[Rasch] quantifying departure from "invariance of item difficulties" or from "unidimensionality"

l.tesio at auxologico.it l.tesio at auxologico.it
Sun Jul 6 19:07:47 EST 2008

Mike's reply is (as usual) the sharpest one can expect. Nonetheless, as a non-statistician may I reinforce  the idea that  measures (including Rasch fitting measures) are not decisions in themselves. Good or bad, enough/not enough etc. come from the interactions with criteria external to the measures themselves. 
Using confidence limits or percentiles is a way to define certain measures (decision: p<0.05,p<0.01)  as unlikely enough to be "significant" with respect to a null hypothethesis (again an expterna decision).  Decisions rarely come from a unique interaction: in clinical practice, a diagnosis is a decision (a given disease is there or not).  Yet, measures (eg blood cell counts, serum levels of glucose or proteins...) must interact with each other and with other decisions (is your lab reliable? is a give disease detected in patient's history? are the patient's relatives affected by the same disease) etc. etc. 
Rasch "enthousiasts" (and I am one) tend to ask  a good measure to behave as a decision in itself.


 Da: "Mike Linacre (RMT)" <rmt at rasch.org>
> Data: Sun, 06 Jul 2008 02:58:59 -0500
> A: rasch at acer.edu.au
> Oggetto: Re: [Rasch] quantifying departure from "invariance of item
	difficulties" or from "unidimensionality"
> Steve, thank you for asking about unidimensionality and invariance.
> Many fit statistics have been derived which report on some of the 
> infinitude of different ways that data can depart from the Rasch 
> specifications for unidimensionality and invariance. Ben Wright's INFIT and 
> OUTFIT are two them.
> Invariance of item difficulties across different person groups can be 
> investigated by means of DIF analysis. ETS have developed rules-of-thumb 
> for identifying when their items exhibit enough DIF for remedial action to 
> be taken. You can see the ETS criteria at http://www.rasch.org/rmt/rmt32a.htm
> You wrote: "The Rasch score will be no worse ..."
> Here we need to define our purpose. If our purpose is to construct linear 
> measures of a unidimensional latent trait based on ordered qualitative 
> observations of the latent trait, then the Rasch measures will be the best. 
> If our purpose is to find numbers which correlate highly with some other 
> variable, then Rasch measures may be better or may be worse.
> You wrote: "doing them is bad, but perhaps you can get away with it".
> Empirical data never exactly fit the Rasch model, just as empirical 
> right-angled triangles never exactly fit Pythagoras' Theorem, and empirical 
> straight lines are never exactly Euclidean. But in any situation, we have 
> to decide, "When is a building brick rectangular enough?", "When is a white 
> line on a tennis court straight enough?", "When does a dataset represent a 
> unidimensional variable well enough?". And, in each case, we reject the 
> empirical data (bricks, white lines, bad items, etc.) which don't meet our 
> needs, and use the empirical data that does.
> Testing organizations develop their own rules for what is "good enough". In 
> high-stakes educational testing, the control over the data, and so the 
> rules, are very strict. In clinical-observation of patients, where there is 
> little control over the nature of the patient's affliction, but a lot of 
> need for tracking patient status, then the rules are much less strict.
> Steve, is this starting to address your concerns?
> Mike L.
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Luigi Tesio
Professore Staordinario
Medicina Fisica e Riabilitativa
Universita'degli Studi di Milano

Unità Clinica e Laboratorio di Ricerche di Riabilitazione Neuromotoria
Istituto Auxologico Italiano,IRCCS

via Mercalli,32
20122 Milano, Italy

tel   +39 02 58218148/154
fax   +39 02 58218152/155

luigi.tesio at unimi.it
l.tesio at auxologico.it

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