基于微评估的组水平推断
Group-Level Inference with Micro-Assessments
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中文总结 AI 辅助
该研究针对组水平推断中长评估效率低的问题，推导了潜在IRT均值估计的渐近标准误近似公式，经基准验证后表明单项目形式也能得到近似无偏的组均值。
中文摘要 AI 辅助
当推断目标是组均值而非个体得分时，长评估在统计上效率低下。我们从似然的边际得分出发，推导了随机项目抽样下潜在IRT均值的边际最大似然估计量的渐近标准误，并通过项目信息的高斯卷积处理得到闭式近似。该公式明确了测验长度与样本量的权衡关系，且包含一个膨胀因子，用于在项目库未匹配目标时联合估计总体方差。我们通过精确基准、项目库与总体不匹配下的蒙特卡洛模拟以及NAEP数学重抽样研究对其进行验证；即使采用单项目形式，组均值仍近似无偏。
英文摘要
When the target of inference is a group mean rather than an individual score, long assessments can be statistically inefficient. From the marginal score of the likelihood, we derive the asymptotic standard error of the marginal maximum likelihood estimator of a latent IRT mean under random item sampling, and obtain a closed-form approximation via a Gaussian-convolution treatment of the item information. The formula makes the test-length--sample-size trade-off explicit and includes an inflation factor for jointly estimating the population variance when the item pool is mistargeted. We validate it against exact benchmarks, Monte Carlo simulation under pool--population mismatch, and a NAEP mathematics resampling study; group means remain approximately unbiased even with single-item forms.
