[Rasch] Invariance

Stephen Humphry stephen.humphry at uwa.edu.au
Thu Jan 10 12:11:07 EST 2008

Hi Anthony.
Rasch certainly maintaned invariance to be essential for measurement, and that separability is a requirement for invariance. In his words ...

"The comparison between two stimuli should be independent of which particular individuals were instrumental for the comparison; and it should also be independent of which other stimuli within the considered class were or might also have been compared ... Symmetrically, a comparison between two individuals should be independent of which particular stimuli within the class considered were instrumental for the comparison; and it should also be independent of which other individuals were also compared, on the same or some other occasion" (Rasch, 1961, p. 332).

Rasch demonstrated that the principle of invariance is characteristic of measurement in physics using, as an example, a two-way experimental frame of reference like that in Rasch (1960, p. 112), in which instruments exert mechanical forces upon solid bodies to produce accelerations. Rasch (1960/1980, pp. 112‑3) stated of this context: “Generally: If for any two objects we find a certain ratio of their accelerations produced by one instrument, then the same ratio will be found for any other of the instruments”. This is again the essence of invariance.

I can't speak for others, but personally I wouldn't state it as a matter of belief, rather as a matter of a fundamental necessary requirement of measurement, generally, shown on the basis of careful analysis of measurement in physics.
Hope that helps.


From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Anthony James
Sent: Thursday, 10 January 2008 6:45 AM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Invariance

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.

Anthony James <luckyantonio2003 at yahoo.com> wrote:

Hi all,
I’m starting the new year with one of my half-understood concepts in the Rasch model.
During the X-mas hols I did some reading about the “invariance” property of the Rasch model.
I found out that the logistic function can be written as a linear regression equation. In fact the ICC is the regression of raw scores on measures. Invariance is the property of the regression model. That is, the same regression line can be obtained in any subpopulation of the X variable to predict the Y variable from. This means that the slope and intercept of the regression line is the same along the variable. 
That’s the reason why invariance exists under Rasch model.
This sounds logical to me. I mean with my weak grounding in stats and algebra I can understand it. I’d be thankful for any comments to further complicate the problem!
Can this also be related to the linearity issue and a common metric and unit issue?
Where can I find an algebraic proof for invariance?

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