[Rasch] Unidimensionality (follow up with the practical issue)

Stephen Humphry shumphry at cyllene.uwa.edu.au
Sun May 11 12:12:27 EST 2008

I think Rasch models allow us to infer measurements of levels of  
latent traits from task performance and that hierarchical task  
complexity is generally necessary to do so. I refer to the ability or  
trait as the dimension. Perhaps we use terminology differently.

I am sure you can experimentally control levels of trait and my point  
was simply that correlational methods are not a substitute for  
experimentation, a point that I consider relevant to the historical  
use of the term "multidimensional" with respect to geometric  
representation of correlations.

I don't understand exactly what you mean by "dimensionalize the  
stimulus directly". To me, we don't dimensionalize, we measure  
dimensions if they exist and are measurable given our instruments and  
procedures. Many physical phenomena are measured ‘indirectly’ through  
effects on other physical properties under controlled conditions,  
including temperature.

On pyschophysics, Thurstone showed that given a specific condition,  
Weber's law will lead to the Weber-Fechner law. Not surprisingly, on  
analysis this condition amounts to having a fixed unit. Under the same  
condition, the Rasch model follows from Fechner's law. So I agree  
there is a close connection, although it was not of course Rasch's  
motivation for developing the models.

Interesting topic.



Quoting commons <commons at tiac.net>:

>  My claim goes against what you are saying.  I am not talking about
> performance.  Rasch is about performance.  That is why it finds a single
> dimension for difficulty when in fact there are many dimensions of tasks
> that are totally independent dimensions.  Two of these dimensions are
> hierarchical complexity of tasks.  See the Wikipedia entry for it.  The
> other dimension is traditional complexity.  The problem with a simplistic
> use of Rasch is it cannot find these dimensions.  By the way, one can
> experimentally vary the values of the two dimensions.  One could also see if
> performance on each of these dimensions are correlated.  Across a species or
> large age span, they should be because both depend on brain development.
> But experimentally they are totally independent.
> Psychometrics including Rasch analysis was developed to supplement
> psychophysics when one could not dimensionalize the stimulus directly.  In
> the case we have been discussing psychophysics works well.  The use of Rasch
> is to linearize the performance measure but one could use raw data.
> My best,
> Michael Lamport Commons, Ph.D.
> Assistant Clinical Professor
> Department of Psychiatry
> Harvard Medical School
> Beth Israel Deaconess Medical Center
> 234 Huron Avenue
> Cambridge, MA 02138-1328
> commons at tiac.net
> http://www.dareassociation.org/
> 617-497-5270 Telephone
> 617-320-0896  Cellular
> 617-491-5270  Facsimile
> -----Original Message-----
> From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
> Of Stephen Humphry
> Sent: Saturday, May 10, 2008 8:00 AM
> To: rasch at acer.edu.au
> Subject: Re: [Rasch] Unidimensionality (follow up with the practical issue)
> I think the problem lies in confusion regarding the terms
> 'multidimensionality' and 'unidimensional'.
> To claim that ability or mental attributes are 'multidimensional'
> potentially confuses the geometric representation of correlations with
> the idea of an actual mental or psychological "space" in which things
> and phenomena genuinely exist statically and/or dynamically. Physical
> pace is actually three-dimensional, but nothing else has been shown to
> be actually multidimensional in this sense.
> And correlation is contingent; correlation doesn't reveal causes, only
> experiments do. If physicists measurement using methods premised on
> correlation, confusion would reign.
> Otherwise, multidimensional might simply mean test results depend on
> more than one attribute, each of which could in principle be measured
> interpedently, with relationships contingent on other factors. In the
> latter sense, most dimensions in physics could be called
> 'multidimensional'. The mass of an object depends on its volume and
> density, but that doesn't mean it can't be measured.
> Steve
> Quoting Trevor Bond <trevor.bond at jcu.edu.au>:
>> Dear Steve et al,
>> Let's start with the final pre-supposition:
>> But using a Rasch model this way would require treating the data as
>> though it were unidimensional, even though we have strong reason to
>> believe that it is not.
>> We should treat the data as unidimensional only to the extent that we
>> have evidence to support that for the purpose of the decisions we make.
>> Different aspects of a (maths) test do not (necessarily) imply several
>> measurement dimensions.
>> That's where we got into this discussion with the Ferguson ref claiming
>> factors can be artifactual (artifacts of the difficulty range)
>> consequences of the FA (correlations based) analyses. (see ppxii-xiii
>> of B&F 2001 for details)
>> So that is why I need better to understand what happens when you
>> extract a Rasch Dimension from what is truly a multi-dimensional
>> situation.
>> Multidimensions are perhaps better analysed using the MCMLM model used
>> for PISA (B&F 2007, pp258-260).
>> Then we get back to the criticism I have of much educational testing:
>> if mere exposure to test items invalidates their use / changes their
>> test characteristics, I wonder what they really test. My guess it is
>> not understanding of the maths concepts.
>> Translator's note:
>> maths in Oz = math in US
>> Best
>> TGB
>> --
>> 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-isbn97808
> 05854626
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