9 Wimmer et al Latent Variable Models for Decathlon Published by De Gruyter

9 wimmer et al latent variable models for decathlon

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9 Wimmer et al.: Latent Variable Models for Decathlon Published by De Gruyter, 2011
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3.2 Model Description Figure 3 shows a path diagram of the specific LVM considered in our analysis, combining model equations (2.2) and (2.4) in Section 2. Altogether, our model includes ten indicator variables for the competition results, four latent factors, two indirect covariates for the month of the competition and the age of an athlete, and one direct covariate for the year of the competition. We chose four latent factors because this number provides the best trade-off between model complexity and model adaptation. Also, this choice leads to a model where each of the ten indicators is covered by at least one latent factor. month age M100 LJ M1500 year factor 1 factor 4 Figure 3: Path diagram of the specific LVM considered here. Our model includes ten indicator variables, four latent factors, two indirect covariates for month and age , and one direct covariate for year . Arrows without origin denote variables with measurement error. The indirect non-linear covariate effect for month is included in the structural model (2.4) for the following reason. The considered competitions took place at many different times during the year, ranging from March to Oc- tober. In one season, an athlete usually participates in up to four decathlons. 10 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 4, Art. 6 DOI: 10.2202/1559-0410.1307
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Therefore, the conditions for each decathlon differ due to weather, training, and competition schedule. Usually, the most important competitions are in the late season. Previous analyses, such as Dawkins et al. (1994), had to restrict their data to results from one competition, since additional covariate infor- mation could not be taken into account due to methodical limitations. LVMs allow for the inclusion of a non-linear indirect covariate effect for the variable month . This enables us to combine performance results from different compe- titions in one data set, and to investigate seasonal performance patterns. The indirect non-linear covariate effect for age is included to assess the influence of age on performance results, since athletes’ ages range from 16 to 40 years. The indirect non-linear effects of age and month in the structural model (2.4) are estimated with P-splines of degree 3 and 20 equally spaced knots. In addition we include a direct effect of year to investigate if a general performance change has occured over the years in any of the ten track and field events. For example, it would be possible that new specific training methods or techniques have led to significantly better results in a specific event. One may think of the beginning of the use of the Fosbury Flop in 1968 as a new high jump technique. Such effects can be observed on the level of indicator levels directly and will therefore not appear in the structural model.
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  • Fall '20
  • Statistics, De Gruyter, LVMs, Valentin Wimmer, Journal of Quantitative Analysis

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