Checking dimensionality in rasch measurement with standardized residual

Checking model assumptions is extremely important in Rasch measurement as well as item response theory (IRT). Principal component analysis (PCA) is one widely used method to examine the dimensionality. The first objective of this study is to verify whether a fixed-criterion is appropriate for the determination of dimensionality by investigating distributional properties of the first three eigenvalues when PCA is applied to standardized residuals. Multivariate independence procedure is another method to check the dimensionality. Three statistics have been proposed to assess whether a sample correlation matrix comes from a population with an identity matrix. The second objective of this study is to compare the performances of these statistics when checking dimensionality in Rasch measurement.