[Rasch] Invariance

Mike Linacre (RMT) rmt at rasch.org
Thu Jan 10 10:02:12 EST 2008

Dear Anthony:

Thank you for your questions.

Hambleton is touching on these concepts: "the item difficulty parameter 
estimate is statistically invariant (i.e., the same) irrespective of the 
person sample distribution within a population",  and similarly for the 
person ability estimate and the distribution of items within a population 
of items.

This is what Ben Wright meant by "sample-free" and "test-free" measurement. 
It has been a feature of Rasch measurement from the beginning: 
www.rasch.org/memo1.htm Ben Wright, 1967, "Sample-free Test Calibration and 
Person Measurement"

It is the separability of parameters in Rasch models (first noticed by 
Ragnar Frisch) that is the mathematical reason for the invariance of Rasch 
estimates. Rasch, 1977, www.rasch.org/rmt/memo18.htm - "On Specific 
Objectivity: An Attempt at Formalizing the Request for Generality and 
Validity of Scientific Statements."

Mike L.

At 1/9/2008, you wrote:
>I read this in an IRT book (Hambelton, Swaminathan & Rogers, 1991).
>Is this what Rasch folks also believe in?
>Your silence gives me the impression that , this is not true.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  21:2 Autumn 2007
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