In addition to the latent factors we were able to estimate direct and

In addition to the latent factors we were able to

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In addition to the latent factors, we were able to estimate direct and (potentially non-linear) indirect covariate effects. This is a unique feature pro- vided by semi-parametric LVMs. Our results could not have been obtained with classical factor analysis since these models neglect any covariate informa- tion. With regards to the direct effect of the year of the competition, we did not detect any significant increase of the number of points in any of the disciplines over the last decade. Instead, for the 100m and 400m races, a significant decrease in the mean points was estimated. The inclusion of a non-linear indirect effect for the month of the compe- tition enabled us to combine performance results from different competitions in one data set, and to investigate seasonal performance patterns. The well known performance peak in the middle of the season could be confirmed. This peak seemed to be more pronounced for jumping and endurance abilities than for sprint and throwing abilities. Sprint abilities are quite poor in spring which might be due to winter training shedule which usually focuses on strength and endurance. Therefore, sprint abilities are not yet fully trained at the beginning of the season. In the late season, a certain degree of fatigue occurs because of the previous competitions. An interesting result could be obtained for the non-linear indirect effect of age. Older athletes still perform very well compared to younger athletes, especially with respect to throwing and endurance abilities. For sprint and jumping abilities, a performance decrease for athletes older than 30 years was estimated. This confirms the theory that for some events experience and tech- nical skills of older athletes overwhelm the negative effect of age. 16 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 4, Art. 6 DOI: 10.2202/1559-0410.1307
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In comparison to previous analyses, our results confirm the grouping structure of decathlon disciplines found by Woolf et al. (2007) or Schomaker and Heumann (2011). Yet, we also used data from non-elite athletes who achieved less than 7500 total points. Thus, we conclude that the grouping structure does not seem to depend on the total points but is true for a large number of athletes. Also, the empirical correlation coefficients from our anal- ysis are almost similar to those from Ward et al. (2002). Finally, LVMs are also a good option for analyzing data from other sports. Applying LVMs generally makes sense when several continuous, corre- lated variables are observed – like multiple competition results in swimming or player characteristics in soccer – and underlying performance patterns should be investigated depending on covariates, like personal or training data. In Pyrka, Wimmer, Fenske, Fahrmeir, and Schwirtz (2011), we analyzed training data from 99 Ski Jumpers and 92 Nordic Combined athletes from all German national teams with classical factor analysis. In future work, we plan to collect additional performance data for these athletes and, then, to apply LVMs to combine both data bases.
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  • Statistics, De Gruyter, LVMs, Valentin Wimmer, Journal of Quantitative Analysis

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