[Rasch] What in Winsteps tells how uni dimensional a fit is?

rsmith rsmith at jampress.org
Wed Sep 4 00:42:51 EST 2013

Actually, Smith and Miao (1994) and Smith (1996) demonstrate that the answer depends on the degree to whifh the two dimensions are correlated and the number of items on each dimension.  When the dimensions are correlated PCA does not work as well and when 80% of the items measure one dimension Rasch fit statistics work better that PCA of raw scores.

Richard M. Smith, Editor
Journal of Applied Measurement
P.O. Box 1283
Maple Grove, MN  55311, USA
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-------- Original Message --------
> From: Mike Linacre <mike at winsteps.com>
> Sent: Monday, September 02, 2013 3:35 AM
> To: rasch at acer.edu.au
> Subject: Re: [Rasch] What in Winsteps tells how uni dimensional a fit is?
> 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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