An optimized Bayesian hierarchical two-parameter logistic model for small-sample item calibration

  • Accurate item calibration in models of item response theory (IRT) requires rather large samples. For instance, N > 500 respondents are typically recommended for the two-parameter logistic (2PL) model. Hence, this model is considered a large-scale application, and its use in small-sample contexts is limited. Hierarchical Bayesian approaches are frequently proposed to reduce the sample size requirements of the 2PL. This study compared the small-sample performance of an optimized Bayesian hierarchical 2PL (H2PL) model to its standard inverse Wishart specification, its nonhierarchical counterpart, and both unweighted and weighted least squares estimators (ULSMV and WLSMV) in terms of sampling efficiency and accuracy of estimation of the item parameters and their variance components. To alleviate shortcomings of hierarchical models, the optimized H2PL (a) was reparametrized to simplify the sampling process, (b) a strategy was used to separate item parameter covariances and their variance components, and (c) the variance components were given Cauchy and exponential hyperprior distributions. Results show that when combining these elements in the optimized H2PL, accurate item parameter estimates and trait scores are obtained even in sample sizes as small as N = 100. This indicates that the 2PL can also be applied to smaller sample sizes encountered in practice. The results of this study are discussed in the context of a recently proposed multiple imputation method to account for item calibration error in trait estimation.

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Author:Christoph KönigORCiDGND, Christian SpodenORCiDGND, Andreas FreyORCiDGND
Parent Title (German):Applied psychological measurement
Publisher:SAGE Publications
Place of publication:London
Document Type:Article
Year of Completion:2020
Date of first Publication:2019/12/21
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2020/12/03
Tag:Bayesian; calibration; hierarchical models; item response theory; simulation; small samples
Page Number:16
First Page:311
Last Page:326
Institutes:Psychologie und Sportwissenschaften / Psychologie
Dewey Decimal Classification:1 Philosophie und Psychologie / 15 Psychologie / 150 Psychologie
Licence (German):License LogoDeutsches Urheberrecht