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Imagine I have objects with 5 different properties which are either present (1) or not (0). Further, I have some other variables that I expect to predict the presence of a property.

Focusing on a single property out of the five, I could use a logistic regression to infer the influence of my variables on the properties presence. This, however, would give me five different models and I'd need to assume that the properties are independent of each other.

Is there an elegant way to combine all five attributes in a single model? Probably using some hierarchical model? For the implementation I use rstan, but some theoretical idea where to start would be helpful.

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What you are describing is a multivariate logistic regression, NOT a multiple logistic regression. Note that by convention:

  1. multivariate implies >1 dependent/target variable
  2. multiple implies >1 independent/predictor variable and only 1 dependent/target variable

This important difference is frequently confused, so be careful when you read papers using the terms.

Also note that if the 5 properties (i.e. dependent variables) are uncorrelated, you will not benefit from a multivariate analysis; you might as well use 5 separate logistic regressions in this case.

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