[Rasch] Rasch analysis of interval data

Michael Lamport Commons commons at tiac.net
Thu Jul 24 03:42:00 EST 2008

There is a stage transition model.  But orders are discrete and 
ordinal.  Rasch stage scores are continuous.  We see that people and 
other organisms might mix responding at two different adjacent stages.  
This yields intermediate scores.  There are also other variables in 
items that determine stage of performance.  That again would lead to 
intermediate performances.  I really do not see the problem. 

Michael Lamport Commons

Paul Barrett wrote:
>> -----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
> variable.
> 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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