[Rasch] Average Threshold Measure in PCM

Mike Linacre rmt at rasch.org
Wed Mar 30 10:00:57 EST 2011


Communicating the functioning of a rating scale is challenging, especially 
if your audience think of its categories as separate and equally-spaced 
points on the latent variable.

If you want to communicate the categories as points, then the best points 
for the intermediate categories are the locations on the latent variable at 
which the probability of observing each category is the highest. These are 
also the points where the expected score on the item is the category value. 
In Winsteps these are the "AT CAT" measures in the ISFILE= output 
file.  These points are at infinity for the extreme categories, so Winsteps 
reports the  measures for expected scores of "lowest category + 0.25" ( = 
CAT +0.25) and "highest category - 0.25" (= CAT - 0.25).

The Rasch item difficulty (in IFILE=) is the point on the latent variable 
at which the highest and lowest categories are equally probable.

The Rasch-Thurstone thresholds (50%PRB in ISFILE=) dichotomize the rating 
scale at each category boundary into 50% probability of being observed 
below the category and 50% probability of being observed in or above the 

The points on the latent variable where the expected scores are 2.5, etc., 
are called the CAT-0.5 points in ISFILE=.

Does this help?

Mike L.

At 3/29/2011, you wrote:
>interpretation of the threshold resulting from the partial credit model 
>seems straightforward to me. however, while attempting to not overwhelm my 
>audience i would like to present and discuss fewer parameters by using the 
>average threshold ("average measure" in the winsteps IFILE). but how do i 
>interpret this parameter? does it represent the point on the theta 
>continue at which subjects have a 50% chance of being above/below the 
>average score?
>for example, given an item scored 0-5 there are 5 thresholds (-2,-1,0,1,2) 
>an average threshold = 0. does this mean that 0 is the theta value 
>corresponding to an equal chance of scoring above or below 2.5 points on 
>this item?

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  24:4 Spring 2011
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