IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v30y2015i1p279-292.html
   My bibliography  Save this article

Generalized data-fitting factor analysis with multiple quantification of categorical variables

Author

Listed:
  • Naomichi Makino

Abstract

In this study, a recently proposed data-fitting factor analysis (DFFA) procedure is generalized for categorical variable analysis. For generalized DFFA (GDFFA), we develop an alternating least squares algorithm consisting of a multiple quantification step and a model parameters estimation step. The differences between GDFFA and similar statistical methods such as multiple correspondence analysis and FACTALS are also discussed. The developed algorithm and its solution are illustrated with a real data example. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Naomichi Makino, 2015. "Generalized data-fitting factor analysis with multiple quantification of categorical variables," Computational Statistics, Springer, vol. 30(1), pages 279-292, March.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:1:p:279-292
    DOI: 10.1007/s00180-014-0536-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-014-0536-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-014-0536-8?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. Forrest Young, 1981. "Quantitative analysis of qualitative data," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 357-388, December.
    2. Schneeweiss, H. & Mathes, H., 1995. "Factor Analysis and Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 105-124, October.
    3. Eeke Burg & Jan Leeuw & Renée Verdegaal, 1988. "Homogeneity analysis withk sets of variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 177-197, June.
    4. Michel Tenenhaus & Forrest Young, 1985. "An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 91-119, March.
    5. Steffen Unkel & Nickolay T. Trendafilov, 2010. "Simultaneous Parameter Estimation in Exploratory Factor Analysis: An Expository Review," International Statistical Review, International Statistical Institute, vol. 78(3), pages 363-382, December.
    6. Masahiro Kuroda, 2012. "Acceleration of Convergence of the Alternating Least Squares Algorithm for Nonlinear Principal Components Analysis," Chapters, in: Parinya Sanguansat (ed.), Principal Component Analysis, IntechOpen.
    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. Kohei Adachi & Nickolay T. Trendafilov, 2018. "Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 407-424, June.

    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. Jan Leeuw, 1988. "Multivariate analysis with linearizable regressions," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 437-454, December.
    2. 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.
    3. Eeke Burg & Jan Leeuw & Renée Verdegaal, 1988. "Homogeneity analysis withk sets of variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 177-197, June.
    4. Michael Pargett & Ann E Rundell & Gregery T Buzzard & David M Umulis, 2014. "Model-Based Analysis for Qualitative Data: An Application in Drosophila Germline Stem Cell Regulation," PLOS Computational Biology, Public Library of Science, vol. 10(3), pages 1-18, March.
    5. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
    6. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    7. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," Working Papers halshs-03626503, HAL.
    8. 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.
    9. Kohei Adachi & Nickolay T. Trendafilov, 2018. "Sparsest factor analysis for clustering variables: a matrix decomposition approach," 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. 12(3), pages 559-585, September.
    10. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    11. Uno, Kohei & Satomura, Hironori & Adachi, Kohei, 2016. "Fixed factor analysis with clustered factor score constraint," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 265-274.
    12. Gardner, Sugnet & Gower, John C. & le Roux, N.J., 2006. "A synthesis of canonical variate analysis, generalised canonical correlation and Procrustes analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 107-134, January.
    13. Sara Casacci & Adriano Pareto, 2018. "Subjective Indicators Construction by Distance Indices: An Application to Life Satisfaction Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 137(3), pages 831-846, June.
    14. K. Fernández-Aguirre & M. Garín-Martín & J. Modroño-Herrán, 2014. "Visual displays: analytical study and applications to graphs and real data," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 2209-2224, July.
    15. Takayuki Saito & Tatsuo Otsu, 1988. "A method of optimal scaling for multivariate ordinal data and its extensions," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 5-25, March.
    16. Kim, Jung Seek & Ratchford, Brian T., 2013. "A Bayesian multivariate probit for ordinal data with semiparametric random-effects," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 192-208.
    17. Saudi-Yulieth Enciso-Alfaro & Víctor Amor-Esteban & Tânia-Cristina Azevedo & Isabel-María García-Sánchez, 2023. "Multivariate Analysis of Clean Technologies in Agricultural and Livestock Companies in Castilla y León," Agriculture, MDPI, vol. 13(11), pages 1-25, November.
    18. Vartan Choulakian, 1988. "Exploratory analysis of contingency tables by loglinear formulation and generalizations of correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 235-250, June.
    19. Antonello D’Ambra & Pietro Amenta & Anna Crisci & Antonio Lucadamo, 2022. "The generalized Taguchi’s statistic: a passenger satisfaction evaluation," METRON, Springer;Sapienza Università di Roma, vol. 80(1), pages 41-60, April.
    20. van Rosmalen, J.M. & Koning, A.J. & Groenen, P.J.F., 2007. "Optimal Scaling of Interaction Effects in Generalized Linear Models," Econometric Institute Research Papers EI 2007-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    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:compst:v:30:y:2015:i:1:p:279-292. 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.