The aim of the present analysis is to explore the performance of decath letes

# The aim of the present analysis is to explore the

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The aim of the present analysis is to explore the performance of decath- letes based on competition, training and personal data. In particular, we are 1 Wimmer et al.: Latent Variable Models for Decathlon Published by De Gruyter, 2011
interested in the effect of age and training on the competition performance. Our data set comprises 3103 competition results from the world’s best perfor- mances lists from 1998 to 2009. It contains not only the resulting points for the ten track and field events, but also covariate information on athletes’ age as well as month and year of the competition. Decathlon and heptathlon were subject to many statistical analyses in the past. Dawkins, Andreae, and O’Connor (1994) used cluster algorithms, regression trees and correspondance analysis to characterize leading athletes for 1992 Olympic heptathlon data. Cox and Dun (2002) clustered results from the world Athletic Championships from 1991 to 1999 in order to identify track and field events with big impact on the total points. Woolf, Ansley, and Bidgood (2007) grouped the ten events into clusters. Yet, to the best of our knowledge, past analyses rely on data of performance results only and do not include any additional covariate information, as will be the case here. We present and apply semi-parametric Latent Variable Models (LVMs), a new class of statistical models which is well suited to analyze decathlon data. LVMs can be seen as a synthesis between classical factor analysis and semi- parametric regression. They consist of two models, which will be described in Section 2. First, the measurement model describes effects of latent factors on the response variables of interest – in our analysis the ten point results. At the same time, covariates with direct impact on the response variables can be included in the measurement model – in our analysis the year of the competition. The structural model formulates and quantifies (potentially non- linear) relationships between the latent factors and covariates – we will consider age of the athletes and month of the competition as covariates. In particular, we apply semi-parametric LVMs allowing for non-linear covariate effects on the latent factors in the second model (Fahrmeir and Raach, 2007). Latent factors are a natural concept for decathlon data. Since every athlete has his personal strength and weaknesses, there is usually no athlete who performs well in every track and field event. For example, a classical fac- tor analysis in Schomaker and Heumann (2011) detected typical performance patterns: On the one hand, there are athletes with great leg speed who per- form well in the sprint events, such as 100m, 400m, and 110m hurdles race. On the other hand, there are athletes who perform well in throwing events because of their arm strength. These results suggest to assume the presence of a few latent factors explaining the performance of an athlete. Even though these latent factors cannot be observed directly, their level is indicated by the results obtained in the ten events. An example could be a latent factor called “throwing ability”. An athlete’s overall throwing ability cannot be measured

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• Fall '20
• Statistics, De Gruyter, LVMs, Valentin Wimmer, Journal of Quantitative Analysis

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