[Rasch] What measure is halfway?

Mike Linacre (RMT) rmt at rasch.org
Sun Nov 18 09:24:17 EST 2007


Dear Rasch practitioners ....

Here's a question I've been asked - and your viewpoints would be appreciated.

Imagine a rating scale for an item from 0 to 7 (8 categories). So the 
categories are 0, 1, 2, 3, 4, 5, 6, 7. The central categories are 3 and 4.
What person measure corresponds to half-way along the rating scale?

A. The person measure for which the expected score on the item is half-way 
between 0 and 7, i.e., 3.5 rating points.
B. The person measure for which the probability of being observed in the 
bottom half of the rating scale (categories 3 and below) is the same as the 
probability of being observed in the top half of the rating scale 
(categories 4 and above).
C. The person measure for which the probability of being observed in 
central category 3 is the same as the probability of being observed in 
central category 4.

Which do you think? Or do you have a fourth answer?

Let's make the rating scale from 0 to 6 (7 categories): 0,1,2,3,4,5,6, so 
that the central category is 3.
What person measure corresponds to half-way along the rating scale?

D1. The person measure for which the expected score on the item is half-way 
between 0 and 6, i.e., 3 rating points
D2. The person measure at which central category 3 has the highest 
probability (which is the same as D1 for the usual Rasch models).
E. The person measure for which the probability of being observed in the 
lower section of the rating scale (categories 0,1,2) is the same as the 
probability of being observed in the upper section (categories 4,5,6 and 
above).

Now which do you think? Or do you have another answer?

Mike Linacre




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