# [Rasch] Average Threshold Measure in PCM

Matthew Gushta matthew at allinonemove.com
Thu Mar 31 08:59:13 EST 2011

```mike--
this helps tremendously, thank you.
just to confirm:
* the "rasch-thurstone thresholds" (50%PRB) indicate the point on the latent
scale where where an examinee has equal probability of being below the
current category or *at/above* the current category. these parameters are
never disordered.
* the "rasch-andrich thresholds" (MEASURE) indicate the point on the latent
scale where an examinee has equal probability of being below the current
category or *in* the current category. these parameters may be disordered.

now, if the categories are, in fact, disordered,does the interpretation of
the rasch item difficulty (from the IFILE) still hold?

--matthew

On Tue, Mar 29, 2011 at 7:00 PM, Mike Linacre <rmt at rasch.org> wrote:

> Matthew:
>
> 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 category.
>
> 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:
>
> rasch'ers--
> 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?
>
> thanks!
>
> --matthew
>
>  Mike Linacre
> Editor, Rasch Measurement Transactions
> rmt at rasch.org *www.rasch.org/rmt/* <http://www.rasch.org/rmt/> Latest
> RMT:  24:4 Spring 2011
>
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