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Efficient Variable Screening for Multivariate Analysis

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  • Duarte Silva, António Pedro

Abstract

It is shown how known algorithms for the comparison of all variables subsets in regression analysis can be adapted to subset comparisons in multivariate analysis, according to any index based on Wilks, Lawley-Hotelling, or Bartllet-Pillai statistics and, in some special cases, according to any function of the sample squared canonical correlations. The issues regarding the choice of an appropriate comparison criterion are discussed. The computational effort of the proposed algorithms is studied, and it is argued that, for a moderate number of variables, they should be preferred to stepwise selection methods. A software implementation of the methods discussed is freely available and can be downloaded from the Internet.

Suggested Citation

  • Duarte Silva, António Pedro, 2001. "Efficient Variable Screening for Multivariate Analysis," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 35-62, January.
    • Handle: RePEc:eee:jmvana:v:76:y:2001:i:1:p:35-62
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    References listed on IDEAS

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    1. Elliot Cramer & W. Nicewander, 1979. "Some symmetric, invariant measures of multivariate association," Psychometrika, Springer;The Psychometric Society, vol. 44(1), pages 43-54, March.
    2. Gordon D. Murray, 1977. "A Cautionary Note on Selection of Variables in Discriminant Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 246-250, November.
    3. C. E. McHenry, 1978. "Computation of a Best Subset in Multivariate Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 291-296, November.
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    Cited by:

    1. Brusco, Michael J. & Steinley, Douglas, 2011. "Exact and approximate algorithms for variable selection in linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 123-131, January.
    2. du Jardin, Philippe & Séverin, Eric, 2012. "Forecasting financial failure using a Kohonen map: A comparative study to improve model stability over time," European Journal of Operational Research, Elsevier, vol. 221(2), pages 378-396.
    3. Brusco, Michael J., 2014. "A comparison of simulated annealing algorithms for variable selection in principal component analysis and discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 38-53.
    4. Nkiet, Guy Martial, 2012. "Direct variable selection for discrimination among several groups," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 151-163.
    5. Ester Gutiérrez & Sebastián Lozano, 2014. "A DEA Approach to Performance-Based Budgeting of Formula One Constructors," Journal of Sports Economics, , vol. 15(2), pages 180-200, April.
    6. Pedro Duarte Silva, A., 2011. "Two-group classification with high-dimensional correlated data: A factor model approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2975-2990, November.
    7. A. Pedro Duarte Silva, 2009. "Exact and heuristic algorithms for variable selection: Extended Leaps and Bounds," Working Papers de Economia (Economics Working Papers) 01, Católica Porto Business School, Universidade Católica Portuguesa.
    8. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
    9. António Pedro Duarte Silva, 2002. "Discarding Variables in a Principal Component Analysis: Algorithms for All-Subsets Comparisons," Computational Statistics, Springer, vol. 17(2), pages 251-271, July.
    10. Cadima, Jorge & Cerdeira, J. Orestes & Minhoto, Manuel, 2004. "Computational aspects of algorithms for variable selection in the context of principal components," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 225-236, September.
    11. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.

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