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Exploring Competition Performance in Decathlon Using Semi-Parametric Latent Variable Models

Author

Listed:
  • Wimmer Valentin

    (Technische Universität München)

  • Fenske Nora

    (Ludwig-Maximilians-Universität München)

  • Pyrka Patricia

    (Technische Universität München)

  • Fahrmeir Ludwig

    (Ludwig-Maximilians-Universität München)

Abstract

In this paper, we explore competition performance in decathlon based on competition, training and personal data. Our data set comprises 3103 competition results from the decathlon world's best performance lists from 1998 to 2009. The aim of our analysis is to estimate latent factors describing the performance results and--at the same time--to model effects of age, season, and year of the competition on the results. Thus, we apply a new statistical method, semi-parametric latent variable models (LVMs), which can be seen as a synthesis between classical factor analysis and semi-parametric regression. LVMs are especially well-suited for modeling decathlon data, because (i) they permit the assumption of latent factors and therefore take the correlation structure between the ten performance results into account, and (ii) they enable us to model (potentially non-linear) relationships between response variables and covariates--contrary to classical factor analysis. In our analysis, we apply LVMs with a semi-parametric predictor allowing for non-linear covariate effects on the latent factors. Thereby, we obtain well interpretable results: four latent factors standing for sprint, jumping, throwing, and endurance abilities, as well as interesting non-linear effects of age and season on these latent factors. We also compare our results from LVMs to those obtained from classical factor analysis.

Suggested Citation

  • Wimmer Valentin & Fenske Nora & Pyrka Patricia & Fahrmeir Ludwig, 2011. "Exploring Competition Performance in Decathlon Using Semi-Parametric Latent Variable Models," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(4), pages 1-21, October.
    • Handle: RePEc:bpj:jqsprt:v:7:y:2011:i:4:n:6
    DOI: 10.2202/1559-0410.1307
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    References listed on IDEAS

    as
    1. Pyrka Patricia & Wimmer Valentin & Fenske Nora & Fahrmeir Ludwig & Schwirtz Ansgar, 2011. "Factor Analysis in Performance Diagnostic Data of Competitive Ski Jumpers and Nordic Combined Athletes," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(3), pages 1-22, July.
    2. Schomaker Michael & Heumann Christian, 2011. "Model Averaging in Factor Analysis: An Analysis of Olympic Decathlon Data," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(1), pages 1-15, January.
    3. Woolf Anne & Ansley Les & Bidgood Penelope, 2007. "Grouping of Decathlon Disciplines," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 3(4), pages 1-15, October.
    4. Ludwig Fahrmeir & Alexander Raach, 2007. "A Bayesian Semiparametric Latent Variable Model for Mixed Responses," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 327-346, September.
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    Cited by:

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    2. Griffin Jim E. & Hinoveanu Laurenţiu C. & Hopker James G., 2022. "Bayesian modelling of elite sporting performance with large databases," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 18(4), pages 253-268, December.
    3. Dziadek Bartosz & Iskra Janusz & Mendyka Wiesław & Przednowek Krzysztof, 2022. "Principal Component Analysis in the Study of the Structure of Decathlon at Different Stages of Sports Career," Polish Journal of Sport and Tourism, Sciendo, vol. 29(4), pages 21-28, December.
    4. Santos-Fernandez Edgar & Wu Paul & Mengersen Kerrie L., 2019. "Bayesian statistics meets sports: a comprehensive review," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(4), pages 289-312, December.
    5. Fröhlich, Michael & Gassmann, Freya & Emrich, Eike (ed.), 2015. "Zur Strukturanalyse des Mehrkampfes in der Leichtathletik: Eine empirische Studie zum Zusammenhang von Leistung und Erfolg im Siebenkampf der Frauen und Zehnkampf der Männer," Schriften des Europäischen Instituts für Sozioökonomie e.V., European Institute for Socioeconomics (EIS), Saarbrücken, volume 11, number 11, July.

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