Many item-fit statistics have been proposed for
assessing whether the responses to test items aggregated
across examinees conform to IRT test
models. Conversely, person-fit statistics have been
proposed for assessing whether an examinee’s responses
aggregated across items are congruent with
a specified IRT model. Statistical procedures to assess
item fit have differed from those to assess person
fit. This research compared a x² item-fit index
with a likelihood-based person-fit index. Eight 0,1
data matrices were simulated under the three-parameter
logistic test model. Both the likelihood-based
and x² fit statistics were then computed for
examinees and items, and Type I and Type II error
rates were analyzed. With data simulated to fit the
IRT model, the x² test overidentified examinees and
items as being misfitting, while the likelihood-based
fit index held closer to the specified α levels.
The two fit indices gave consistent (mis)fit-to-model
results in 94 and 97 percent of cases for
items and examinees, respectively, across simulations.
Under simulated conditions of data misfit,
the x² statistic detected misfit at a higher rate than
the likelihood-based statistic, indicating that the x² statistic was slightly more sensitive to response pattern
aberrancy. However, other considerations led
to a recommendation for employing the likelihood-based
index in applied fit analyses to evaluate both
examinee and item model-data (mis)fit. Index
terms: chi-square index, item fit, item response theory,
model fit, person fit, response aberrancy.
Reise, Steven P. (1990). A comparison of item- and person-fit methods of assessing model-data fit in IRT. Applied Psychological Measurement, 14, 127-137. doi:10.1177/014662169001400202
Reise, Steven P..
A comparison of item- and person-fit methods of assessing model-data fit in IRT.
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