Reliability is a crucial index of measurement precision and is commonly reported in substantive research using latent variable measurement models. However, reliability coefficients, often treated as fixed values, are estimated from sample data and thus inherently subject to sampling variability. Building on the recently proposed regression framework of reliability (Liu, Pek, & Maydeu-Olivares, 2025), this study classifies reliability coefficients in item response theory (IRT) into classical test theory (CTT) reliability and proportional reduction in mean squared error (PRMSE) and derives their asymptotic standard errors (SEs) to quantify this variability. Unlike existing approaches (e.g., Andersson & Xin, 2018), which requires computing population moments, we focus on cases using sample moments instead. This allows for estimation of reliability and SEs in long tests. By incorporating sampling variability arising from both item parameter estimation and the use of sample moments, we present a more general strategy for computing SEs of model-based reliability coefficients. Simulation results confirm that the derived SEs accurately capture the sampling variability across various test lengths in moderate to large samples.

翻译：可靠性是衡量测量精度的关键指标，在基于潜变量测量模型的实证研究中被广泛报告。然而，可靠性系数通常被视为固定值，实则基于样本数据估计得出，因而本质上受抽样变异性影响。本研究基于近期提出的可靠性回归框架（Liu, Pek, & Maydeu-Olivares, 2025），将项目反应理论（IRT）中的可靠性系数划分为经典测验理论（CTT）可靠性与均方误差比例缩减（PRMSE）两类，并推导其渐近标准误（SEs）以量化该变异性。与现有方法（如Andersson & Xin, 2018）需计算总体矩不同，我们聚焦于使用样本矩的情形。这使得长测验中的可靠性及标准误估计成为可能。通过综合考虑项目参数估计与样本矩使用带来的抽样变异性，我们提出了一种更通用的基于模型的可靠性系数标准误计算策略。模拟结果证实，在中等至大样本中，推导出的标准误能准确捕捉不同测验长度下的抽样变异性。