A variety of methods have been developed to determine
the extent to which a person’s response vector fits
an item response theory model. These person-fit methods
are statistical methods that allow researchers to
identify nonfitting response vectors. The most promising method has been the lz statistic, which is a standardized
person-fit index. Reise & Due (1991) concluded that under
the null condition (i.e., when data were simulated to
fit the model) lz performed reasonably well. The present
study extended the findings of past researchers (e.g.,
Drasgow, Levine, & McLaughlin, 1987; Molenaar &
Hoijtink, 1990; Reise and Due). Results show that lz
may not perform as expected when estimated person parameters
(θˆ) are used rather than true θ. This study also
examined the influence of the pseudo-guessing parameter,
the method used to identify nonfitting response
vectors, and the method used to estimate θ. When θ was
better estimated, lz, was more normally distributed, and the false positive rate for a single cut score did not characterize the distribution of lz. Changing the c parameter
from .20 to 0.0 did not improve the normality of the lz.
distribution. Index terms: appropriateness measurement,
Bayesian estimation, item response theory, maximum
likelihood estimation, person fit.
Nering, Michael L. (1995). The distribution of person fit using true and estimated person parameters. Applied Psychological Measurement, 19, 121-129. doi:10.1177/014662169501900201
Nering, Michael L..
The distribution of person fit using true and estimated person parameters.
Retrieved from the University of Minnesota Digital Conservancy,
Content distributed via the University of Minnesota's Digital Conservancy may be subject to additional license and use restrictions applied by the depositor.