d_nascar: NASCAR Data (partial orderings)

In PLMIX: Bayesian Analysis of Finite Mixtures of Plackett-Luce Models for Partial Rankings/Orderings

Description

The NASCAR dataset (d_nascar) collects the results of the 2002 season of stock car racing held in the United States. The 2002 championship consisted of N=36 races, with 43 car drivers competing in each race. A total of K=87 drivers participated in the 2002 season, taking part to a variable number of races: some of them competed in all the races, some others in only one. The results of the entire 2002 season were collected in the form of top-43 orderings, where the position of the not-competing drivers in each race is assumed lower than the 43th, but undetermined. Missing positions are denoted with zero entries.

Usage

data(d_nascar)

Format

Object of S3 class c("top_ordering","matrix") gathering a matrix of partial orderings with N=36 rows and K=87 columns. Each row lists the car drivers from the top position (Rank_1) to the bottom one (Rank_87) in a given race. Columns from the 44th to the 87th are filled with zeros, because only 43 drivers competed in each race.

Source

The NASCAR dataset in the MATLAB format used by Hunter, D. R. (2004) can be downloaded from http://sites.stat.psu.edu/~dhunter/code/btmatlab/. At the same link, a .xls file with drivers' names is also available.

References

Caron, F. and Doucet, A. (2012). Efficient Bayesian inference for Generalized Bradley-Terry models. J. Comput. Graph. Statist., 21(1), pages 174–196.

Guiver, J. and Snelson, E. (2009). Bayesian inference for Plackett-Luce ranking models. In Bottou, L. and Littman, M., editors, Proceedings of the 26th International Conference on Machine Learning - ICML 2009, pages 377–384. Omnipress.

Hunter, D. R. (2004). MM algorithms for Generalized Bradley-Terry models. Ann. Statist., 32(1), pages 384–406.

Examples

data(d_nascar)
head(d_nascar)

## Compute the number of races for each of the 87 drivers
table(c(d_nascar[,1:43]))

## Identify drivers arrived last (43th position) in all the races
which(colSums(rank_summaries(d_nascar, format="ordering")$marginals[1:42,])==0)

## Obscure drivers 84, 85, 86 and 87 to get the reduced dataset 
## with 83 racers employed by Hunter, D. R. (2004)
d_nascar_hunter=d_nascar[,1:83]
d_nascar_hunter[is.element(d_nascar_hunter,84:87)]=0

Example output

     rank1 rank2 rank3 rank4 rank5 rank6 rank7 rank8 rank9 rank10 rank11 rank12
[1,]    83    18    20    48    53    51    67    72    32     42      2     31
[2,]    52    72     4    82    60    31    32    66     3     44      2     48
[3,]    72    34    51    67    82    37    13     2    31     38     66      4
[4,]    82    12    37    52    60    66    83    51    72     67     48      7
[5,]    72    18    45    12    67    37    66    52    32      2     31     61
[6,]    48    38    61    12     4    52    37    35    66     45     51     49
     rank13 rank14 rank15 rank16 rank17 rank18 rank19 rank20 rank21 rank22
[1,]     62     13     37      6     60     66     33     77     56     63
[2,]     83     67     41     77     33     61     45     38     51     14
[3,]     61     52     35     12     32     14     39     48     83     53
[4,]     13     77     49     32     14     62     18     61     31     44
[5,]      3     49     53     34     39     35      7     55      4     41
[6,]     60     34     82     77     14      9     72     62      2     43
     rank23 rank24 rank25 rank26 rank27 rank28 rank29 rank30 rank31 rank32
[1,]     55     70     14     43     71     35     12     44     79      3
[2,]     42     62     35     12     25     37     34      6     18     79
[3,]      7     25     45     43     44     18     79     49     60     42
[4,]     34     43     39     38     42     55      3     35     71      9
[5,]     77     59     33      9     71     48     51     14     83     25
[6,]     55     74     83     31     33      3     13     53     32     23
     rank33 rank34 rank35 rank36 rank37 rank38 rank39 rank40 rank41 rank42
[1,]     52      4      9     45     41     61     34     39     49     15
[2,]     39     59     43     55     49     56      9     53      7     13
[3,]     33     55      6     41     62     77     71     59      9     70
[4,]     59     70      2     41      4      6     45     53     33     17
[5,]     42     62     43     82     38      6     74     13     60     70
[6,]     59     41     25      6     67     71     42      7     18     17
     rank43 rank44 rank45 rank46 rank47 rank48 rank49 rank50 rank51 rank52
[1,]     82      0      0      0      0      0      0      0      0      0
[2,]     71      0      0      0      0      0      0      0      0      0
[3,]      3      0      0      0      0      0      0      0      0      0
[4,]     25      0      0      0      0      0      0      0      0      0
[5,]     84      0      0      0      0      0      0      0      0      0
[6,]     39      0      0      0      0      0      0      0      0      0
     rank53 rank54 rank55 rank56 rank57 rank58 rank59 rank60 rank61 rank62
[1,]      0      0      0      0      0      0      0      0      0      0
[2,]      0      0      0      0      0      0      0      0      0      0
[3,]      0      0      0      0      0      0      0      0      0      0
[4,]      0      0      0      0      0      0      0      0      0      0
[5,]      0      0      0      0      0      0      0      0      0      0
[6,]      0      0      0      0      0      0      0      0      0      0
     rank63 rank64 rank65 rank66 rank67 rank68 rank69 rank70 rank71 rank72
[1,]      0      0      0      0      0      0      0      0      0      0
[2,]      0      0      0      0      0      0      0      0      0      0
[3,]      0      0      0      0      0      0      0      0      0      0
[4,]      0      0      0      0      0      0      0      0      0      0
[5,]      0      0      0      0      0      0      0      0      0      0
[6,]      0      0      0      0      0      0      0      0      0      0
     rank73 rank74 rank75 rank76 rank77 rank78 rank79 rank80 rank81 rank82
[1,]      0      0      0      0      0      0      0      0      0      0
[2,]      0      0      0      0      0      0      0      0      0      0
[3,]      0      0      0      0      0      0      0      0      0      0
[4,]      0      0      0      0      0      0      0      0      0      0
[5,]      0      0      0      0      0      0      0      0      0      0
[6,]      0      0      0      0      0      0      0      0      0      0
     rank83 rank84 rank85 rank86 rank87
[1,]      0      0      0      0      0
[2,]      0      0      0      0      0
[3,]      0      0      0      0      0
[4,]      0      0      0      0      0
[5,]      0      0      0      0      0
[6,]      0      0      0      0      0

 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 
 1 36 31 36  2 32  7  2 35  1  1 36 36 36  1  7  3 36  6 10  7  1 10  2 22  3 
27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 
 6  2  1  2 36 36 36 36 28  1 36 34 33  1 36 31 36 21 35  3  2 36 36  1 36 36 
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 
36  1 36 21  5  1  9 36 36 36  1  1  3 36 36  1  3  7 21 29 10 32  2  5 36  2 
79 80 81 82 83 84 85 86 87 
24  1  7 36 36  2  1  1  1 
Item_84 Item_85 Item_86 Item_87 
     84      85      86      87 

PLMIX documentation built on Sept. 4, 2019, 5:03 p.m.