[Rasch] Unidimensionality

Markus Quandt markus.quandt at gesis.org
Thu May 8 16:27:57 EST 2008

Let me jump on to this (seeking confirmation or correction of my 

Going back to Anthony's original question, and assuming that the answer 
to Trevor's rhethorical question is that the measure comes first, this 
seems to imply the following:

1. A RM that shows good fit is a RM that shows good fit. Meaning that - 
trivially? - the estimated Rasch scores from that RM must reflect one 
single, meaningful difficulty dimension underlying the stimuli. 
Consequently, there is no validity problem with using these scores as 
indicators of ability of the respondents.

2. Regardless of that difficulty/ability dimension having been isolated 
by the RM, there still CAN be additional dimensions in the data. Those, 
you might identify by FA on the residuals. Identifying them might point 
to problems in your measurement instruments - why do some items show 
poorer fit, (for some respondents)? - and/or increase one's general 
understanding of the stimulus-response process.

BUT such additional dimensions do not invalidate the use of the Rasch 
scores, as these have already separated out the ability dimension of 
interest! Therefore, the RM does indeed establish uni-dimensionality, in 
a way. But not in the same understanding of the term that you would use 
in confirmatory factor analysis, where it means that you have shown a 
set of manifest items to reflect only a single latent dimension. Rather, 
the uni-dimensionality is 'established' by removing influences other 
than common difficulty from the manifest measures, when the latent 
measure is computed.

This might be vaguely analogous to running exploratory factor analysis 
on a set of items and then using the factor scores of the first 
principal component (or whatever you use). One advantage of using Rasch 
scores is that one has a far clearer definition of what is or should be 
in the latent scores, a definition that is not only driven by an ad hoc 
interpretation of the items loading on that first component.

Is this a useful way to look at it?

Thanks, Markus

Michael Lamport Commons schrieb:
> I agree with Trevor.  The best way to tease the variables apart is to identify them in the stimulus and then regress the single set of rasch scores on them.  See if the r squares go up with two over one variable in a meaningful way.  I am suggesting paying attention to dimensions of the stimuli, making the measurement problem into psychophysics rather than psychometrices.  MLC
> -----Original Message-----
>> From: Trevor Bond <trevor.bond at jcu.edu.au>
>> Sent: May 7, 2008 7:12 PM
>> To: luckyantonio2003 at yahoo.com, rasch at acer.edu.au
>> Subject: Re: [Rasch] Unidimensionality
>>> Dear Antony
>> what comes first, the measure or the residuals ?
>>> In a couple of papers I noticed that the researchers before using 
>>> Rasch model or IRT models first use factor analysis to ascertain 
>>> unidimensionality. Since unidimensionality is a prerequisite to use 
>>> IRT models. They give the impression that only after FA has shown 
>>> that the test is unidimensioanl, one can use Rasch or IRT models.
>>> Is this really necessary? Isn't the Rasch model itself a technique, 
>>> superior to FA, to demonstrate unidimensionality?
>> my view is:
>> 1 find and remove the Rasch dimension
>> 2 use FA of the residuals to determine if sufficient structure exists 
>> in those residuals to infer more than one dimension in the data - the 
>> residuals should be randomly distributed.
>> For mine: FA used before RM misses the point of RM
>> best
>> T
>> -- 
>> Trevor G BOND Ph D
>> Professor and Head of Dept
>> Educational Psychology, Counselling & Learning Needs
>> D2-2F-01A EPCL Dept.
>> Hong Kong Institute of Education
>> 10 Lo Ping Rd, Tai Po
>> New Territories HONG KONG
>> http://www.ied.edu.hk/epcl/about/staff_bondt.htm
>> Book: 
>> http://www.researchmethodsarena.com/books/Applying-the-Rasch-Model-isbn9780805854626
>> Voice: (852) 2948 8473
>> Fax:  (852) 2948 7983
>> Mob:
>> _______________________________________________
>> Rasch mailing list
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> My best,
> Michael Lamport Commons, Ph.D.
> Assistant Clinical Professor
> Department of Psychiatry
> Harvard Medical School
> Program in Psychiatry and the Law
> Beth Israel Deaconess Medical Center
> commons at tiac.net
> http://www.dareassociation.org/
> 617-497-5270 Telephone
> 617-491-5270 Fax
> _______________________________________________
> Rasch mailing list
> Rasch at acer.edu.au
> http://mailinglist.acer.edu.au/mailman/listinfo/rasch

Markus Quandt
GESIS-ZA (Zentralarchiv fuer empirische Sozialforschung /
          Central Archive for Empirical Social Research) Bachemer Str. 40
50931 Koeln
tel +49-221-47694-25, fax +49-221-47694-44 

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