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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.

Bing
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  • Why not write separate likelihood functions for the two models? Else, tell us more about your real proble (what is this variables representing ....) Or even better, ask again at Cross Validated , with link here, and mentioning you got little response here. – kjetil b halvorsen May 17 '15 at 17:48
  • @kjetilbhalvorsen Because both model include Y and Z, I'm not sure if it's a good idea to write the two likelihoods separately, but how to combine the two likelihoods? Thank you for your advice. I reposted it at Cross Validated. Here's the link if you're interested. http://stats.stackexchange.com/questions/153467/statistical-modeling-with-the-combination-of-two-models – Bing May 21 '15 at 21:47

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