基于概化理论的方差分量变异量估计

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。     

概化理论方差分量估计的跨分布分析

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。     

非正态分布下概化理论方差分量变异量估计

方差分量估计是概化理论的必用技术,但受限于抽样,需要对其变异量进行探讨。采用Monte Carlo数据模拟技术,探讨非正态数据分布对四种方法估计概化理论方差分量变异量的影响。结果表明：（1）不同非正态数据分布下,各种估计方法的“性能”表现出差异性;（2）数据分布对方差分量变异量估计有影响,适合于非正态分布数据的方差分量变异量估计方法不一定适合于正态分布数据。     

概化理论方差分量及其变异量估计:跨分布的模拟研究

为考察概化理论中方差分量及其变异量估计的准确性,采用模拟研究的方法,探究Traditional法、Jackknife法、Bootstrap法和MCMC法在p×i×h和p×(i:h)2种双侧面设计和正态、二项、多项、偏态分布4种数据类型下的表现。结果显示:(1)4种方法均能准确估计方差分量;(2)估计方差分量的标准误时,若数据正态分布,Traditional法最优,非正态分布时Bootstrap法最优;(3)估计方差分量的90%置信区间时,Bootstrap法在不同分布的数据下表现稳定,但容易受到侧面水平数的影响。综合来说,若数据呈正态分布,建议选用Traditional法; 若数据呈非正态分布,建议选用Bootstrap法。     

概化理论G研究方差分量及其变异量估计影响因素

概化理论是关于行为测量可靠性的统计理论。G研究是进行概化理论分析的关键步骤,其主要目的是进行方差分量及其变异量估计。总结了影响概化理论G研究方差分量及其变异量估计的多种因素,包括估计方法、数据分布、研究设计、样本容量、模型效应和数据形态等,并指出了相关研究存在的六方面不足,如缺乏估计方法的综合比较、较少考察非正态分布数据、较少考虑不平衡或缺失数据等。     

概化理论缺失数据方差分量估计

各种心理调查、心理实验中, 数据的缺失随处可见。由于数据缺失, 给概化理论分析非平衡数据的方差分量带来一系列问题。基于概化理论框架下, 运用Matlab 7.0软件, 自编程序模拟产生随机双面交叉设计p×i×r缺失数据, 比较和探讨公式法、REML法、拆分法和MCMC法在估计各个方差分量上的性能优劣。结果表明：(1) MCMC方法估计随机双面交叉设计p×i×r缺失数据方差分量, 较其它3种方法表现出更强的优势; (2) 题目和评分者是缺失数据方差分量估计重要的影响因素。     

考试评分缺失数据的概化理论分析

考试评分缺失数据较为常见,如何有效利用现有数据进行统计分析是个关键性问题。在考试评分中,题目与评分者对试卷得分的影响不容忽视。根据概化理论原理,按考试评分规则推导出含有缺失数据双侧面交叉设计（p×i×r）方差分量估计公式,用Matlab7.0软件模拟多组缺失数据,验证此公式的有效性。结果发现：（1）推导出的公式较为可靠,估计缺失数据的方差分量偏差相对较小,即便数据缺失率达到50％以上,公式仍能对方差分量进行较为准确地估计;（2）题目数量对概化理论缺失数据方差分量的估计影响最大,评分者次之,当题目和评价者数量分别为6和5时,公式能够趋于稳定地估计;（3）学生数量对各方差分量的估计影响较小,无论是小规模考试还是大规模考试,概化理论估计缺失数据的多个方差分量结果相差不大。     

不同参数分布形态下GIRM方法和传统GT方法的对比研究

GIRM(Generalizability in Item Response Modeling)是一种将概化理论GT和项目反应理论IRT相结合后计算概化理论中方差分量的一种方法.当GIRM方法下θp和βi的抽样分布与GIRM方法中的MCMC先验分布一致时,GIRM方法对方差分量估计具有较高的准确性.为了进一步检验GIRM方法对IRT参数分布形态的敏感性,研究在将MCMC先验分布固定的情况下,探讨不同IRT参数分布形态下GIRM方法的适用性,并将所得结果与传统GT方法相比较.结果表明:(1)在各种参数分布形态下,采用GIRM方法估计IRT模型的参数是可行的;(2)GIRM方法在被试能力参数为标准正态分布时对σ2(p)估计的准确性高于传统GT方法,但在均匀分布和偏态分布下略差于传统GT方法;(3) GIRM方法在题目难度参数为偏态分布情况下对σ2(i)的估计准确性显著差于传统GT方法;(4)两种方法对于σ2(pie)估计的准确性在任何参数分布形态下都大致相当,优劣并无统一规律.     

概化理论不同评分方案缺失数据方差分量估计

包含评分者侧面的测验通常不符合任意一种概化理论设计,因此从概化理论的角度来看这类测验下的数据应属于缺失数据,而决定缺失结构的就是测验的评分方案。用R软件模拟出三种评分方案下的数据,并比较传统法、评价法和拆分法在各评分方案下的估计效果,结果表明：（1）传统法估计准确性较差;（2）评分者一致性较高时,适宜用评价法进行估计;（3）拆分法的估计结果最准确,仅在固定评分者评分方案下需注意评分者与考生数量之比,该比值小于等于0.0047 时估计结果较为准确。     

概化理论不同评分方案缺失数据方差分量估计

包含评分者侧面的测验通常不符合任意一种概化理论设计,因此从概化理论的角度来看这类测验下的数据应属于缺失数据,而决定缺失结构的就是测验的评分方案。用R软件模拟出三种评分方案下的数据,并比较传统法、评价法和拆分法在各评分方案下的估计效果,结果表明：（1）传统法估计准确性较差;（2）评分者一致性较高时,适宜用评价法进行估计;（3）拆分法的估计结果最准确,仅在固定评分者评分方案下需注意评分者与考生数量之比,该比值小于等于0.0047 时估计结果较为准确。     

Some developments in multivariate generalizability

This article is concerned with estimation of components of maximum generalizability in multifacet experimental designs involving multiple dependent measures. Within a Type II multivariate analysis of variance framework, components of maximum generalizability are defined as those composites of the dependent measures that maximize universe score variance for persons relative to observed score variance. The coefficient of maximum generalizability, expressed as a function of variance component matrices, is shown to equal the squared canonical correlation between true and observed scores. Emphasis is placed on estimation of variance component matrices, on the distinction between generalizability- and decision-studies, and on extension to multifacet designs involving crossed and nested facets. An example of a two-facet partially nested design is provided.Appreciation is expressed to the Office of Research in Medical Education, University of Texas Medical Branch, for permitting use of their data.     

Estimating Standard Errors in Exploratory Factor Analysis

The article describes 6 issues influencing standard errors in exploratory factor analysis and reviews 7 methods of computing standard errors for rotated factor loadings and factor correlations. These 7 methods are the augmented information method, the nonparametric bootstrap method, the infinitesimal jackknife method, the method using the asymptotic distributions of unrotated factor loadings, the sandwich method, the parametric bootstrap method, and the jackknife method. Standard error estimates are illustrated using a personality study with 537 men and an intelligence study with 145 children.     

Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife

The infinitesimal jackknife provides a simple general method for estimating standard errors in covariance structure analysis. Beyond its simplicity and generality what makes the infinitesimal jackknife method attractive is that essentially no assumptions are required to produce consistent standard error estimates, not even the requirement that the population sampled has the covariance structure assumed. Commonly used covariance structure analysis software uses parametric methods for estimating parameters and standard errors. When the population sampled has the covariance structure assumed, but fails to have the distributional form assumed, the parameter estimates usually remain consistent, but the standard error estimates do not. This has motivated the introduction of a variety of nonparametric standard error estimates that are consistent when the population sampled fails to have the distributional form assumed. The only distributional assumption these require is that the covariance structure be correctly specified. As noted, even this assumption is not required for the infinitesimal jackknife. The relation between the infinitesimal jackknife and other nonparametric standard error estimators is discussed. An advantage of the infinitesimal jackknife over the jackknife and the bootstrap is that it requires only one analysis to produce standard error estimates rather than one for every jackknife or bootstrap sample.     

Standard errors and confidence intervals for correlations corrected for indirect range restriction: A simulation study comparing analytic and bootstrap methods

A frequent topic of psychological research is the estimation of the correlation between two variables from a sample that underwent a selection process based on a third variable. Due to indirect range restriction, the sample correlation is a biased estimator of the population correlation, and a correction formula is used. In the past, bootstrap standard error and confidence intervals for the corrected correlations were examined with normal data. The present study proposes a large-sample estimate (an analytic method) for the standard error, and a corresponding confidence interval for the corrected correlation. Monte Carlo simulation studies involving both normal and non-normal data were conducted to examine the empirical performance of the bootstrap and analytic methods. Results indicated that with both normal and non-normal data, the bootstrap standard error and confidence interval were generally accurate across simulation conditions (restricted sample size, selection ratio, and population correlations) and outperformed estimates of the analytic method. However, with certain combinations of distribution type and model conditions, the analytic method has an advantage, offering reasonable estimates of the standard error and confidence interval without resorting to the bootstrap procedure's computer-intensive approach. We provide SAS code for the simulation studies.     

Four applications of permutation methods to testing a single-mediator model

Four applications of permutation tests to the single-mediator model are described and evaluated in this study. Permutation tests work by rearranging data in many possible ways in order to estimate the sampling distribution for the test statistic. The four applications to mediation evaluated here are the permutation test of ab, the permutation joint significance test, and the noniterative and iterative permutation confidence intervals for ab. A Monte Carlo simulation study was used to compare these four tests with the four best available tests for mediation found in previous research: the joint significance test, the distribution of the product test, and the percentile and bias-corrected bootstrap tests. We compared the different methods on Type I error, power, and confidence interval coverage. The noniterative permutation confidence interval for ab was the best performer among the new methods. It successfully controlled Type I error, had power nearly as good as the most powerful existing methods, and had better coverage than any existing method. The iterative permutation confidence interval for ab had lower power than do some existing methods, but it performed better than any other method in terms of coverage. The permutation confidence interval methods are recommended when estimating a confidence interval is a primary concern. SPSS and SAS macros that estimate these confidence intervals are provided.