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Comparison of Dimensionality Reduction Methods Applied to Ordinal Variables
[Srovnání metod pro redukci dimenzionality aplikovaných na ordinální proměnné]

Author

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  • Lukáš Sobíšek
  • Hana Řezanková

Abstract

Questionnaire survey data are usually characterized by a great amount of ordinal variables. For multivariate analysis, it is suitable to reduce task dimensionality. The aim of this paper is a comparison of the results obtained by the analysis of data files with ordinal variables using selected methods for dimensionality reduction. The results are in the form of individual component values (e.g. factor loadings). For better interpretation and comparability, these component values were consequently analyzed by fuzzy clustering. On the basis of the obtained clusters of variables, we determined the optimal number of dimensions. We applied silhouette and Dunn's partition coefficients. Furthermore, we tried to merge the results received by individual methods on the basis of the sCSPA technique (soft version of cluster-based similarity partitioning algorithm). We considered groups of different methods and searched the best solution. The problems are illustrated by means of two real data files obtained from questionnaire surveys. We used SPSS, STATISTICA, Latent GOLD and S-PLUS systems.

Suggested Citation

  • Lukáš Sobíšek & Hana Řezanková, 2011. "Comparison of Dimensionality Reduction Methods Applied to Ordinal Variables [Srovnání metod pro redukci dimenzionality aplikovaných na ordinální proměnné]," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2011(1), pages 3-19.
    • Handle: RePEc:prg:jnlaop:v:2011:y:2011:i:1:id:323:p:3-19
    DOI: 10.18267/j.aop.323
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    References listed on IDEAS

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    1. Forrest Young & Jan Leeuw & Yoshio Takane, 1976. "Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 505-529, December.
    2. Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 471-503, December.
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    More about this item

    Keywords

    categorical principal component analysis; multidimensional scaling; latent class cluster models; discrete factor analysis; fuzzy cluster analysis;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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