[Rasch] Rasch analysis of interval data

Mark Moulton markhmoulton at gmail.com
Thu Jul 17 09:16:11 EST 2008


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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