# [Rasch] Simulated eigenvalues greater than empirical data analysis?

Imogene Rothnie irothnie at usyd.edu.au
Sun Mar 11 16:16:41 EST 2012

```Hello,

I recently ran an MFRM (FACETS) analysis of some data with examiner/item/student as facets. I produced a winsteps output file to investigate unidimensionality using PCA of residuals in Winsteps, with items as columns and students as rows.

Table 23.0 for this Winsteps analysis looked like the following, which I thought was quite a good result:
Table of STANDARDIZED RESIDUAL variance (in Eigenvalue units)
-- Empirical --    Modeled
Total raw variance in observations     =        131.8 100.0%         100.0%
Raw variance explained by measures   =         45.8  34.8%          35.3%
Raw variance explained by persons  =         38.1  28.9%          29.3%
Raw Variance explained by items    =          7.7   5.9%           5.9%
Raw unexplained variance (total)     =         86.0  65.2% 100.0%   64.7%
Unexplned variance in 1st contrast =          1.9   1.5%   2.2%
Unexplned variance in 2nd contrast =          1.8   1.4%   2.1%
Unexplned variance in 3rd contrast =          1.8   1.3%   2.0%
Unexplned variance in 4th contrast =          1.7   1.3%   2.0%
Unexplned variance in 5th contrast =          1.6   1.2%   1.9%

HOWEVER, I then ran a couple of Winsteps analyses with simulated data files (as recommended) and got the below result (or similar) :
As you can see there is now very little variance explained by measures and the strength of the 1st and 2nd contrasts is high! Is this a plausible result? I feel like I must be making a technical error but the simfiles look plausible (right number of items and people with scores in the correct range...)
Has anyone experienced this or know of a plausible explanation?

Table of STANDARDIZED RESIDUAL variance (in Eigenvalue units)
-- Empirical --    Modeled
Total raw variance in observations     =        103.3 100.0%         100.0%
Raw variance explained by measures   =         17.3  16.8%          16.9%
Raw variance explained by persons  =          3.1   3.0%           3.1%
Raw Variance explained by items    =         14.2  13.7%          13.8%
Raw unexplained variance (total)     =         86.0  83.2% 100.0%   83.1%
Unexplned variance in 1st contrast =          9.2   8.9%  10.7%
Unexplned variance in 2nd contrast =          7.1   6.9%   8.2%
Unexplned variance in 3rd contrast =          2.9   2.8%   3.4%
Unexplned variance in 4th contrast =          2.6   2.5%   3.0%
Unexplned variance in 5th contrast =          2.1   2.0%   2.4%

Many thanks
IMOGENE ROTHNIE | Lecturer (Assessment)
Office of Medical Education | Faculty of Medicine
THE UNIVERSITY OF SYDNEY
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