[Rasch] Unidimensionality

Andrew Kyngdon akyngdon at lexile.com
Tue May 13 02:05:10 EST 2008


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...Otherwise, 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 interdimensional additivity
and intradimensional 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


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.







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
www.lexile.com/conference2008 <http://www.lexile.com/conference2008> 


-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://mailinglist.acer.edu.au/pipermail/rasch/attachments/20080512/3df7f781/attachment.html 

More information about the Rasch mailing list