# [Rasch] Separation

Mike Linacre (RMT) rmt at rasch.org
Tue May 12 11:09:05 EST 2009

Anthony:

"Conditional" methods of estimation use parameter-separation to "condition
out" the person parameters when estimating the item parameters. For
instance, RUMM2020 implements a conditional estimation algorithm.

"Rating Scale Analysis" (Wright & Masters, 1982) provides details of
conditional estimation algorithms.

Here is a simple equation for estimating the difference in difficulty
between two dichotomous items which conditions out the person abilities.

item 1 difficulty - item 2 difficulty = log( F01 / F10)
where
F01 is the count of persons who failed on item 1 but succeeded on item 2
F10 is the count of persons who succeeded on item 1 but failed on item 2

We can do the same for two person abilities, conditioning out the item
difficulties.

Does this help?

Mike L.

At 5/11/2009, you wrote:
>Dear folks,
>A friend of mine and I have always had this question:
>It is possible to mathematically separate perosn measures from the item
>measures in the Rasch model. This can be shown by some maths exercises.
>However, when it comes to practical estimation of person and item
>parameters, we resort to jointly estimating them from one single equation
>(this is the only estimation method that I know,which is JML). I can't
>grasp the point of separation. That is, there's no single equation to give
>person  parameters independent of item parameters and vice versa. I'm
>wondring how separation is implemented in parameter estimation.
>Cheers
>Anthony

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  22:4 Spring 2009

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