[Rasch] Why are Rasch measures linear?

Anthony James luckyantonio2003 at yahoo.com
Mon Sep 3 18:30:27 EST 2007


Mike, Andrew & David,
  Thanks for your input.
   Andrew wrote: "In the case of a Rasch measurement scale the probabilistic definition of the logit is the same anywhere on the scale and the logit is in a linear relationship with the amount of the measured variable.  The logit is a probabilistic unit of measurement while one test score point is not a unit of measurement at all". 
  I can grasp the general idea of this comment about the Rasch measures. However, I don't understand what the Rasch model does to produce these linear relationships.The paper Mike introduced is rather difficult for me.
   The simplest form of Rasch measures in the case of dichotomies when there's no missing data is log (right/wrong). What is in this operation of logarithm that constructs additive linear measures?
  I and a number of my colleagues have problems understanding the linearity and additivity of Rasch measures. I think it's worth if someone wrote a simple note for the RMT to provide a proof for this with the simplest algebra possible.
  Regards
  Anthony

       
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