# [Rasch] Unidimensionality

Steven L. Kramer skramer1958 at verizon.net
Fri May 9 00:00:21 EST 2008

```Dear Antony, Trevor, and Rasch Modelers,

Understanding "dimensionality" is very important to the work I do--and I
need some help on this.

I have looked at math curriculum effects on student learning.  And at the
intersection between testing, instruction, and math curriculum.

When you compare curricula, the "unidimensionality" assumption is often
violated by-design.  As an extreme example:  imagine testing tenth graders
in algebra and geometry knowledge.  Half of them have taken Algebra 1
followed by Algebra 2.  (They are scheduled to take Euclidean Geometry until
eleventh grade) The other half have taken Algebra 1 followed by Geometry.
(They are scheduled to take Algebra 2 in eleventh grade.)  Clearly, the test
cannot be unidimensional.  And I know that forcing the test at that time
into a Rasch model would be a bad idea--but what if the school system does
it anyway?  What flags would show up to indicate a problem?  And what would
the "Rasch dimension" mean when it was extracted?

This is an extreme example of a practical problem I run into all the time.
I'll send another email with the actual practical problem--but dealing with
the extreme case (above) would give me a sense of the "boundary" solution
and probably help me understand the theory better than would dealing with my
current "real" issue.  (To avoid distraction, I'm not including the actual
problem in this email.)

Steve Kramer

----- Original Message -----
From: "Trevor Bond" <trevor.bond at jcu.edu.au>
To: <luckyantonio2003 at yahoo.com>; <rasch at acer.edu.au>
Sent: Wednesday, May 07, 2008 7:12 PM
Subject: Re: [Rasch] Unidimensionality

> >Dear Antony
>
> what comes first, the measure or the residuals ?
>
>>In a couple of papers I noticed that the researchers before using Rasch
>>model or IRT models first use factor analysis to ascertain
>>unidimensionality. Since unidimensionality is a prerequisite to use IRT
>>models. They give the impression that only after FA has shown that the
>>test is unidimensioanl, one can use Rasch or IRT models.
>>
>>Is this really necessary? Isn't the Rasch model itself a technique,
>>superior to FA, to demonstrate unidimensionality?
>
> my view is:
> 1 find and remove the Rasch dimension
> 2 use FA of the residuals to determine if sufficient structure exists in
> those residuals to infer more than one dimension in the data - the
> residuals should be randomly distributed.
>
> For mine: FA used before RM misses the point of RM
> best
> T
> --
> 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
> Book:
> http://www.researchmethodsarena.com/books/Applying-the-Rasch-Model-isbn9780805854626
> Voice: (852) 2948 8473
> Fax:  (852) 2948 7983
> Mob:
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>

```