HOW SHOULD WE ASSESS THE FIT OF RASCH-TYPE MODELS?
APPROXIMATING THE POWER OF GOODNESS-OF-FIT STATISTICS
IN CATEGORICAL DATA ANALYSIS
ALBERTO MAYDEU-OLIVARES
FACULTY OF PSYCHOLOGY, UNIVERSITY OF BARCELONA
The purpose of this article is to compare the performance of certain goodness-of-fit statistics to test Rasch-type models. The authors investigate the performance of three statistics, R1, R2, and M2 to assess the overall fit of a one-parameter logistic model (1PL) estimated by (marginal) maximum likelihood (ML). The statistics R1 and R2 were proposed by Glas (1988) to assess the fit of the oneparameter logistic model, and M2 was proposed by Maydeu-Olivares and Joe (2005, 2006) for testing general composite null hypotheses in multivariate discrete data. The simulation study was conducted first. The asymptotic power rates under some interesting violations of model assumptions, as well as empirical rejection rates for correctly specified models and some misspecified models are reported. Two empirical studies were used for future evaluation.
Comments:
I have to say it is really mathematic and difficult to understand the mathematic process.
As we can see from the simulation study, when M2 is the best in almost all the situation, while the sample size is close to 1000, R1 is better than R2, sometimes is as good as M2 to distinguish 1pl form 3pl/2PL(see table3 & table5). While in the numerical examples.R2 is more powerful than M2. So how to deal with such situation: you design a simulation study which has the expected results, however the results are inconsistent with the real data?