[Rasch] What in Winsteps tells how uni dimensional a fit is?
Mike Linacre
mike at winsteps.com
Mon Sep 2 18:34:53 EST 2013
A profound question, Michael: "What in Winsteps tells how unidimensional
a fit is?"
The Rasch measures estimated by unidimensional Rasch models are forced
to be unidimensional. Off-dimensional aspects of the data are in the
part of the data not explained by the Rasch measures, i.e., the Rasch
residuals. The Rasch residuals decompose into (a) the randomness
predicted by the Rasch model, and (b) components on dimensions other
than the unidimensional Rasch variable, (c) off-dimensional noise, such
as random guessing.
In empirical data, (a) and (c) usually dominate (b), so that item-level
or person-level fit statistics tend to be insensitive to
multidimensionality, as R.P. Macdonald (1985) reports. Accordingly we
must focus on techniques that quantify (b), such as PCA of residuals. If
the eigenvalues reported by PCA approximate the size predicted by the
Rasch model, then the data are effectively unidimensional. Otherwise,
the bigger the eigenvalues, the less unidimensional are the data.
Does this help?
Mike L.
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