ISSN 0439-755X
CN 11-1911/B

心理学报 ›› 2009, Vol. 41 ›› Issue (09): 889-901.

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  1. 华南师范大学心理应用研究中心, 广州 510631
  • 收稿日期:2009-03-05 修回日期:1900-01-01 出版日期:2009-09-30 发布日期:2009-09-30
  • 通讯作者: 张敏强

Estimating the Variability of Estimated Variance Components for Generalizability Theory

LI Guang-Ming;ZHANG Min-Qiang   

  1. Center for Studies of Psychological Application, South China Normal University, Guangzhou 510631, China
  • Received:2009-03-05 Revised:1900-01-01 Online:2009-09-30 Published:2009-09-30
  • Contact: ZHANG Min-Qiang

摘要: 概化理论广泛应用于心理与教育测量实践中, 方差分量估计是进行概化理论分析的关键。方差分量估计受限于抽样, 需要对其变异量进行探讨。采用蒙特卡洛(Monte Carlo)数据模拟技术, 在正态分布下讨论不同方法对基于概化理论的方差分量变异量估计的影响。结果表明: Jackknife方法在方差分量变异量估计上不足取; 不采取Bootstrap方法的“分而治之”策略, 从总体上看, Traditional方法和有先验信息的MCMC方法在标准误及置信区间这两个变异量估计上优势明显。

关键词: 概化理论, 方差分量, 方差分量变异量, MCMC方法, 蒙特卡洛模拟

Abstract: Generalizability theory is widely applied in psychological and educational measurement.The variability of estimated variance component, which is constrained by sampling, is the “Achilles heel” of generalizability the-ory. Therefore, estimating the variability of estimated variance components needs to be further explored. In pre-vious literature, some problems remain to be settled: first, the previous studies failed to compare the variability of estimated variance components among different methods simultaneously: traditional, bootstrap, jackknife and Markov Chain Monte Carlo (MCMC); second, some studies only focused on such variability of estimated vari-ance components as the standard error, while neglected other variability such as confidence interval; last but not least, MCMC method which can be used in generalizability theory hasn’t gained sufficient exploration.
There are different methods to estimate the variability of variance components: standard error and confi-dence interval, including traditional, bootstrap, jackknife and MCMC. Based on these four methods, the study adopts Monte Carlo data simulation technique to compare the variability of estimated variance components for normal distribution data. For traditional method, ANOVA is used to estimate the variance components and their standard errors. Satterthwaite and TBGJL are used to estimate the confidence intervals. For bootstrap method, twelve bootstrap strategies are adopted, but only three strategies are considered in jackknife method and only two strategies, i.e., informative and non-informative priors, for MCMC method. Some criteria are set to compare the four methods. The bias is cared about when variance components and their standard errors are estimated. The smaller the absolute bias is, the more reliable the result is. The criterion of confidence intervals is “80% interval coverage”. If the “80% interval coverage” is more closed to 0.80, the confidence interval is more reliable.
The simulation is implemented in R statistical programming environment. To link R program with Win-BUGS, R2WinBUGS and Coda package are adopted. And the simulation results are as follows. First, it is more accurate to use traditional, jackknife, adjusted bootstrap and MCMC method with informative priors to estimate variance components. But unadjusted bootstrap and MCMC method with non-informative priors are not ade-quate. Second, traditional and MCMC method with informative priors are accurate to estimate standard errors of three variance components, while jackknife method is not. Bootstrap method needs to adopt a “di-vide-and-conquer” strategy to obtain good estimated standard errors: the most accurate estimation of standard error for person is consistently provided by adjusted boot-p or boot-ir; adjusted boot-pi is the clear winner in estimating standard error for item; adjusted boot-ir, boot-pir or boot-pr give good estimate of standard error for person and item. Finally, using traditional and MCMC method to estimate confidence intervals is suitable be-cause their respective interval coverages are close to 0.80. But jackknife method is not accurate in estimating confidence intervals. There is no great difference between Bootstrap-PC and Bootstrap-BCa method that are used to estimate confidence intervals of three variance components. Bootstrap method should apply the “di-vide-and-conquer” strategy to get desirable estimated confidence intervals as following: adjusted boot-p for person; adjusted boot-pi for item; adjusted boot-ir, boot-pr or boot-p for person and item.
This study shows that jackknife method is not accurate to estimate the variability of estimated variance components. If the “divide-and-conquer” strategy is not used in bootstrap method, it is advisable to use tradi-tional method or MCMC method with informative priors.

Key words: Generalizability Theory, variance component, variability of estimated variance components, Markov Chain Monte Carlo (MCMC) method, Monte Carlo simulation