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

Mike Linacre (RMT) rmt at rasch.org
Sun Jul 6 17:58:59 EST 2008

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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