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Weighted least squares fitting using ordinary least squares algorithms

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  • Henk Kiers

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  • Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 251-266, June.
    • Handle: RePEc:spr:psycho:v:62:y:1997:i:2:p:251-266
    DOI: 10.1007/BF02295279
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    1. Verboon, Peter & Heiser, Willem J., 1994. "Resistant lower rank approximation of matrices by iterative majorization," Computational Statistics & Data Analysis, Elsevier, vol. 18(4), pages 457-467, November.
    2. Norman Cliff, 1966. "Orthogonal rotation to congruence," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 33-42, March.
    3. Henk Kiers, 1989. "An alternating least squares algorithm for fitting the two- and three-way dedicom model and the idioscal model," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 515-521, September.
    4. Henk Kiers & Jos Berge & Yoshio Takane & Jan Leeuw, 1990. "A generalization of Takane's algorithm for dedicom," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 151-158, March.
    5. Harry Harman & Wayne Jones, 1966. "Factor analysis by minimizing residuals (minres)," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 351-368, September.
    6. Bert Green, 1952. "The orthogonal approximation of an oblique structure in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 429-440, December.
    7. Richard A. Harshman & Paul E. Green & Yoram Wind & Margaret E. Lundy, 1982. "A Model for the Analysis of Asymmetric Data in Marketing Research," Marketing Science, INFORMS, vol. 1(2), pages 205-242.
    8. Catrien Bijleveld & Jan Leeuw, 1991. "Fitting longitudinal reduced-rank regression models by alternating least squares," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 433-447, September.
    9. Peter Verboon & Willem Heiser, 1992. "Resistant orthogonal procrustes analysis," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 237-256, December.
    10. Heiser, Willem J., 1987. "Correspondence analysis with least absolute residuals," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 337-356, September.
    11. Henk Kiers, 1990. "Majorization as a tool for optimizing a class of matrix functions," Psychometrika, Springer;The Psychometric Society, vol. 55(3), pages 417-428, September.
    12. Henk Kiers & Jos Berge, 1992. "Minimization of a class of matrix trace functions by means of refined majorization," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 371-382, September.
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    Cited by:

    1. Zhu, Ziwei & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional principal component analysis with heterogeneous missingness," LSE Research Online Documents on Economics 117647, London School of Economics and Political Science, LSE Library.
    2. Michailidis, George & De Leeuw, Jan, 2005. "Homogeneity analysis using absolute deviations," Computational Statistics & Data Analysis, Elsevier, vol. 48(3), pages 587-603, March.
    3. Qing Li & Long Hai Vo, 2021. "Intangible Capital and Innovation: An Empirical Analysis of Vietnamese Enterprises," Economics Discussion / Working Papers 21-02, The University of Western Australia, Department of Economics.
    4. Joost Ginkel & Pieter Kroonenberg, 2014. "Using Generalized Procrustes Analysis for Multiple Imputation in Principal Component Analysis," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 242-269, July.
    5. Julie Josse & Marie Chavent & Benot Liquet & François Husson, 2012. "Handling Missing Values with Regularized Iterative Multiple Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 29(1), pages 91-116, April.
    6. Husson, François & Josse, Julie & Saporta, Gilbert, 2016. "Jan de Leeuw and the French School of Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i06).
    7. Groenen, P.J.F. & Giaquinto, P. & Kiers, H.A.L., 2003. "Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models," Econometric Institute Research Papers EI 2003-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. de Leeuw, Jan, 2006. "Principal component analysis of binary data by iterated singular value decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 21-39, January.
    9. Julie Josse & Jérôme Pagès & François Husson, 2011. "Multiple imputation in principal component analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(3), pages 231-246, October.
    10. Josse, Julie & Husson, François, 2016. "missMDA: A Package for Handling Missing Values in Multivariate Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i01).
    11. Jose Giovany Babativa-Márquez & José Luis Vicente-Villardón, 2021. "Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    12. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    13. Sébastien Loisel & Yoshio Takane, 2019. "Comparisons among several methods for handling missing data in principal component analysis (PCA)," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 495-518, June.
    14. A. Iodice D’Enza & A. Markos & F. Palumbo, 2022. "Chunk-wise regularised PCA-based imputation of missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 365-386, June.
    15. Schoonees, P.C. & Groenen, P.J.F. & van de Velden, M., 2015. "Least-squares Bilinear Clustering of Three-way Data," Econometric Institute Research Papers EI2014-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Camila Kolling & José Luis Duarte Ribeiro & Donato Morea & Gianpaolo Iazzolino, 2023. "Corporate social responsibility and circular economy from the perspective of consumers: A cross‐cultural analysis in the cosmetic industry," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 30(3), pages 1226-1243, May.
    17. Ziwei Zhu & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional principal component analysis with heterogeneous missingness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 2000-2031, November.
    18. Unkel, S. & Trendafilov, N.T., 2010. "A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3348-3358, December.
    19. Josse, Julie & Husson, François, 2012. "Selecting the number of components in principal component analysis using cross-validation approximations," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1869-1879.
    20. Mohammad Naim Azimi, 2016. "Assessing the Exchange Rate Volatility as an External Shock to Chinese Economy," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 8(5), pages 277-285, May.
    21. Wasito, Ito & Mirkin, Boris, 2006. "Nearest neighbours in least-squares data imputation algorithms with different missing patterns," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 926-949, February.
    22. Namgil Lee & Jong-Min Kim, 2018. "Block tensor train decomposition for missing data estimation," Statistical Papers, Springer, vol. 59(4), pages 1283-1305, December.

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