IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v62y1997i2p251-266.html
   My bibliography  Save this article

Weighted least squares fitting using ordinary least squares algorithms

Author

Listed:
  • Henk Kiers

Abstract

No abstract is available for this item.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF02295279
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF02295279?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Heiser, Willem J., 1987. "Correspondence analysis with least absolute residuals," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 337-356, September.
    4. 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.
    5. 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.
    6. Norman Cliff, 1966. "Orthogonal rotation to congruence," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 33-42, March.
    7. 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.
    8. Harry Harman & Wayne Jones, 1966. "Factor analysis by minimizing residuals (minres)," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 351-368, September.
    9. 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.
    10. 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.
    11. Peter Verboon & Willem Heiser, 1992. "Resistant orthogonal procrustes analysis," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 237-256, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Michailidis, George & De Leeuw, Jan, 2005. "Homogeneity analysis using absolute deviations," Computational Statistics & Data Analysis, Elsevier, vol. 48(3), pages 587-603, March.
    11. 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.
    12. 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.
    13. Marcon, Arthur & Ribeiro, José Luis Duarte & Olteanu, Yasmin & Fichter, Klaus, 2024. "How the interplay between innovation ecosystems and market contingency factors impacts startup innovation," Technology in Society, Elsevier, vol. 76(C).
    14. 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.
    15. 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.
    16. Chan, Tak-Shing T. & Gibberd, Alex, 2025. "Feasible model-based principal component analysis: Joint estimation of rank and error covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 201(C).
    17. Qing Li & Long Hai Vo, 2024. "Determinants of intangible capital investment in Vietnam: A firm‐level analysis," The World Economy, Wiley Blackwell, vol. 47(3), pages 1055-1088, March.
    18. 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.
    19. 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.
    20. Namgil Lee & Jong-Min Kim, 2018. "Block tensor train decomposition for missing data estimation," Statistical Papers, Springer, vol. 59(4), pages 1283-1305, December.
    21. 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.
    22. 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).
    23. 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.
    24. 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.
    25. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Krijnen, Wim P., 2006. "Convergence of the sequence of parameters generated by alternating least squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 481-489, November.
    2. Robert Jennrich, 2001. "A simple general procedure for orthogonal rotation," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 289-306, June.
    3. Henk Kiers & Patrick Groenen, 1996. "A monotonically convergent algorithm for orthogonal congruence rotation," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 375-389, June.
    4. Henk Kiers & Yoshio Takane, 1993. "Constrained DEDICOM," Psychometrika, Springer;The Psychometric Society, vol. 58(2), pages 339-355, June.
    5. 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.
    6. Kohei Adachi, 2009. "Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 667-683, December.
    7. 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.
    8. Henk Kiers, 1997. "Techniques for rotating two or more loading matrices to optimal agreement and simple structure: A comparison and some technical details," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 545-568, December.
    9. Michael Browne & Walter Kristof, 1969. "On the oblique rotation of a factor matrix to a specified pattern," Psychometrika, Springer;The Psychometric Society, vol. 34(2), pages 237-248, June.
    10. Takane, Yoshio, 2016. "My Early Interactions with Jan and Some of His Lost Papers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i07).
    11. Mohammed Bennani Dosse & Jos Berge, 2010. "Anisotropic Orthogonal Procrustes Analysis," Journal of Classification, Springer;The Classification Society, vol. 27(1), pages 111-128, March.
    12. Lafosse, Roger & ten Berge, Jos M.F., 2006. "A simultaneous CONCOR algorithm for the analysis of two partitioned matrices," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2529-2535, June.
    13. 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.
    14. J. Ramsay & Jos Berge & G. Styan, 1984. "Matrix correlation," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 403-423, September.
    15. Henk Kiers, 1995. "Maximization of sums of quotients of quadratic forms and some generalizations," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 221-245, June.
    16. Hanafi, Mohamed & Kiers, Henk A.L., 2006. "Analysis of K sets of data, with differential emphasis on agreement between and within sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1491-1508, December.
    17. 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.
    18. Robert Boik, 1996. "An efficient algorithm for joint correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 255-269, June.
    19. Edmund Peay, 1988. "Multidimensional rotation and scaling of configurations to optimal agreement," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 199-208, June.
    20. Peter Verboon & Ivo Lans, 1994. "Robust canonical discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 59(4), pages 485-507, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:62:y:1997:i:2:p:251-266. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.