Exploring Competition Performance in Decathlon Using Semi-Parametric Latent Variable Models
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 andat the same timeto 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 covariatescontrary 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.
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Volume (Year): 7 (2011)
Issue (Month): 4 (October)
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- 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.
- 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.
- 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.
- 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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