variables with Applica- tion to the Demand for Durable Goods. Econometrica, 39(5):829–844.
Chaloupka, F. J. and Warner, K. E. (1999). The Handbook of Health Economics, volume 1B, chapter The Economics of Smoking, pages 1539–1612. Elsevier Science and Technology.
A: As to your main question, I don't think you need to conceptualize your analysis as "model within model."  You simply have a supposed variable, golf/no golf, which is itself a function of other variables (that you haven't specified here).  These can be built in as predictors of sale/no sale in their own right.  The fact that they function well because of the golf implication may be relevant to you and your audience but need not be an explicit part of your regression.  So there is no need either for a logit or a probability of the dealer being a golfer.  (Though for the purpose of predicting sale/no sale it wouldn't hurt to use logits or probabilities in place of the multiple variables used to create them.)
Another consideration is nesting.  If you have a set of cars on one lot with one (or several) dealers, and another set of cars on another lot with one (or more) other dealers, you've got a nested situation.  The lot "containing" the dealers is itself relevant because it will have its own location, type of customers, type of inventory, reputation, advertising activity, and so on.  So you'd want to look into hierarchical modeling, a.k.a. multilevel or nested modeling. 
