Table 1: Contains the parameter estimates and respective HPD interval
Table 2: Contains the posterior probability for the combination of all players
Table 3: Contains the ranking of the players' abilities based on the posterior distribution of the ranks
# S3 method for bpc summary( object, digits = 2, credMass = 0.95, HPDI = TRUE, show_probabilities = TRUE, ... )
| object | bpc object |
|---|---|
| digits | number of decimal digits in the table |
| credMass | the probability mass for the credible interval |
| HPDI | True if show HPDI interval, False to show the credible (quantile) intervals |
| show_probabilities | should the tables of probabilities (Table 2) be displayed or not. Default to T but it is recommended to turn to F if either it has a large number of players (15+) or a large number of players and cluster, the table grows combinatorially. |
| ... | additional parameters for the generic summary function. Not used. |
# \donttest{ m<-bpc(data = tennis_agresti, player0 = 'player0', player1 = 'player1', result_column = 'y', model_type = 'bt', solve_ties = 'none') #> Running MCMC with 4 parallel chains... #> #> Chain 1 finished in 3.2 seconds. #> Chain 2 finished in 3.2 seconds. #> Chain 4 finished in 3.2 seconds. #> Chain 3 finished in 3.3 seconds. #> #> All 4 chains finished successfully. #> Mean chain execution time: 3.2 seconds. #> Total execution time: 3.4 seconds. summary(m) #> Estimated baseline parameters with 95% HPD intervals: #> #> Table: Parameters estimates #> #> Parameter Mean Median HPD_lower HPD_higher #> -------------------- ------ ------- ---------- ----------- #> lambda[Seles] 0.51 0.50 -2.07 3.36 #> lambda[Graf] 0.94 0.92 -1.81 3.56 #> lambda[Sabatini] -0.35 -0.36 -3.05 2.33 #> lambda[Navratilova] 0.05 0.03 -2.71 2.72 #> lambda[Sanchez] -1.12 -1.13 -3.82 1.71 #> NOTES: #> * A higher lambda indicates a higher team ability #> #> Posterior probabilities: #> These probabilities are calculated from the predictive posterior distribution #> for all player combinations #> #> #> Table: Estimated posterior probabilites #> #> i j i_beats_j j_beats_i #> ------------ ------------ ---------- ---------- #> Graf Navratilova 0.70 0.30 #> Graf Sabatini 0.67 0.33 #> Graf Sanchez 0.86 0.14 #> Graf Seles 0.63 0.37 #> Navratilova Sabatini 0.62 0.38 #> Navratilova Sanchez 0.78 0.22 #> Navratilova Seles 0.40 0.60 #> Sabatini Sanchez 0.66 0.34 #> Sabatini Seles 0.34 0.66 #> Sanchez Seles 0.21 0.79 #> #> Rank of the players' abilities: #> The rank is based on the posterior rank distribution of the lambda parameter #> #> Table: Estimated posterior ranks #> #> Parameter MedianRank MeanRank StdRank #> ------------ ----------- --------- -------- #> Graf 1 1.40 0.63 #> Seles 2 2.12 0.89 #> Navratilova 3 2.98 0.94 #> Sabatini 4 3.69 0.80 #> Sanchez 5 4.80 0.49 # }