PLMIX (version 2.1.1)

d_nascar: NASCAR Data (partial 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.

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

# NOT RUN {
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
# }