IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/1904.html
   My bibliography  Save this paper

VIPSCAL: A combined vector ideal point model for preference data

Author

Listed:
  • van Deun, K.
  • Groenen, P.J.F.
  • Delbeke, L.

Abstract

In this paper, we propose a new model that combines the vector model and the ideal point model of unfolding. An algorithm is developed, called VIPSCAL, that minimizes the combined loss both for ordinal and interval transformations. As such, mixed representations including both vectors and ideal points can be obtained but the algorithm also allows for the unmixed cases, giving either a complete ideal pointanalysis or a complete vector analysis. On the basis of previous research, the mixed representations were expected to be nondegenerate. However, degenerate solutions still occurred as the common belief that distant ideal points can be represented by vectors does not hold true. The occurrence of these distant ideal points was solved by adding certain length and orthogonality restrictions on the configuration. The restrictions can be used both for the mixed and unmixed cases in several ways such that a number of different models can be fitted by VIPSCAL.

Suggested Citation

  • van Deun, K. & Groenen, P.J.F. & Delbeke, L., 2005. "VIPSCAL: A combined vector ideal point model for preference data," Econometric Institute Research Papers EI 2005-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1904
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/1904/ei200503.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wayne DeSarbo & J. Douglas Carroll, 1985. "Three-way metric unfolding via alternating weighted least squares," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 275-300, September.
    2. Clyde Coombs, 1975. "A note on the relation between the vector model and the unfolding model for preferences," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 115-116, March.
    3. Forrest Young & Yoshio Takane & Jan Leeuw, 1978. "The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 43(2), pages 279-281, June.
    4. Patrick Groenen & Bart-Jan Os & Jacqueline Meulman, 2000. "Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 511-524, December.
    5. 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.
    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. Frank Busing & Mark Rooij, 2009. "Unfolding Incomplete Data: Guidelines for Unfolding Row-Conditional Rank Order Data with Random Missings," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 329-360, 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. K. Van Deun & P. J. F. Groenen, 2005. "Majorization Algorithms for Inspecting Circles, Ellipses, Squares, Rectangles, and Rhombi," Operations Research, INFORMS, vol. 53(6), pages 957-967, December.
    2. Kuroda, Masahiro & Mori, Yuichi & Iizuka, Masaya & Sakakihara, Michio, 2011. "Acceleration of the alternating least squares algorithm for principal components analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 143-153, January.
    3. DeSarbo, Wayne S. & Selin Atalay, A. & Blanchard, Simon J., 2009. "A three-way clusterwise multidimensional unfolding procedure for the spatial representation of context dependent preferences," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3217-3230, June.
    4. 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.
    5. Wayne DeSarbo & Kamel Jedidi & Joel Steckel, 1991. "A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 279-307, June.
    6. S. Winsberg & J. Ramsay, 1983. "Monotone spline transformations for dimension reduction," Psychometrika, Springer;The Psychometric Society, vol. 48(4), pages 575-595, December.
    7. K Hourihan, 1979. "The Evaluation of Urban Neighbourhoods 2: Preference," Environment and Planning A, , vol. 11(12), pages 1355-1366, December.
    8. Maximilian Matthe & Daniel M. Ringel & Bernd Skiera, 2023. "Mapping Market Structure Evolution," Marketing Science, INFORMS, vol. 42(3), pages 589-613, May.
    9. Geert Soete & J. Carroll & Anil Chaturvedi, 1993. "A modified CANDECOMP method for fitting the extended INDSCAL model," Journal of Classification, Springer;The Classification Society, vol. 10(1), pages 75-92, January.
    10. Li, Guoqi & Tang, Pei & Meng, Ziyang & Wen, Changyun & Pei, Jing & Shi, Luping, 2018. "Optimization on matrix manifold based on gradient information and its applications in network control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 481-500.
    11. Groenen, P.J.F. & Bioch, J.C. & Nalbantov, G.I., 2006. "Nonlinear support vector machines through iterative majorization and I-splines," Econometric Institute Research Papers EI 2006-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Antonio Calcagnì & Luigi Lombardi & Lorenzo Avanzi & Eduardo Pascali, 2020. "Multiple mediation analysis for interval-valued data," Statistical Papers, Springer, vol. 61(1), pages 347-369, February.
    13. 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).
    14. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    15. Duncan Fong & Wayne DeSarbo & Zhe Chen & Zhuying Xu, 2015. "A Bayesian Vector Multidimensional Scaling Procedure Incorporating Dimension Reparameterization with Variable Selection," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1043-1065, December.
    16. Groenen, P.J.F. & Winsberg, S. & Rodriguez, O. & Diday, E., 2006. "I-Scal: Multidimensional scaling of interval dissimilarities," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 360-378, November.
    17. Ng, Serena, 2013. "Variable Selection in Predictive Regressions," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 752-789, Elsevier.
    18. Groenen, P.J.F. & Nalbantov, G.I. & Bioch, J.C., 2007. "SVM-Maj: a majorization approach to linear support vector machines with different hinge errors," Econometric Institute Research Papers EI 2007-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    19. Hansohm, Jürgen, 2004. "Algorithmus und Programm zur Bestimmung der monotonen Kleinst-Quadrate Lösung bei partiellen Präordnungen," Arbeitspapiere zur mathematischen Wirtschaftsforschung 187, Universität Augsburg, Institut für Statistik und Mathematische Wirtschaftstheorie.
    20. Laura Vicente-Gonzalez & Jose Luis Vicente-Villardon, 2022. "Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation," Mathematics, MDPI, vol. 10(15), pages 1-23, July.

    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:ems:eureir:1904. 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: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    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.