Goodness of fit for the logistic regression model using relative belief.

A logistic regression model is a specialized model for product-binomial data. When a proper, noninformative prior is placed on the unrestricted model for the product-binomial model, the hypothesis H ₀ of a logistic regression model holding can then be assessed by comparing the concentration of the posterior distribution about H ₀ with the concentration of the prior about H ₀. This comparison is effected via a relative belief ratio, a measure of the evidence that H ₀ is true, together with a measure of the strength of the evidence that H ₀ is either true or false. This gives an effective goodness of fit test for logistic regression.