The formulae from wwwiaaforg were used to convert the raw results into the

# The formulae from wwwiaaforg were used to convert the

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The formulae from were used to convert the raw results into the points system. Table 1 gives an overview of the data set, including the raw performance measures and corresponding points of the ten continuous perfor- mance variables. The lower triangle in Figure 1 displays a scatterplot matrix 6 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 4, Art. 6 DOI: 10.2202/1559-0410.1307
Our correlation coefficients are similar to the results in Ward, Sprevak, and Boreham (2002) who analyzed decathlon data from the 5 Olympic Games from 1984 to 2000. Also, Table 1 indicates that mean and variance of the points differ for each event. For this reason, we standardized all response variables to a mean of zero and a standard deviation of one before using them in LVM estimation. Furthermore, athletes’ ages and dates (year and month) of the decathlon competitions are known, see Table 1 and Figure 2. for univariate descriptions of these covariates. summary of raw athletes’ performances (points) name description [unit] min q25 mean q75 max M100 100m race [s] 12.19(615) 11.41(772) 11.23(812) 11.04(852) 10.31(1021) LJ Long jump [m] 6.06(600) 6.78(762) 7(814) 7.21(864) 8.11(1089) SP Shot put [m] 9.04(429) 12.37(629) 13.23(682) 14.1(735) 17.78(962) HJ High jump [cm] 165(504) 188(697) 194(749) 200(804) 222(1012) M400 400m race [s] 56.57(538) 51.5(747) 50.54(792) 49.52(837) 46.15(1001) MH110 110m hurdles [s] 18.05(520) 15.51(789) 15.14(834) 14.77(878) 13.67(1018) Disc Discus [m] 17.78(231) 36.83(601) 39.79(661) 42.64(719) 54.08(956) PV Pole vault [cm] 0(0) 420(674) 446(752) 470(820) 555(1084) Jav Javelin [m] 19.1(150) 49.94(588) 54.06(650) 58.23(712) 77.47(1004) M1500 1500m race [s] 355(285) 293(601) 284.15(658) 274(719) 248(896) covariates for each competition min q25 mean q75 max age athlete’s age [years] 16 22 24.13 26 40 year year 1998 2001 2003.68 2007 2009 month month 3 5 6.4 7 10 pT total points 6800 7050 7394.19 7660 9026(WR) Table 1: Variable names and descriptive summary statistics (minimum, 25%- quantile, mean, 75%-quantile and maximum) of each variable in the decathlon data set with 3103 observations. of the resulting performance variables for all ten track and field events. The upper triangle shows corresponding empirical correlations. High correlations between groups of events suggest the presence of latent factors in decathlon. 7 Wimmer et al.: Latent Variable Models for Decathlon Published by De Gruyter, 2011
M100 700 0.49 0.22 600 0.15 0.61 600 0.51 0.20 500 0.16 0.054 400 650 950 0.065 700 LJ 0.17 0.30 0.38 0.49 0.14 0.25 0.19 0.14 SP 0.15 0.11 0.23 0.77 0.26 0.44 500 900 0.062 600 HJ 0.12 0.26 0.10 0.12 0.047 0.044 M400 0.39 0.12 0.18 0.032 600 0.43 600 MH110 0.23 0.20 0.13 0.086 Disc 0.26 0.39 500 0.066 500 PV 0.20 0.15 Jav 400 900 0.087 650 950 400 500 900 600 500 400 900 M1500 Figure 1: Diagonal shows histograms for the ten performance variables. Lower triangle displays a scatterplot matrix, whereas upper triangle gives Pearson’s pairwise empirical correlation coefficients. 8 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 4, Art. 6 DOI: 10.2202/1559-0410.1307
age [years] 20 25 30 35 40 0 200 400 600 800 3 4 5 6 7 8 9 10 month of competition 0 200 400 600 800 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 year of competition 0 50 100 150 200 250 300 350 total points 7000 7500 8000 8500 9000 0 200 400 600 800 Figure 2: Univariate descriptions of covariates age , month , year and total points in the decathlon data set (number of observations in absolute frequen- cies).

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