Soccer

#MODEL DIFINIITION
m3_string <- "model {
for(i in 1:n_games) {
  HomeGoals[i] ~ dpois(lambda_home[Season[i], HomeTeam[i],AwayTeam[i]])
  AwayGoals[i] ~ dpois(lambda_away[Season[i], HomeTeam[i],AwayTeam[i]])
}

for(season_i in 1:n_seasons) {
  for(home_i in 1:n_teams) {
    for(away_i in 1:n_teams) {
      lambda_home[season_i, home_i, away_i] <- exp( home_baseline[season_i] + skill[season_i, home_i] - skill[season_i, away_i])
      lambda_away[season_i, home_i, away_i] <- exp( away_baseline[season_i] + skill[season_i, away_i] - skill[season_i, home_i])
    }
  }
}

skill[1, 1] <- 0
for(j in 2:n_teams) {
  skill[1, j] ~ dnorm(group_skill, group_tau)
}

group_skill ~ dnorm(0, 0.0625)
group_tau <- 1/pow(group_sigma, 2)
group_sigma ~ dunif(0, 3)

home_baseline[1] ~ dnorm(0, 0.0625)
away_baseline[1] ~ dnorm(0, 0.0625)

for(season_i in 2:n_seasons) {
  skill[season_i, 1] <- 0
  for(j in 2:n_teams) {
    skill[season_i, j] ~ dnorm(skill[season_i - 1, j], season_tau)
  }
  home_baseline[season_i] ~ dnorm(home_baseline[season_i - 1], season_tau)
  away_baseline[season_i] ~ dnorm(away_baseline[season_i - 1], season_tau)
}

season_tau <- 1/pow(season_sigma, 2)
season_sigma ~ dunif(0, 3)
}"

#initialization
m3 <- jags.model(textConnection(m3_string), data = data_list, n.chains = 3,
    n.adapt = 10000)
#Update burn in
update(m3, 10000)

#Draw sample
s3 <- coda.samples(m3, variable.names = c("home_baseline", "away_baseline",
    "skill", "season_sigma", "group_sigma", "group_skill"), n.iter = 40000,
    thin = 8)
ms3 <- as.matrix(s3)