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

commons commons at tiac.net
Sun May 11 03:17:17 EST 2008


 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
> Voice: (852) 2948 8473
> Fax:  (852) 2948 7983
> Mob:



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