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

Stuart Luppescu slu at ccsr.uchicago.edu
Wed Mar 7 02:58:18 EST 2012

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?

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

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