PRCOMP= residual type for principal components analyses in Tables 23, 24 = S, standardized

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