KEYWORDS latent variable model factor analysis semi parametric regression track

# Keywords latent variable model factor analysis semi

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compare our results from LVMs to those obtained from classical factor analysis. KEYWORDS: latent variable model, factor analysis, semi-parametric regression, track & field Author Notes: Valentin Wimmer, Lehrstuhl für Pflanzenzüchtung, Technische Universität München. Nora Fenske, Institut für Statistik, Ludwig-Maximilians-Universität München. Patricia Pyrka, Fachgebiet Biomechanik im Sport,Technische Universität München. Ludwig Fahrmeir, Institut für Statistik, Ludwig-Maximilians-Universität München.
1 Introduction Decathlon is a competition which is held over two consecutive days and consists of ten track and field events. Usually around 20 to 30 male athletes participate at one competition. The winner is the athlete with the most cumulated points after the last event. The events are always tested in the following order: Day 1 : (1) 100m race, (2) long jump, (3) shot put, (4) high jump, (5) 400m race; Day 2 : (6) 110m hurdles, (7) discus, (8) pole vault, (9) javelin, (10) 1500m race. The procedure of measuring the performance depends on the event: For the track events, e.g., 100m, 400m, 110m hurdles, and 1500m, each athlete has one attempt in order to obtain a valid time. The remaining field events are further divided into two groups: In long jump, shot put, discus, and javelin, every athlete has three attempts and his best result in each discipline will be taken for the later scoring. In high jump and pole vault, each athlete tries to jump over a horizontal bar. If he succeeds, the bar will be raised by 3 and 10 centimeters, respectively. If he fails, the bar remains at the same height for the next try. After three consecutive misses an athlete will be eliminated and his best height will be taken for the later scoring. If an athlete does not manage to achieve a valid result in an event, he gains zero points in this event but is allowed to continue the decathlon. The performance of each event is converted into a points system devel- oped by the International Association of Athletics Federations (IAAF). Since 2001, the points have been calculated according to the following formulae: Points = ( a · ( b - x ) c for track events a · ( x - b ) c for field events where x is the raw performance measure (in seconds, meters or centimeters) and a , b , and c are constant parameters varying between the ten events. Their exact values can be found on . For each of the ten events the resulting points are rounded to zero decimal places. Theoretically, this points system should lead to an equal weighting of all ten track and field events. However, after an empirical analysis Cox and Dun (2002) arrive at the conclusion that the current points system favors those athletes who do well at the field events. Altogether, decathlon is a combination of ten track and field events which measure sprint, jumping, throwing and technical abilities of the athletes, as well as their endurance and mental strength. Thus, it is a complex task to investigate fundamental determinants of decathlon performance.

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

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