[Rasch] Unidimensionality

Trevor Bond trevor.bond at jcu.edu.au
Tue May 13 10:21:39 EST 2008

```Dear Joe,

While we have these important theoretical
discussions about what we can't yet do or what we
should be doing etc., at least this is a forum
where we have such discussions.

At present, the use of the Rasch model, as you
summarize it below, is the best we have on offer
to do just what you want.

things together and move forward carefully and
reflectively.

Steve's original question arose in a particular
(and not infrequent) context: a bunch of
curriculum experts and accountability bureaucrats
got together and constructed tests and decided
cut scores by working from merely adding raw
scores together.

Steve's question was based on his idea that RM
could do better than that...but how?

Too often we are called upon to make a silk purse
out of a sow's ear...but if you have to , use RM
reflectively and iteratively and aim to have
people LEARN about testing and cut-scores in the
process.

Gregory STONE (UToleo) has done some good work on
using RM to develop defensible cut scores.

best
TGB

At 5:28 PM -0400 5/12/08, Joe Albano wrote:
>Content-Type: multipart/alternative;
>Content-Language: en-us
>
>Pardon my ignorance, but I'm trying (1) to learn
>and (2) to apply some of this to upcoming work.
>Does this all translate into a practical
>observation that if fix statistics are
>reasonable (without entering into a debate about
>what constitutes reasonable fit stats) and
>residuals are sufficiently low (ibid) the
>measure can be considered unidimensional (even
>if, in "fact" the measure characterizes multiple
>"dimensions" that co-vary in lock step)? Said
>another way, can a measure be unidimensional, by
>Rasch standards, without the requirement that
>the underlying phenomenon of interest be
>unidimensional?
>
>*IF* this is true I have another question - but
>I'll wait to have this attempt to test my
>knowledge shot down first, before asking an
>equally naïve follow-up J
>
>Best regards,
>
>Joe.
>
>Joe Albano
>From: Andrew Kyngdon [mailto:akyngdon at lexile.com]
>Sent: Monday, May 12, 2008 12:05 PM
>To: rasch at acer.edu.au
>Subject: [Rasch] Unidimensionality
>
>
>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 senseŠOtherwise,
>multidimensional might simply mean test results
>depend on more than one attribute, each of which
>could in principle be measured independently,
>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.
>
>Well done Steve, you hit the nail right on the
>head here. There exists endemic confusion in the
>behavioural sciences as to what
>"multidimensionality" is, and you correctly
>state that the term can be used to describe
>different kinds of structures.
>
>In the case of multidimensional scaling,
>psychological attributes are assumed to be
>multidimensional metric spaces, in that the
>distance between any two points in
>multidimensional space is positive, symmetric
>and satisfies the triangle inequality (Beals,
>Krantz & Tversky, 1968). Dissimilarities
>judgments often fail the triangle inequality
>(Tversky & Gati, 1982) so it is unwise merely to
>assume that psychological attributes form metric
>spaces. Also, when the Minkowski R metric (or
>"power" metric) is used, the properties of
>subtractivity often fail when more than just one
>dimension is involved (Michell, 1990).
>
>In physics and in polynomial conjoint
>measurement theory more generally, single
>quantities can be decomposed into many other
>variables. Examples in physics are density,
>force, and electrical resistance; and possible
>examples in psychology are Hull's (1952) and
>Spence's (1956) theories of response strength.
>Indeed, most quantities in physics are
>compositions of other variables, yet they
>nonetheless are "unidimensional" and
>measureable. Krantz, Luce, Suppes & Tversky
>(1971) detail several kinds of composition
>rules, their attendant cancellation conditions
>and proofs.
>
>However, as you imply, most behavioural
>scientists aren't this specific in their
>understanding of "multidimensionality". Most
>prefer to entertain an informal understanding
>and for guidance will solely rely on the results
>of applying a "multidimensional" model to their
>data. Until they start developing substantive
>theories of sufficient depth, there will be no
>firm bases for claiming that this or that
>psychological system is multidimensional.
>
>Cheers,
>
>Andrew
>
>
>Andrew Kyngdon, PhD
>Senior Research Scientist
>MetaMetrics, Inc.
>1000 Park Forty Plaza Drive
>Durham NC 27713 USA
>Tel. 1 919 354 3473
>Fax. 1 919 547 3401
>MetaMetrics' 2008 Lexile National Conference & Quantile Symposium
>Successful Teachers, Successful Students
>June 16-19  |  San Antonio Marriott Rivercenter
><http://www.lexile.com/conference2008>www.lexile.com/conference2008
>
>
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--
Trevor G BOND Ph D
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