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Factor Analysis and Principal Components

Author

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  • Schneeweiss, H.
  • Mathes, H.

Abstract

The principal components of a vector of random variables are related to the common factors of a factor analysis model for this vector. Conditions are presented under which components and factors as well as factor proxies come close to each other. A similar analysis is carried out for the matrices of loadings of principal components and factor analysis.

Suggested Citation

  • Schneeweiss, H. & Mathes, H., 1995. "Factor Analysis and Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 105-124, October.
    • Handle: RePEc:eee:jmvana:v:55:y:1995:i:1:p:105-124
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    Cited by:

    1. Wim Krijnen & Theo Dijkstra & Richard Gill, 1998. "Conditions for factor (in)determinacy in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 63(4), pages 359-367, December.
    2. Hong Xie & Saina Zheng & Yue Zhai & Jingfeng Yuan & Qiming Li, 2024. "Unveiling Urban Regeneration Risks in China: A Social Perspective," Sustainability, MDPI, vol. 16(4), pages 1-21, February.
    3. Sergio Consoli & Luca Tiozzo Pezzoli & Elisa Tosetti, 2022. "Neural forecasting of the Italian sovereign bond market with economic news," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 197-224, December.
    4. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
    5. Sue-Fen Huang & Ching-Hsue Cheng, 2013. "GMADM-based attributes selection method in developing prediction model," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(6), pages 3335-3347, October.
    6. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Steffen Grønneberg & Julien Patrick Irmer, 2024. "Non-parametric Regression Among Factor Scores: Motivation and Diagnostics for Nonlinear Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 822-850, September.
    8. Sundberg, Rolf & Feldmann, Uwe, 2016. "Exploratory factor analysis—Parameter estimation and scores prediction with high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 49-59.
    9. Lazzarino, Marco & Berrill, Jenny & Šević, Aleksandar, 2022. "The importance of distinguishing between precious and industrial metals when investing in mining stocks," Resources Policy, Elsevier, vol. 78(C).
    10. Wim Krijnen, 2002. "On the construction of all factors of the model for factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 161-172, March.
    11. Rania Salem & Sarah Shah, 2019. "Economic rationales for kin marriage: Assessing the evidence using Egyptian panel data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(19), pages 545-578.
    12. Naomichi Makino, 2015. "Generalized data-fitting factor analysis with multiple quantification of categorical variables," Computational Statistics, Springer, vol. 30(1), pages 279-292, March.
    13. Wim Krijnen, 2006. "Necessary Conditions for Mean Square Convergence of the Best Linear Factor Predictor," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 593-599, September.
    14. Randy Carter & Netsanet Michael, 2022. "Factor Analysis Regression for Predictive Modeling with High-Dimensional Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 115-132, September.
    15. Haruhiko Ogasawara, 2000. "Some relationships between factors and components," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 167-185, June.
    16. Shelby Haberman, 2006. "Bias in Estimation of Misclassification Rates," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 387-394, June.
    17. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," Working Papers halshs-03626503, HAL.
    18. Omer Bayar, 2022. "Reducing large datasets to improve the identification of estimated policy rules," Empirical Economics, Springer, vol. 63(1), pages 113-140, July.
    19. Wim Krijnen, 2006. "Implications of Indeterminate Factor-Error Covariances for Factor Construction, Prediction, and Determinacy," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 503-519, September.
    20. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," PSE Working Papers halshs-03626503, HAL.
    21. Thomas Despois & Catherine Doz, 2023. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 533-555, June.
    22. Thomas Augustin & Helmut Küchenhoff & Matthias Schmid, 2022. "Nachruf Hans Schneeweiß," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 16(2), pages 149-154, June.
    23. Tao Yu & Qi Tang & Yongxiang Wu & Yaowu Wang & Zezhou Wu, 2019. "What Determines the Success of Culture-Led Regeneration Projects in China?," Sustainability, MDPI, vol. 11(18), pages 1-21, September.

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