[Rasch] Rasch analysis of interval data

Paul Barrett pbarrett at hoganassessments.com
Thu Jul 24 02:57:54 EST 2008


> -----Original Message-----
> From: rasch-bounces at acer.edu.au 
> [mailto:rasch-bounces at acer.edu.au] On Behalf Of Theo Dawson
> Sent: Wednesday, July 23, 2008 11:25 AM
> To: Rasch Mailing List
> Subject: Re: [Rasch] Rasch analysis of interval data
> Although the complexity scale is based on a complex model of 
> development that posits qualitative transformations (hierarchical
> integrations) as opposed to additive learning, developmental 
> level is measurable. In fact, one could argue that scores on 
> a lectical assessment are less arbitrary than measures of 
> space, time, or, temperature, because each level represents 
> an identical transformation (an advance of one order of 
> hierarchical complexity).
> Rasch modeling, combined with some trig, shows that cognitive 
> development is well-represented by a sequence of sine waves.  
> Performances can be assigned to points along this wavy 
> continuum, even though developmental progress is not smooth. 
> Each point along the continuum has a specific meaning, 
> including implications for understanding, behavior, and 
> learning. If this isn't measurement, then we need a new definition!

It isn't quantitative measurement as defined by Holder's axioms.
Clearly, there is no continuous, real-valued, additive function for
which continuous magnitudes of "hierarchical Order" or "Stage" might be
adduced - you are simply mapping order-classes to stage-classes - both
of which use discrete integers to represent magnitudes. These might as
well be A, B, C, Ds etc. for both class categories. Yes, the mapping is
approximated well by a linear function, but that itself is illusory as
there is nothing on your theory which says what lies between each stage
or order, and whether that should be linear at all, let alone what
standard unit should be used to express ratios of magnitudes on either

I don't think this matters greatly - as the theory and mapping is
probably about the best you can get considering the realities of
developmental neuroscience and the properties of neural self-organizing
systems-complexity, even under specific development constraints. 

I'm curious as to why you propose such processes could ever be
considered as measurable in the manner of a physical scale?

Let me ask you and Michael a really tough question ... While you might
assign two children to the same integer stage of hierachical complexity,
how do you know they are truly equal? That is, what properties of this
equality might you test so as to demonstrate the absolute
"psychological-variable" equivalence implied by the absolute
mathematical equivalence of the integers you have assigned?? 

Regards .. Paul

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