Principal components analysis of item-response or person-response residuals can help identify structure in the misfit patterns across items or persons. The measures have been extracted from the residuals, so only uncorrelated noise would remain, if the data fit the Rasch model.
PRCOMP=S or Y Analyze the standardized residuals, (observed - expected)/(model standard error).
Simulation studies indicate that PRCOMP=S gives the most accurate reflection of secondary dimensions in the items.
PRCOMP=R Analyze the raw score residuals, (observed - expected) for each observation. These report Wendy Yen's Q3 in Table 23.99
PRCOMP=L Analyze the logit residuals, (observed - expected)/(model variance).
PRCOMP=O Analyze the observations themselves.
PRCOMP=K Observation probability
PRCOMP=H Observation log-probability
PRCOMP=G Observation logit-probability
PRCOMP=N Do not perform PCA analysis
Example 1: Perform a Rasch analysis, and then see if there is any meaningful other dimensions in the residuals:
PRCOMP=S Standardized residuals
Example 2: Analysis of the observations themselves is more familiar to statisticians.
PRCOMP=O Observations
In the PCA of th observations, Chien's (2012) Dimension Coefficient is DC = (R12/R23)/(1 + (R12/R23)) which simplifies to (eigenvalue of first component in the raw observations) / (first eigenvalue + third eigenvalue). Chien suggests values below 0.67 indicate a lack of unidimensionality.
Cronbach's Alpha with the Dimension Coefficient to Jointly Assess a Scale's Quality. Tsair-Wei Chien … Rasch Measurement Transactions, 2012, 26:3 p. 1379 www.rasch.org/rmt/rmt263c.htm
