多成员线性混合模型的高效最大似然估计及其在教育增值评估中的应用
Efficient Maximum Likelihood Estimation of Multiple Membership Linear Mixed Models, with an Application to Educational Value-Added Assessments
AI总结：
针对多成员线性混合模型的计算挑战，开发基于稀疏结构的EM算法实现高效最大似然估计，通过R包GPvam验证了其在教育增值评估场景的效率提升。
摘要：
广义持续性（GP）模型是在估计单个教师对学生当前及未来考试分数的“增值”贡献背景下开发的，是文献中最灵活的增值模型之一。尽管该模型在教育场景中开发，但它可潜在应用于任意结构，其中较低层级单元的每个顺序响应可能与不同的较高层级单元相关联，且较高层级单元的效应可随时间持续。然而，GP模型的灵活性及其多成员随机效应结构带来了计算挑战，限制了该模型的可用性。我们开发了一种EM算法，利用随机效应和误差协方差矩阵的稀疏结构，高效计算GP模型的最大似然估计。该算法在R统计软件的GPvam包中实现。我们给出了计算示例，并说明了我们的估计程序所实现的计算效率提升。
英文摘要：
The generalized persistence (GP) model, developed in the context of estimating ``value added'' by individual teachers to their students' current and future test scores, is one of the most flexible value-added models in the literature. Although developed in the educational setting, the GP model can potentially be applied to any structure where each sequential response of a lower-level unit may be associated with a different higher-level unit, and the effects of the higher-level units may persist over time. The flexibility of the GP model, however, and its multiple membership random effects structure lead to computational challenges that have limited the model's availability. We develop an EM algorithm to compute maximum likelihood estimates efficiently for the GP model, making use of the sparse structure of the random effects and error covariance matrices. The algorithm is implemented in the package GPvam in R statistical software. We give examples of the computations and illustrate the gains in computational efficiency achieved by our estimation procedure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
