ERIC Number: EJ1019164
Record Type: Journal
Publication Date: 2013-Dec
Abstractor: As Provided
l[subscript z] Person-Fit Index to Identify Misfit Students with Achievement Test Data
Seo, Dong Gi; Weiss, David J.
Educational and Psychological Measurement, v73 n6 p994-1016 Dec 2013
The usefulness of the l[subscript z] person-fit index was investigated with achievement test data from 20 exams given to more than 3,200 college students. Results for three methods of estimating ? showed that the distributions of l[subscript z] were not consistent with its theoretical distribution, resulting in general overfit to the item response theory model and underidentification of potentially nonfitting response vectors. The distributions of l[subscript z] were not improved for the Bayesian estimation method. A follow-up Monte Carlo simulation study using item parameters estimated from real data resulted in mean l[subscript z] approximating the theoretical value of 0.0 for one of three ? estimation methods, but all standard deviations were substantially below the theoretical value of 1.0. Use of the l[subscript z] distributions from these simulations resulted in levels of identification of significant misfit consistent with the nominal error rates. The reasons for the nonstandardized distributions of l[subscript z] observed in both these data sets were investigated in additional Monte Carlo simulations. Previous studies showed that the distribution of item difficulties was primarily responsible for the nonstandardized distributions, with smaller effects for item discrimination and guessing. It is recommended that with real tests, identification of significantly nonfitting examinees be based on empirical distributions of l[subscript z] generated from Monte Carlo simulations using item parameters estimated from real data.
Descriptors: Achievement Tests, College Students, Goodness of Fit, Item Response Theory, Bayesian Statistics, Computation, Monte Carlo Methods, Statistical Distributions, Test Items, Difficulty Level, Guessing (Tests), Maximum Likelihood Statistics
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
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