[Rasch] Dimensionality & variances

Mike Linacre (RMT) rmt at rasch.org
Tue Jun 10 07:48:06 EST 2008

Thank you for your question, Scott.

"Variance explained by the measures" depends on the spread of the persons 
and the spread of the items. The greater the spread, the more variance 
explained. If every person had the same ability, and every item the same 
difficulty, then no variance in the data would be explained by the measures.

The "Unexplained Variance" in the data should be the randomness predicted 
by the Rasch model.

"Unexplained variance in 1st contrast was 9.4%." - if this is 9.4% of the 
total variance, then it is part of the 100-28.1 = 71.9% unexplained 
variance. There are 32 items, so the 1st contrast has the strength of 32 x 
9.4 / 71.9 =  4 items, bigger than the less than 2 expected by chance. 
Please look at the plot of loadings on the 1st contrast (1st principal 
component in the residuals). Do you see a pattern indicating 4 or so 
outliers? These could be a indicative of a sub-dimension. In the list of 
items for the 1st Contrast, is there a substantive difference between the 
items at one end and the items at the other end? This defines the 


Mike L.

At 6/9/2008, you wrote:
>I'm fitting a dichotomous Rasch model with 32 items and 873 persons.  My 
>INFITs and OUTFITs range from .76-1.76. However, the PCA of the residuals 
>from that variance explained by the measures was only 28.1. Unexplained 
>variance in 1st contrast was 9.4%.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  21:4 Spring 2008
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