Controlling for Individual Heterogeneity in Longitudinal Models, with Applications to Student Achievement
Controlling for Individual Heterogeneity in Longitudinal Models, with Applications to Student Achievement
复制标题
DOI：
10.1214/07-ejs057
复制
发表时间：
2007-06
影响因子：
1.1
通讯作者：
J. R. Lockwood;D. McCaffrey
中科院分区：
文献类型：
--
作者：
J. R. Lockwood;D. McCaffrey
追踪个体重复测量的纵向数据对于研究来说非常有价值，因为它们为未测量的个体异质性提供了控制，否则可能会使结果产生偏差。随机效应或混合模型方法将个体异质性视为模型误差项的一部分，并使用广义最小二乘法来估计模型参数，因此经常受到批评，因为未观察到的个体效应与其他模型变量之间的相关性可能导致参数估计存在偏差和不一致。本文从考察标准不可观测效应模型中随机效应和固定效应估计量之间的关系入手，通过分析和模拟证明，混合模型方法在个体异质性通用模型下具有“偏差压缩”特性，可以减轻由于个体之间不可控差异而导致的偏差。一般模型的动机是纵向学生成绩测量的复杂性，但结果对纵向建模具有广泛的适用性。
Longitudinal data tracking repeated measurements on individuals are highly valued for research because they offer controls for unmeasured individual heterogeneity that might otherwise bias results. Random effects or mixed models approaches, which treat individual heterogeneity as part of the model error term and use generalized least squares to estimate model parameters, are often criticized because correlation between unobserved individual effects and other model variables can lead to biased and inconsistent parameter estimates. Starting with an examination of the relationship between random effects and fixed effects estimators in the standard unobserved effects model, this article demonstrates through analysis and simulation that the mixed model approach has a ``bias compression'' property under a general model for individual heterogeneity that can mitigate bias due to uncontrolled differences among individuals. The general model is motivated by the complexities of longitudinal student achievement measures, but the results have broad applicability to longitudinal modeling.