The Equivalence of the Test Response Function to the Maximum Likelihood Ability Estimate for the Dichotomous Rasch Model: A Proof.

While several proofs exist that the number keyed (or number correct) score is a sufficient statistic to estimate person measure (or ability, beta) in the dichotomous Rasch model, there are few proofs about the direct mathematical link from beta to the number correct score. This manuscript proves that the estimation link going from score to beta is the test response function, which is the sum of the probabilities correct for all items given the difficulty (delta) values and beta.