# [Rasch] Why are Rasch measures linear?

Mike Linacre (RMT) rmt at rasch.org
Mon Sep 3 09:59:34 EST 2007

```Anthony et al.:

It is always useful when considering this type of question to think about
the same situation in physical measurement. How would you prove that
"meters" are linear or "grams" or "temperature degrees"? Whatever method
you would choose to use, we can think of a parallel situation with Rasch
measures.

For instance, if you choose "concatenation" (putting sticks end-to-end for
length, or piling up bricks for weight) as physicist Norman Campbell did,
then we can do an analogous operation with Rasch measures:
http://www.rasch.org/rmt/rmt21b.htm - Unfortunately this is not "in laymen
terms" because, at some point, mathematics become central.

OK?

Cordially,
Mike L.

At 9/2/2007, you wrote:
>I have a basic question on the Rasch model.
>We always hear that Rasch measures are linear while raw scores aren't.
>Linearity is defined as "equal increments to the difficulty or ability
>measures when one more unit is added to a person's or an item's location".
>What I can't grasp is why Rasch measures are linear? What's magic about
>the Rasch measures. Once I heard  "Rasch measures are cnstructed to be
>linear". But how?
>I'd be grateful if someone explains in laymen terms that why Rasch
>measures are linear.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  21:1 Summer 2007
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