期刊
APPLIED PSYCHOLOGICAL MEASUREMENT
卷 -, 期 -, 页码 -出版社
SAGE PUBLICATIONS INC
DOI: 10.1177/01466216231209758
关键词
auxiliary item information; Bayesian estimation; explanatory item response model; graded response model; shrinkage estimator; small sample size
In this study, empirical Bayes and hierarchical Bayes methods are proposed as alternatives to marginal maximum likelihood estimation (MMLE) for item parameter estimation in small sample sizes. Simulation results show that hierarchical Bayes methods can be acceptable alternatives to MMLE.
Marginal maximum likelihood estimation (MMLE) is commonly used for item response theory item parameter estimation. However, sufficiently large sample sizes are not always possible when studying rare populations. In this paper, empirical Bayes and hierarchical Bayes are presented as alternatives to MMLE in small sample sizes, using auxiliary item information to estimate the item parameters of a graded response model with higher accuracy. Empirical Bayes and hierarchical Bayes methods are compared with MMLE to determine under what conditions these Bayes methods can outperform MMLE, and to determine if hierarchical Bayes can act as an acceptable alternative to MMLE in conditions where MMLE is unable to converge. In addition, empirical Bayes and hierarchical Bayes methods are compared to show how hierarchical Bayes can result in estimates of posterior variance with greater accuracy than empirical Bayes by acknowledging the uncertainty of item parameter estimates. The proposed methods were evaluated via a simulation study. Simulation results showed that hierarchical Bayes methods can be acceptable alternatives to MMLE under various testing conditions, and we provide a guideline to indicate which methods would be recommended in different research situations. R functions are provided to implement these proposed methods.
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