Exact tests of the Rasch model based on scalability coefficients Karl Bang Christensen∗

For item responses fitting the Rasch model, the assumptions under-lying the Mokken model of double monotonicity are met. This makes nonparametric item response theory a natural starting point for Rasch item analysis. This paper studies scalability coefficients based on Lo-evingers H coefficient that summarize the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using exact p-values computed using Markov Chain Monte Carlo methods. The power of the tests of unequal item discrimination, and their ability to distinguish between local depen-dence and unequal item discrimination is discussed. The methods are illustrated and motivated using a simulation study and a real data example