[Rasch] Unidimensionality (follow up with the practical issue)
commons at tiac.net
Sun May 11 18:54:51 EST 2008
From: Stephen Humphry [mailto:shumphry at cyllene.uwa.edu.au]
Sent: Saturday, May 10, 2008 10:12 PM
To: commons at tiac.net
Cc: rasch at acer.edu.au; 'Sara Ross'; 'Andrew Richardson'; 'Jonas Miller'
Subject: RE: [Rasch] Unidimensionality (follow up with the practical issue)
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.
MLC: But there are two traits of the tasks that contribute: 1. the order
of hierarchical complexity of the task. This is determined through analysis
of the items. 2. the horizontal odder of complexity. This is determined by
counting how many actions represented in bits is required to complete the
action. As far as I can tell, Rasch is about responses, psychophysics
relates responses in scaled form to stimuli that have been scaled
analytically or measured physically. The outcome of a study is threefold.
One gets a Rasch scale for items and people. This is the normal way. One
also knows the hierarchical complexity of the items and the horizontal
complexity. One regresses the Rasch scores on each of the two independent
variables, order of hierarchical complexity of the item and order of
horizontal complexity of the item. The multiple r should be much better
than any single r. Not that hierarchical complexity of an item does not
correlate with its horizontal complexity so these are independent dimension.
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
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
> 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
> 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
> 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.
> 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
>> 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
>> Trevor G BOND Ph D
>> Professor and Head of Dept
>> Educational Psychology, Counselling & Learning Needs D2-2F-01A EPCL
>> Hong Kong Institute of Education
>> 10 Lo Ping Rd, Tai Po
>> New Territories HONG KONG
>> Voice: (852) 2948 8473
>> Fax: (852) 2948 7983
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