[Rasch] Invariance

Anthony James luckyantonio2003 at yahoo.com
Sat Jan 5 09:39:50 EST 2008

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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