[Rasch] Dimensionality and Correlation
Michael Lamport Commons
commons at tiac.net
Tue Nov 11 10:30:33 EST 2008
That is why we always regress Rasch Score performance on the Items
analytically determined order of hierarchical complexity, a truly
independent variable. This insures that the scales are working. Still,
development and learning are pushed by similar environments as twin
Michael Lamport Commons
Mark Moulton wrote:
> 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 <mailto: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
> <mailto: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.
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