[Rasch] Dimensionality and Correlation

demott at aol.com demott at aol.com
Sat Sep 12 09:18:08 EST 2009


 Of course, the reason that reading and math are correlated in a person can be that both have a high g-loading, and they both occur in that person's brain. Perhaps this is not PC.

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-----Original Message-----
From: Michael Lamport Commons <commons at tiac.net>
To: Trevor Bond <trevor.bond at jcu.edu.au>
Cc: Mark Moulton <markhmoulton at gmail.com>; rasch at acer.edu.au
Sent: Fri, Sep 11, 2009 2:40 pm
Subject: Re: [Rasch] Dimensionality and Correlation












  
  

This is a two way street.? Education also is the best predictor of
stage.



MLC



Trevor Bond wrote:


  
  
  
Well, Mark,

  
That might be your view. But there is another alternative
competing hypothesis: School achievement is driven by cognitive
development- the necessary but not sufficient pre-cursor of all
meaningful school learning.

  
Tendentiously

  
Trevor

  


  

  


  

  
At 2:25 PM -0800 11/10/08, Mark Moulton wrote:

  
Stephen,

  


  

  
Great response to Anthony's
question!

  


  

  
The only thing I want to add is that
dimensions tend to become uncorrelated to the degree the objects
(e.g., persons) are randomly drawn from the population of all possible
objects. ?However, the objects studied in education and social
science, and in science at large, tend to be sampled in highly
non-random ways. ?When kids go to school they study Math and
Language in tandem, causing the subject areas to have high
correlations artifactually caused by the students having school in
common. ?However, in a hypothetical society without school where
people learn things at random, Math and Language scores would have a
lower correlation.

  


  

  
This can bite us in Rasch fit
analysis,
as has been noted in previous discussions. ?Items may appear to
fit very well (i.e., be highly correlated) simply because all the
students experience a similar curriculum. ?When a subsample of
students experiences a different kind of curriculum, the same items
may end up with different relative difficulties. ?In these cases,
Rasch is not giving us sample free statistics and we don't know it.
?The only remedy is either to constrain ourselves to students who
have experienced a similar curriculum, or to use items whose
difficulties are robust across different curricula.

  


  

  
Mark Moulton

  
Educational Data Systems

  

  


  

  


  

  
On Sat, Nov 8, 2008 at 12:46 AM,
Stephen
Humphry <shumphry at cyllene.uwa.edu.au>
wrote:

    


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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