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I have made my response variable as both a binary and a ordinal variable and performed binary logistic regression respective ordinal logistic regression. If I want to test which model fits the data best, which is the best way? So how to test which one of the binary and ordinal logistic model is the best fit?

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I can think of at least three ways:

  1. Smallest Deviance value followed by Likelihood Ratio and Deviance test.

  2. Smallest AIC/BIC value.

  3. Smallest held out error in cross validation.

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