Applications of asymptotic theory to factor analysis and structural equation modeling

渐近理论在因子分析和结构方程建模中的应用

• 批准号: 16500167
• 负责人: OGASAWARA Haruhiko
• 金额: $ 1.28万
• 依托单位: Otaru University of Commerce
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16500167/
• 关键词: factor analysis; principal component analysis; structural eauation modeling; Edgeworth expansion; Studentized statistics; higher-order asymptotic SE; asymptotic bias; asymptotic robustness; 高次標準誤差; 高次モーメント; 陰関数; コーニッシュ-フィッシャー展開; 直交回転; 斜交回転

(1)Derivation of the asymptotic bias in factor analysis (FA)In factor analysis, the estimators of factor loadings are of primary interest. So, the asymptotic biases of the estimators of factor loadings are derived under nonnormality, where the loadings are possibly orthogonally rotated.(2)Derivation of the asymptotic bias in principal component analysis (PCA)In principal component analysis, the asymptotic biases of the orthogonally or obliquely rotated component loading estimators are derived under nonnormality.(3)Asymptotic expansion of the parameter estimatorsEdgeworth expansions of the parameter estimators in covariance structures are given under nonnormality. To have the confidence intervals of the parameters, the Cornish-Fisher expansions of the Studentized estimators are derived.(4)Higher-order asymptotic standard errorHigher-order asymptotic standard errors of the parameter estimators are provided using an extended formula in implicit functions in structural equation modeling.(5)Derivation of the asymptotic robustness of the asymptotic biases in structural equation modelingThe asymptotic robustness of the normal-theory asymptotic biases of the parameter estimators in structural models are derived under some conditions against the violation of the assumption of normality.

（1）因子分析（FA）中渐近偏差的推导在因子分析中，因子载荷的估计量是一个重要的问题。因此，在非正态条件下，当载荷可能正交旋转时，得到了因子载荷估计的渐近偏差。（2）主成分分析（PCA）中渐近偏差的推导在主成分分析中，在非正态分布下，推导了正交或斜旋转分量载荷估计量的渐近偏差。（3）参数估计的渐近展开在非正态条件下，给出了协方差结构中参数估计的Edgeworth展开式。为了得到参数的置信区间，导出了学生化估计量的Cornish-Fisher展开式。（4）高阶渐近标准误差在结构方程模型中，利用隐函数形式的推广公式，给出了参数估计量的高阶渐近标准误差。（5）结构方程模型中渐近偏差的渐近稳健性的推导在一定条件下，证明了结构模型中参数估计量的正态理论渐近偏差的渐近稳健性。

项目成果

Asymptotic robustness of the asymptotic biases in structural equation modeling.

结构方程建模中渐近偏差的渐近鲁棒性。

• 发表时间: 2005
• 期刊: Computational Statistics and Data Analysis 49・3
• 作者: Ogasawara;H.
• 通讯作者: H.

Asymptotic biases in exploratory factor analysis and structural equation modeling.

探索性因素分析和结构方程建模中的渐近偏差。

• 发表时间: 2004
• 期刊: Psychometrika 69・2
• 作者: Ogasawara;H.
• 通讯作者: H.

Asymptotic biases of least squares estimators in structural equation modeling.

结构方程建模中最小二乘估计量的渐近偏差。

• 发表时间: 2004
• 期刊: Advances in psychology research (Shohov, S.P.(Ed.)) Vol.27
• 作者: Ogasawara;H.
• 通讯作者: H.

Bias reduction of estimated standard errors in factor analysis.

因子分析中估计标准误差的偏差减少。

• 发表时间: 2005
• 期刊: Behaviormetrika 32・1
• 作者: Ogasawara;H.
• 通讯作者: H.

Asymptotic biases of least squares estimators in structural equation modeling. Advances in psychology research : Vol. 27, pp.65-94.

结构方程建模中最小二乘估计量的渐近偏差。

• 发表时间: 2004
• 作者: Shohov;S.P.(Ed.);Ogasawara;H.
• 通讯作者: H.