Monte Carlo tests of the Rasch model based on scalability coefficients

TY - JOUR

T1 - Monte Carlo tests of the Rasch model based on scalability coefficients

AU - Christensen, Karl Bang

AU - Kreiner, Svend

PY - 2010/2

Y1 - 2010/2

N2 - For item responses fitting the Rasch model, the assumptions underlying the Mokken model of double monotonicity are met. This makes non-parametric item response theory a natural starting-point for Rasch item analysis. This paper studies scalability coefficients based on Loevinger's H coefficient that summarizes the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using 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 dependence and unequal item discrimination, are discussed. The methods are illustrated and motivated using a simulation study and a real data example.

AB - For item responses fitting the Rasch model, the assumptions underlying the Mokken model of double monotonicity are met. This makes non-parametric item response theory a natural starting-point for Rasch item analysis. This paper studies scalability coefficients based on Loevinger's H coefficient that summarizes the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using 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 dependence and unequal item discrimination, are discussed. The methods are illustrated and motivated using a simulation study and a real data example.

U2 - 10.1348/000711009x424200

DO - 10.1348/000711009x424200

M3 - Journal article

C2 - 19341515

SN - 0007-1102

VL - 63

SP - 101

EP - 111

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

IS - Pt 1

ER -