I have a question for you which I can't get my head around for quite some time now & it all has to do with predicted probabilities. I have a data set with a dichotomous dependent variable (thus a binomial model), about 16 independent variables (including some two and three way interactions). I also have a cross-classified structure of two, let's say for simplicity's sake 'persons' and 'countries', where one person can be in multiple countries, and one country obviously has multiple persons. We only allow the intercept to vary across these two classifications.
Since it's a multiple membership model, I first run a 2nd order PQL and then use the results as starting values for an MCMC. It takes quite some time, but produces results. These results, for the fixed part, are somewhat unexpected and my colleague and I think that somehow this is related to the two classifications.
My questions revolves around this:
Questions:Now, what I want to know is simply the predicted probabilities for the dependent variable, including a standard error/confidence interval. We'd be happy to either calculate probabilities for all included cases and then (manually) calculating our relevant stats, or work with a customised prediction. As long as it takes, in one way or the other, the cross-classified structure into account.
1. Is this possible to do in one way or the other in MLwiN, taking into account the cross-classified structure?
2. If it is not possible, is there a way of manually calculating this, or approximating it?
2b. Am I correct in assuming that, if I do run a customised prediction on an xc-mcmc fitted model, that only the fixed parts are taken into account? Or does it deal with the random effects in one way or the other?
Am I, furthermore, correct in assuming that these kinds of predictions would be fairly easy to do with an hierarchical (or single-grouping structure, such as only countries as a level taken into account)?
Thanks a lot! I'm really interested in the answer to these questions.
- Harmen