手法を比較

	ロバスト因子分析	因子分析	影響診断（Cook距離、DFFITS、レバレッジ）	ロバスト共分散推定 (MCD)
分野	統計学	研究統計	統計学	統計学
系統	Regression model	Process / pipeline	Regression model	Regression model
提唱年	2003	1931	1977	1999
提唱者	Pison, Rousseeuw, Filzmoser & Croux	Louis Leon Thurstone	R. Dennis Cook (Cook's distance); Belsley, Kuh & Welsch (DFFITS, leverage)	Rousseeuw; Rousseeuw & Van Driessen (Fast-MCD)
種類	Robust latent-factor model	Method	Regression diagnostic	Robust multivariate location-scatter estimator
原典	Pison, G., Rousseeuw, P. J., Filzmoser, P., & Croux, C. (2003). Robust factor analysis. Journal of Multivariate Analysis, 84(1), 145-172.	Thurstone, L. L. (1947). Multiple Factor Analysis. University of Chicago Press.	Cook, R. D. (1977). Detection of Influential Observations in Linear Regression. Technometrics, 19(1), 15-18.	Rousseeuw, P. J. & Van Driessen, K. (1999). A Fast Algorithm for the Minimum Covariance Determinant Estimator. Technometrics, 41(3), 212-223.
別名	robust factor analysis, outlier-resistant factor analysis, MCD-based factor analysis, Robust Faktör Analizi	EFA, CFA, latent variable modeling	Cook's distance, DFFITS, leverage, influential observation detection	minimum covariance determinant, MCD estimator, robust covariance estimation, Robust Kovaryans Tahmini (MCD)
関連	5	3	5	4
概要	Robust Factor Analysis recovers the latent factor structure of multivariate continuous data while resisting the distorting pull of outliers. Introduced by Pison, Rousseeuw, Filzmoser and Croux (2003), it replaces the classical sample covariance with a robust estimator such as the Minimum Covariance Determinant (MCD) or an S-estimator before extracting factors.	Factor analysis is a statistical technique for identifying latent (unobserved) dimensions underlying observed variables, developed by Louis Leon Thurstone in the 1930s and formalized by Jöreskog (1969). Exploratory factor analysis (EFA) discovers unknown factor structure from data; confirmatory factor analysis (CFA) tests hypothesized relationships between observed and latent variables. Essential in psychometrics (test development), organizational research (measuring constructs like leadership style), and biomedicine (identifying disease subtypes), factor analysis reduces dimensionality while revealing conceptual organization in multivariate data.	Influence diagnostics are a family of post-fit measures that quantify how much each single observation affects a fitted regression. Cook's distance was introduced by R. Dennis Cook in 1977, with leverage and DFFITS formalised by Belsley, Kuh and Welsch in 1980, to flag the observations that most strongly pull the estimated coefficients.	Robust Covariance via the Minimum Covariance Determinant (MCD) estimates a multivariate mean vector and covariance matrix that are not distorted by outliers. It was made practical by the Fast-MCD algorithm of Rousseeuw and Van Driessen (1999), building on Rousseeuw's earlier work on robust estimation.