概化理论方差分量估计的跨分布分析

Analysis of Cross-distribution for Estimating Variance Components in Generalizability Theory

方差分量估计是进行概化理论分析的关键。采用MonteCarlo模拟技术,探讨心理与教育测量数据分布对概化理论各种方法估计方差分量的影响。数据分布包括正态、二项和多项分布,估计方法包括Traditional、Jackknife、Bootstrap和MCMC方法。结果表明:(1)Traditional方法估计正态分布和多项分布数据的方差分量相对较好,估计二项分布数据需要校正,Jackknife方法准确地估计了三种分布数据的方差分量,校正的Bootstrap方法和有先验信息的MCMC方法(MCMCinf)估计三种分布数据的方差分量结果较好;(2)心理与教育测量数据分布对四种方法估计概化理论方差分量有影响,数据分布制约着各种方差分量估计方法性能的发挥,需要加以区分地使用。

Estimating variability is an essential part of generalizability theory and is of central importance. The study adopted Monte Carlo data simulation technique to explore the effect of three data distribution on four method of estimating variance components for generalizability theory. Three data distribution were normal data distribution, dichotomous data distribution and polytomous data distribution. Four estimated methods were traditional method, bootstrap method, jackknife method and Markov Chain Monte Carlo method （MCMC）. The results show that the performance of four methods is different for three data distribution. Traditional method is good for normal distribution data and polychromous distribution data. But it is not good and needs to be adjusted for dichotomous distribution data. Jackknife method accurately estimates variance components for three data distribution. As for estimating variance components, adjusted bootstrap method is better than unadjusted bootstrap methods. Compared with MCMC method with non-informative priors, MCMC method with informative priors is good for estimating variance components in generalizability theory. Data distribution has an effect on the method of estimating variance components for generalizability theory. Those methods, which can be applied for normal data distribution, could not be applied for other distribution data such as dichotomous data distribution and polytomous data distribution. Data distribution imposes restrictions on estimating variance components for these four methods. So different methods need be distinguished to use to do a good analysis of cross-distribution for estimating variance components in generalizability theory