I'm having a modeling problem now. Assume we have discrete random variable Y and continuous random variables X and Z. First, we assume a logistic regression between Y and Z.(Assumption One) Also, we assume a regression model X~Y+Z. (Y is used as a categorical variable.)(Assumption Two)
If we want to estimate the parameters from the two models at the same time, which kind of likelihood function should we assume? BTW, is this way of modeling reasonable? It looks weird to me. But I couldn't tell which part is missing.