[Rasch] Why are Rasch measures linear?

Svend Kreiner S.Kreiner at biostat.ku.dk
Mon Sep 3 20:01:49 EST 2007

Talking about "linear" measurement has never really made sense to me. We 
would of course like the measure - the estimate - of something to be in 
a 1-to-1 relationship with what we trying to measure, but that is not 
special for Rasch models and so obvious that it of no particular 
interest. What we mean, when we sometimes say that measurement is 
linear, is that the person parameter is measured on an interval scale 
with an arbitrary mean and an arbitrary unit. The unit on the Rasch 
scale has, of course, always been invisible, but it becomes apparent if 
you look at the Rasch scale from the point of view of Stephen Humphrey´s 
and David Andrich's work on multiple frames of references for rasch 

best regards


Anthony James skrev:
> 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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Svend Kreiner
Associate professor
Department of Biostatistics  
University of Copenhagen 

Øster farimagsgade 5, entr. B
P.O. Box 2099
DK-1014 Copenhagen K, Denmark

Email: S.Kreiner at biostat.ku.dk
Phone: (+45) 35 32 75 97     

Fax: (+45) 35 32 79 07

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