[Rasch] Comparison Rasch 3-parm IRT

Mike Linacre mike at winsteps.com
Sat Sep 14 19:55:55 EST 2013

Thank you for your email, Ricardo.

You wrote: In general high ability are estimated with higher S. E. 
because items are relatively easy for the sample.

Reply: Yes. We expect a U-shaped graph when S.E. is plotted against theta.

You wrote:  Suppose two datasets A and B with everything equal but the 
discrimination in A is generally lower (low correlation theta-score) 
than dataset B. Does WINSTEPS will have different discrimination in each 
dataset maintaining it constant within datasets? or will it calibrate as 
1 in both ? Does this differences will impact measures variance ?

Reply: In Winsteps, and in Rasch, differences in test discrimination 
appear as differences in logit range. In general, the higher the test 
discrimination, the higher the range. When the test discrimination 
becomes perfect (a Guttman pattern), the range of the measures in logits 
becomes infinite.

You wrote: And finally if the lower asymptote is really greater than 
zero for most of the items what estimate of reliability should we trust 
more ? Rasch or 3PL ?

Reply: I always tend to trust the lower estimate of reliability more.  
You can estimate a Rasch reliability that approximates the 3-PL 
reliability by using CUTLO= in Winsteps. If c=.2, then CUTLO=1.2


Mike L.

Mike Linacre, mike at winsteps.com
Winsteps: www.winsteps.com/winsteps.htm - current version 3.80.1 - 
September 2013
Facets: www.winsteps.com/facets.htm - current version 3.71.2 - May 2013
Winsteps and Facets Tutorial PDFs at www.winsteps.com/tutorials.htm
Your comments and questions are welcomed.

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