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Educational and Psychological Measurement
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Empirical Histograms in Item Response Theory With Ordinal Data

Carol M. Woods

Washington University in St. Louis, cwoods{at}artsci.wustl.edu

The purpose of this research is to describe, test, and illustrate a new implementation of the empirical histogram (EH) method for ordinal items. The EH method involves the estimation of item response model parameters simultaneously with the approximation of the distribution of the random latent variable ({tau}) as a histogram. Software for the EH method with ordinal items (having more than two response options) has not been readily available in the past but was created for the present research. Simulation results suggest that with larger (but not smaller) numbers of quadrature points, graded-model item parameter estimates from the EH method are highly accurate when the {tau} distribution is either normal or skewed. Results for expected a posteriori scores depend on the magnitude of {tau}.

Key Words: item response theory • IRT • nonnormality • empirical histogram • expectation Maximation • EM • marginal maximum likelihood • MML

Educational and Psychological Measurement, Vol. 67, No. 1, 73-87 (2007)
DOI: 10.1177/0013164406288163
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C. M. Woods
IRT-LR-DIF With Estimation of the Focal-Group Density as an Empirical Histogram
Educational and Psychological Measurement, August 1, 2008; 68(4): 571 - 586.
[Abstract] [PDF]