Interval Estimation of Latent Variable Scores in Item Response Theory

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the c...

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Bibliographic Details
Published inJournal of educational and behavioral statistics Vol. 43; no. 3; pp. 259 - 285
Main Authors Liu, Yang, Yang, Ji Seung
Format Journal Article
LanguageEnglish
Published Los Angeles, CA SAGE Publishing 01.06.2018
SAGE Publications
American Educational Research Association
Subjects
Bayesian Statistics
Equations (Mathematics)
Intervals
Item Response Theory
Maximum Likelihood Statistics
Monte Carlo Methods
Monte Carlo simulation
Parameter estimation
Prediction
Random variables
Sample Size
Scores
Scoring
Statistical Analysis
Statistical Inference
multiple imputation
generalized fiducial inference
scoring
item response theory
Bayesian inference
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Summary:The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a predictive inference problem: The target of prediction is a random variable that follows the true posterior of the LV conditional on the response pattern being scored. Various Bayesian, fiducial, and frequentist prediction intervals of LV scores, which can be obtained from a simple yet generic Monte Carlo recipe, are evaluated and contrasted via simulations based on several measures of prediction quality. An empirical data example is also presented to illustrate the use of candidate methods.
ISSN:1076-9986
1935-1054
DOI:10.3102/1076998617732764