# [Rasch] Negative pt-bis and fit of 1.0? How can this be?

Mark Moulton markhmoulton at gmail.com
Wed Mar 7 05:46:49 EST 2012

```Stuart,

Belay my previous message (coffee hadn't kicked in yet).

You're right.  Variances -- p * (1 - p) at the extreme of p (1 or 0) will
be smaller, which should make the misfits bigger.

Could those cell probabilities p[ni] actually be close to 0.50?  This would
happen if the person measures tended to collapse to the center of the
scale, an artifact of randomness.

Mark

On Tue, Mar 6, 2012 at 7:58 AM, Stuart Luppescu <slu at ccsr.uchicago.edu>wrote:

> Hello, I'm analyzing items suggested for a course final exam. The
> problem is that the students the items are tested on have not taken the
> course yet. This results in very poor performance. The average person
> measure is -0.78, and the average item p-value is 0.33 (for 4-choice
> multiple choice items).
>
> What is confusing me is that all the items have mean-square fit
> statistics (infit and outfit) near 1.0, while many of them have negative
> point-biserial correlations. According to my understanding, the fit
> statistics are calculated from an aggregation of the squared
> standardized residuals, which are calculated from the raw residual
> divided by the score variance. In this case, the expectation of an
> individual response would be low, so raw residuals would be large. And
> the score variance at the extremes are lower than in the middle, so you
> divide a large raw residual by a small score variance and you get a very
> large standardized residual, right? So, how come the fits are close to
> expectation? Especially since the pt-bis are low or negative? I don't
> get it. Can someone explain this to me?
>
> Thanks.
> --
> Stuart Luppescu -=- slu .at. ccsr.uchicago.edu
> University of Chicago -=- CCSR
> 才文と智奈美の父 -=-    Kernel 3.2.1-gentoo-r2
> What we have is nice, but we need something very
>  different.    -- Robert Gentleman
>  Statistical Computing 2003, Reisensburg (June
>  2003)
>
>
>
>
>
>
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