[Rasch] Rasch analysis of interval data

Stephen Humphry shumphry at cyllene.uwa.edu.au
Sat Jul 19 06:54:22 EST 2008


Mark, Thurstone argued Weber's law gives Fechner's 'law' when the  
discriminal dispersions are equal for all stimuli, as in Case V of the  
law of comparative judgment. In this case, the Bradley-Terry-Luce  
model also holds, which has the form of the Rasch model with only one  
kind of parameter.

To the extent the "Weber-Fechner" law holds, therefore, the Rasch  
model holds, and the relationship between physical and perceptual  
magnitudes of stimuli is not linear; rather it is logarithmic.  
Nevertheless, it is likely to appear linear within a relatively small  
range.

> A question I would like to answer is:  "Under what
> conditions must a probabilistic space correspond to a "physical" space, or
> to any other space."  I think an effort to answer this question rigorously
> would prove very fruitful.

Clearly, there are good reasons to suspect some correspondence between  
the perception of certain physical quantities and actual  
three-dimensional physical space. Examples are the perception of the  
locations of objects and sounds in physical space. However, I think it  
is unfortunate that coexistent dimensions are invoked so commonly in  
the social sciences in situations in which there is no connection to  
three-dimensional physical space, and in the absence of any compelling  
theory with direct empircal evicence to support it.

Although I'm not sure what you mean by a probabilistic space in this  
context, I agree that an effort to rigorously answer this kind of a  
question would prove fruitful.

Steve
ting Mark Moulton <markhmoulton at gmail.com>:

> Anthony,
> I did a number of experiments in this vein, almost exactly as you described.
>  I did indeed find that my Rasch logit measures had a strong linear
> relationship with centimeter measures.  While this was suggestive as a
> demonstration, and spurred me to carry the analogy between Rasch measurement
> and spatial geometry quite a bit further, it does not constitute proof that
> Rasch measures must necessarily correspond to such "physical" measures in a
> strictly linear way.  A question I would like to answer is:  "Under what
> conditions must a probabilistic space correspond to a "physical" space, or
> to any other space."  I think an effort to answer this question rigorously
> would prove very fruitful.
>
> Mark Moulton
> Educational Data Systems
>
>
> 2008/7/16 Anthony James <luckyantonio2003 at yahoo.com>:
>
>> Hi all,
>>
>> Has anyone ever tried to Rasch analyse a variable for which there's
>> concatenation-based objective measurement? Suppose we make a height scale
>> with 6 points:
>>
>> Very short (1), short (2), average height (3), quite tall (4), rather all
>> (5), Very Tall (6)
>>
>> We measure some people with this scale and then Rasch analyses it and
>> obtain Rasch height measures. How do these measures compare with persons'
>> heights in centimeters or inches? Does the Rasch measure difference between
>> a person who is 170 cm and a person who is 175cm equal to the Rasch measure
>> difference between a person who is 180cm and one who is 185cm?
>>
>> I'd love to see what happens. Pairing persons' heights in cm and their
>> Rasch heights simultaneously on a vertical line and comparing the
>> calibrations give a good test of Rasch's interval scaling, I guess.
>>
>> Cheers
>>
>> Anthony
>>
>>
>>
>>
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>






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