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.

中文翻译：

---

用于小样本项目校准的优化贝叶斯分层二参数 Logistic 模型。


项目反应理论（IRT）模型中的准确项目校准需要相当大的样本。例如，通常建议 N > 500 名受访者使用双参数逻辑 (2PL) 模型。因此，该模型被认为是大规模应用，并且其在小样本环境中的使用受到限制。经常提出分层贝叶斯方法来减少 2PL 的样本量要求。本研究将优化贝叶斯分层 2PL (H2PL) 模型的小样本性能与其标准逆 Wishart 规范、非分层对应模型以及未加权和加权最小二乘估计量（ULSMV 和 WLSMV）在采样效率和精度方面进行了比较。项目参数及其方差分量的估计。为了缓解分层模型的缺点，优化的 H2PL (a) 被重新参数化以简化采样过程，(b) 使用一种策略来分离项目参数协方差及其方差分量，(c) 方差分量被赋予柯西和指数超先验分布。结果表明，当在优化的 H2PL 中组合这些元素时，即使样本量小至 N = 100，也可以获得准确的项目参数估计和性状得分。这表明 2PL 也可以应用于实践中遇到的较小样本量。这项研究的结果是在最近提出的多重插补方法的背景下讨论的，以解释性状估计中的项目校准误差。