[Rasch] Dimensionality and Correlation

Michael Lamport Commons commons at tiac.net
Fri Nov 14 09:26:43 EST 2008


What about predicting the difficulty of items estimated with Rasch Scores and predicted by a priori order of hierarchical complexity of These items?  It is a true experiment.  The order of hierarchical complexity of the items is the true independent variable.  But the measure of the relationship between the analytic order of hierarchical complexity (a ordinal measure) and Rasch Scores is a correlation.

MLC

-----Original Message-----
>From: Andrew Kyngdon <akyngdon at lexile.com>
>Sent: Nov 13, 2008 4:47 PM
>To: luckyantonio2003 at yahoo.com, rasch at acer.edu.au
>Subject: RE: [Rasch] Dimensionality and Correlation
>
>Anthony,
> 
>Those were not my words, they were Steve Humphry's. I was merely supporting them.
> 
>Steve was making the point that in the social sciences, the calculation of correlation coefficients has largely supplanted experimental investigation of relationships between quantitative attributes. There is nothing wrong in calculating correlations and they may indeed reveal interesting things from time to time. But they are limited.
> 
>The investigation of "trade off" relations is one avenue through which a relationship between two attributes can be ascertained. If the behaviour of the trade offs is consistent with that entailed by the theory of conjoint measurement, then a relationship is discovered without any resort being made to correlation coefficients.
> 
>Cheers,
> 
>Andrew
> 
>Dr Andrew Kyngdon
>Director of Pacific Rim Operations
>MetaMetrics, Inc.
>P.O. Box 754 North Sydney NSW 2059 Australia
>Phone: 0401768090 (Int. +61401768090)
>Email: akyngdon at lexile.com 
>Web: www.lexile.com <http://www.lexile.com/>  
>Lexile Teacher's Lounge: http://lexile-teachers.blogspot.com/ 
>
>________________________________
>
>From: rasch-bounces at acer.edu.au on behalf of Anthony James
>Sent: Fri 14-Nov-08 12:53 AM
>To: rasch at acer.edu.au
>Subject: RE: [Rasch] Dimensionality and Correlation
>
>
>
>
>Andrew,
>Your reply is interesting and raises new questions. What are these
> "experiments that are required to understand relationships between quantitative properties"?
>Cheers
>Anthony
>
>--- On Tue, 11/11/08, Andrew Kyngdon <akyngdon at lexile.com> wrote:
>
>> From: Andrew Kyngdon <akyngdon at lexile.com>
>> Subject: RE: [Rasch] Dimensionality and Correlation
>> To: "Stephen Humphry" <shumphry at cyllene.uwa.edu.au>, rasch at acer.edu.au
>> Date: Tuesday, November 11, 2008, 4:12 PM
>> Also in my view, a lot of people try to use correlations
>> as a substitute for experiments that are required to
>> understand
>> relationships between quantitative properties.
>>
>> Hear, hear!
>> 
>> Dr Andrew Kyngdon
>> Director of Pacific Rim Operations
>> MetaMetrics, Inc.
>> P.O. Box 754 North Sydney NSW 2059 Australia
>> Phone: 0401768090 (Int. +61401768090)
>> Email: akyngdon at lexile.com
>> Web: www.lexile.com <http://www.lexile.com/> 
>> Lexile Teacher's Lounge:
>> http://lexile-teachers.blogspot.com/
>>
>> ________________________________
>>
>> From: rasch-bounces at acer.edu.au on behalf of Stephen
>> Humphry
>> Sent: Sat 08-Nov-08 7:46 PM
>> To: rasch at acer.edu.au
>> Subject: Re: [Rasch] Dimensionality and Correlation
>>
>>
>>
>>
>> Hi Anthony. In my view there's a lot of confusion
>> surrounding this in
>> the social sciences.
>>
>> Think of volume and mass. If the densities of a set of
>> objects is
>> uniform (e.g. they're all made of uranium), then the
>> correlation
>> between measurements of their mass and volume will be near
>> 1.
>>
>> Does that make mass and volume the same quantitative
>> property? Clearly not.
>>
>> Suppose on the other hand, objects are made of a range of
>> substances
>> -- styrofoam, rubbers, metals (even gases). Then
>> measurements of mass
>> and volume will not be highly correlated and may have a
>> very low
>> correlation.
>>
>> It is possible to have a perfect correlation between two
>> sets of
>> measurements yet for those measurements to be of different
>> kinds of
>> quantities (dimensions).
>>
>> So if two sets of measurements (i) are genuinely
>> measurements and (ii)
>> have a low correlation, then they must be different kinds
>> of
>> quantities (dimensions).
>>
>> On the other hand, though, the fact two sets of
>> measurements has a
>> high (even perfect) correlation is not sufficient to
>> demonstrate there
>> is only one kind of quantity (kind of dimension). In my
>> view it's
>> theoretically instructive to consider whether it is
>> conceivable that
>> levels of two properties could be uncorrelated among any
>> group of
>> individuals under any conditions. It's an experimental
>> question
>> whether there are conditions under which two things are not
>>
>> correlated. Also in my view, a lot of people try to use
>> correlations
>> as a substitute for experiments that are required to
>> understand
>> relationships between quantitative properties.
>>
>> I also personally think the word unidimensionality is bit
>> frought with
>> traps. Hope that helps.
>>
>> Steve Humphry
>>
>>
>> Quoting Anthony James <luckyantonio2003 at yahoo.com>:
>>
>> > Dear all,
>> > I have difficulty understanding the difference between
>> 
>> > dimensionality and correlation. I have seen several
>> times in the 
>> > literature that people talk about correlated
>> dimensions and 
>> > uncorrelated dimensions. I was always under the
>> impression that if 
>> > two dimensions are correlated then they are not two
>> separate 
>> > dimensions. They are one. But apparently, this is not
>> true and there
>> >  can be two separate, and at the same time, correlated
>> dimensions.
>> > Is  that right? I'd be grateful for any comments
>> on the relationship
>> >  between correlation and dimensionality. Apparantly
>> corrlation 
>> > doesn't have much to do with unidimensionality.
>> > Cheers
>> > Anthony
>> > 
>> >
>> >
>> >
>>
>>
>>
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My best,

Michael Lamport Commons, Ph.D.

Assistant Clinical Professor
Department of Psychiatry
Harvard Medical School

Program in Psychiatry and the Law
Beth Israel Deaconess Medical Center
commons at tiac.net

http://www.dareassociation.org/
617-497-5270 Telephone
617-491-5270 Fax



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