pp_foot: Posterior predictive checks for football models

In LeoEgidi/footBayes: Fitting Bayesian and MLE Football Models

Posterior predictive checks for football models

Description

The function provides posterior predictive plots to check the adequacy of the Bayesian models as returned by the stan_foot function.

Usage

pp_foot(object, data, type = "aggregated", coverage = 0.95)

Arguments

object	An object either of class stanFoot, CmdStanFit, stanfit.
data	A data frame containing match data with columns: periods: Time point of each observation (integer >= 1). home_team: Home team's name (character string). away_team: Away team's name (character string). home_goals: Goals scored by the home team (integer >= 0). away_goals: Goals scored by the away team (integer >= 0).
type	Type of plots, one among "aggregated" or "matches". Default is "aggregated".
coverage	Argument to specify the width 1-\alpha of posterior probability intervals. Default is 0.95.

Details

Posterior predictive plots: when "aggregated" (default) is selected, the function returns a frequency plot for some pre-selected goal-difference values, along with their correspondent Bayesian p-values, computed as Pr(y_rep \ge y)|y), where y_rep is a data replication from the posterior predictive distribution (more details in Gelman et al., 2013). Bayesian p-values very close to 0 or 1 could exhibit possible model misfits.

When "matches" is selected an ordered-frequency plot for all the goal-differences in the considered matches is provided, along with the empirical Bayesian coverage at level 1-\alpha.

Value

A list with elements:

• pp_plot: A ggplot object for the selected type of plot.

• pp_table: A data frame of summary statistics:

  • For "aggregated": Goal differences and their Bayesian p‑values.

  • For "matches": Nominal 1-alpha and observed empirical Bayesian coverage.

Author(s)

Leonardo Egidi [e-mail] and Roberto Macrì Demartino [e-mail]

References

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.

Examples

## Not run: 
if (instantiate::stan_cmdstan_exists()) {
  library(dplyr)

  data("italy")
  italy_2000 <- italy %>%
    dplyr::select(Season, home, visitor, hgoal, vgoal) %>%
    dplyr::filter(Season == "2000")

  colnames(italy_2000) <- c("periods", "home_team", "away_team", "home_goals", "away_goals")

  fit <- stan_foot(italy_2000, "double_pois", iter_sampling = 200)

  pp_foot(fit, italy_2000)
}

## End(Not run)

LeoEgidi/footBayes documentation built on June 2, 2025, 11:32 a.m.