[Rasch] Unidimensionality

l.tesio at auxologico.it l.tesio at auxologico.it
Tue May 13 21:56:56 EST 2008

So far, I understood that -within a statistical perspective like Rasch's one- unidimensionality is not an all-or-none attribute. Therefore, it is a matter of distance of observation: the carachter A is a vowel in latin alphabet, but if you magnify this object it becomes a series of dots.  Furthermore, it is a concept superimposed to real (unknown in their very essence) latent properties. In a disability scale for paraplegia, motor and sphincterial items can be enough unidimensional if you take them as items of "minutes of care", but they are no longer unidimensional if you take them as items of "improvement after rehabilitation" (they can be very much "bi-dimensional" under this perspective). So, everything can be or not unidimensional, depending on a) observation distance; b)the supposed latent trait 

Now: let's face the philosophical issue of the "reality" of the unidimensionality claimed by a successful Rasch Analysis.
      You are looking at measures of "latent traits" which you hypothesized in advance (e.g. Quality of Life, depression..whatever). For Rasch and conventional coefficients (Cronbach alpha) the same reasoning applies: all properties that "exist" are potentially measurable (items could be found that are consistent/correlated/unidimensional) , but measures do not demostrate existence: they are necessary, not sufficient. First, it is well known that correlation is not a proffo of a cause-effect relationship (a third variable explanation is often  possible) .  

Second (perhaps more subtle): "existence" , in this context, means not only "something being there", but "being the thing -the meaningful entity-you suppose", i.e. the  construct you hypothesized a priori .  Flowers exist since millions of years, but the "beauty" of flowers require a person  perceiving the "beauty".  

I remember a funny dialog: a pharmaceutic dealer claimed that his drug was fostering growth, because it made tadpoles to become frogs SIGNIFICANTLY faster than the placebo made. The physcian replied: a-ha, I'd rather say it fosters aging. "Change" was consistently observed but...change of what? 

If properties exist their items must be "unidimensional", but not all unidimensional series of items hits a "real" property. Let's admit, optimistically, that  there is not a "third variable" explaining the correlation: the second pitfall  is still in ambush, that you hit something, but not what you predicted.

Perhaps I'm off target: hope this helps.


> Da: Trevor Bond <trevor.bond at jcu.edu.au>
> Data: Tue, 13 May 2008 08:21:39 +0800
> A: "Joe Albano" <joealbano2 at earthlink.net>, <rasch at acer.edu.au>
> Oggetto: RE: [Rasch] Unidimensionality
> 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.
> Take Theo's warning to heart about adding unlike 
> 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
> At 5:28 PM -0400 5/12/08, Joe Albano wrote:
> >Content-Type: multipart/alternative;
> >	boundary="----=_NextPart_000_001D_01C8B455.A8DFFAD0"
> >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
> >joealbano2 at earthlink.net
> >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 
> >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 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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> >Rasch at acer.edu.au
> >http://mailinglist.acer.edu.au/mailman/listinfo/rasch
> -- 
> 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-isbn9780805854626
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> Mob:

Luigi Tesio
Professore Staordinario
Medicina Fisica e Riabilitativa
Universita'degli Studi di Milano

Unità Clinica e Laboratorio di Ricerche di Riabilitazione Neuromotoria
Istituto Auxologico Italiano,IRCCS

via Mercalli,32
20122 Milano, Italy

tel   +39 02 58218148/154
fax   +39 02 58218152/155

luigi.tesio at unimi.it
l.tesio at auxologico.it

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