# [Rasch] Measures in Rasch Model

Stephen Humphry shumphry at cyllene.uwa.edu.au
Sat Jun 21 22:55:21 EST 2008

```Hi. For dichotomous items, there is a single threshold at which it is
equally probably a person will respond incorrectly or correctly. This
threshold is the item difficulty.

For polytomous item, the item parameters are also thresholds. Each
threshold is the location at which it is equally likely a person's
response will be in one of two adjacent categories, or be judged in
one of two adjacent categories. At the first threshold, the scores 0
and 1 are equally likely, at the second threshold, the scores 1 and 2
are equally likely, and so on.

The polytomous model is sometimes written with an item difficulty and
parameters that represent the distance of each threshold from the item
difficutly. In this case, item difficulty is by definition the average
threshold location.

However, to understand how the parameters of the polytomous model are
an extension of the single parameter of the dichotomous model, it is
probably simpler for you to think about one threshold (item
difficulty) for dichotomous items, and more than one threshold for
polytomous items with 3 or more categories.

Item difficulty is simply the single threshold in the special case in
which there is only one threshold and two categories, such as
incorrect and correct responeses. Different terms may be used to refer
to the thresholds but the concept remains the same whatever these
parameters are called.

Hope that helps,

Steve

Quoting Juanito Talili <talilij at yahoo.com>:

> Dear Rasch Modelers,
>
> For a dichotomous case, the item measure is called "item difficulty"
> while the person measure is called "person ability".  I have a
> difficulty of understanding the measures for the polytomous(rating
> scale) case.  Can somebody have a kind heart to explain these things?
>
> Thank you.
> J. Talili
>
>
>

```