# [Rasch] Dimensionality and Correlation

Andrew Kyngdon akyngdon at lexile.com
Sat Nov 15 00:10:17 EST 2008

```Michael,

Not exactly sure of what you are communicating here ("order of hierarchical complexity is ordinal" is tautologous). I imagine you have collected data from persons consisting of their rank of heirarchical complexity and a set of Rasch person locations (of some attribute) for these same people. Have you converted the Rasch person locations into ranks and then calculated a non-parametric correlation coefficient?

Andrew

________________________________

From: rasch-bounces at acer.edu.au on behalf of Michael Lamport Commons
Sent: Fri 14-Nov-08 2:38 PM
To: Stephen Humphry; rasch at acer.edu.au
Subject: RE: [Rasch] Dimensionality and Correlation

What about the case I gave where the order of hierarchical complexity is ordinal and the Rasch Scale is conjount, the the r is over .95

MLC

-----Original Message-----
>From: Stephen Humphry <shumphry at cyllene.uwa.edu.au>
>Sent: Nov 13, 2008 10:22 PM
>To: rasch at acer.edu.au
>Subject: RE: [Rasch] Dimensionality and Correlation
>
>
>Precisely Andrew. A complementary way of saying the same thing is that
>there may be a correlation between a quantitative property A and
>another quantitative property B that is produced in an experiment for
>a *fixed level* of a property C.
>
>The structure of many physical definitions and laws implies, though,
>that in relevant cases, the measurement itself must be conjoint;
>whereas the description in terms of correlations presupposes the
>properties can be measured separately then correlated. As an example,
>you cannot measure the mass of an object without a force and,
>symmetrically, you cannot measure a force without using an object with
>mass. Acceleration, in some form, is the experimental outcome. Force
>and mass are measured conjointly -- so I agrue at least, and I
>maintain that Poincaré made this point in 'Science and Hypothesis'.
>
>Steve
>
>Quoting Andrew Kyngdon <akyngdon at lexile.com>:
>
>> 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
>>> >
>>> >
>>> >
>>> >
>>>
>>>
>>>
>>> _______________________________________________
>>> Rasch mailing list
>>> Rasch at acer.edu.au
>>> https://mailinglist.acer.edu.au/mailman/listinfo/rasch
>>>
>>>
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>>> Rasch at acer.edu.au
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>>
>>
>>
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>
>
>
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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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