# [Rasch] Invariance

Thomas Salzberger Thomas.Salzberger at wu-wien.ac.at
Fri Jan 6 00:28:06 EST 2006

```Zitat von Rama Guinda <guinda36 at hotmail.com>:

Rama,

you can take your ability split as a person factor. Estimate the item measures
from the pooled data and do a test for differential item functioning (low
versus high ability) which esentially is a test of invariance.

Best wishes
Thomas

> Dear All,
> I have a question. Thanks for any reaction to my problem.
> I Rasch analysed 4 polytomous items with the Winsteps. The items where 4
> texts each with 20 gaps to be filled by the test-takers. In order to avoid
> the problem of local dependence I considered each text a super item. I had
> 160 cases.
> The item measures are .74, .06, -.29 and -.50.
> Then I divided the group into two (a high ability and a low ability group)
> on the basis of a  reading test which contains 14 dichotomously scored
> items. Students with scores from 0 to 7 went into the low ability group and
> the ones with scores from 8 to 14 went into the high ability group. The
> reading test has a significant but low correlation with the gap fill task
> (.53).
> I had 98 cases in the low ability group and 62 cases in the high ability
> group. To study the item invariance I separately analysed the data for each
> group.
> The item measures for the low ability group are: .62, .10, -.25, -.47.
> The item measures for the high ability group are: .94, .02, -.38, -.58.
> The order of the difficulty of the items remains the same in all three
> groups.
> Question 1: What is the test of invariance for the item measures? Have they
> really remained invariant within the allowable range of error?
>
> Best
> Rama
>
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--
Liebe Gruesse / Kind regards
Thomas Salzberger

```