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This might be a trivial problem but wondering if there's a known model formulation for this problem:

  • Ordered Categorical observed variable with k levels
  • Trying to estimate the parameter (theta) of a latent Bernoulli/Binomial variable
  • The latent and observed related by a k-length vector of probabilities
    • e.g. if observed=5 for a particular data point, data point has a 0.92 probability of success on the latent, observed=4 data point=0.81 success etc.

Does what I'm asking make sense? Or have I thought myself into a corner?

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    $\begingroup$ Are you, in effect, trying to integrate out the categorical variable to get an estimate of the unconditional probability of the latent Bernoulli variable? $\endgroup$ – jbowman Nov 29 '13 at 15:31
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    $\begingroup$ I hadn't thought of it that way - but in effect that might be what I'm trying to do. I should've also made explicit that the categorical is ordered, although I don't know whether that actually changes the complexity of the model. $\endgroup$ – Miles Dec 3 '13 at 22:35

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