[Rasch] Unidimensionality (follow up with the practical issue)

Stephen Humphry shumphry at cyllene.uwa.edu.au
Sat May 10 22:00:07 EST 2008

```I think the problem lies in confusion regarding the terms
'multidimensionality' and 'unidimensional'.

To claim that ability or mental attributes are 'multidimensional'
potentially confuses the geometric representation of correlations with
the idea of an actual mental or psychological "space" in which things
and phenomena genuinely exist statically and/or dynamically. Physical
pace is actually three-dimensional, but nothing else has been shown to
be actually multidimensional in this sense.

And correlation is contingent; correlation doesn't reveal causes, only
experiments do. If physicists measurement using methods premised on
correlation, confusion would reign.

Otherwise, multidimensional might simply mean test results depend on
more than one attibute, each of which could in principle be measured
indepdently, with relationships contingent on other factors. In the
latter sense, most dimensions in physics could be called
'multidimensional'. The mass of an object depends on its volume and
density, but that doesn't mean it can't be measured.

Steve

Quoting Trevor Bond <trevor.bond at jcu.edu.au>:

> Dear steve et al,
>
> But using a Rasch model this way would require treating the data as
> though it were unidimensional, even though we have strong reason to
> believe that it is not.
>
> We should treat the data as unidimensional only to the extent that we
> have evidence to support that for the purpose of the decisions we make.
>
> Different aspects of a (maths) test do not (necessarily) imply several
> measurement dimensions.
>
> That's where we got into this discussion with the Ferguson ref claiming
> factors can be artifactual (artifacts of the difficulty range)
> consequences of the FA (correlations based) analyses. (see ppxii-xiii
> of B&F 2001 for details)
>
> So that is why I need better to understand what happens when you
> extract a Rasch Dimension from what is truly a multi-dimensional
> situation.
> Multidimensions are perhaps better analysed using the MCMLM model used
> for PISA (B&F 2007, pp258-260).
>
> Then we get back to the criticism I have of much educational testing:
> if mere exposure to test items invalidates their use / changes their
> test characteristics, I wonder what they really test. My guess it is
> not understanding of the maths concepts.
>
> Translator's note:
> maths in Oz = math in US
>
> Best
> TGB
> --
> 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