Hi all,

I am working on a my own version of the paper of Baio and Blangiardo. They create a Bayesian hierarchical model on *team* level to determine the attack and defense parameters of each team. They use these parameters and *home-advantage*-parameter to forecast game scores. Visually, their layout looks as follows:

My interpretation of their model in Stan is

`data { int<lower=1> n_teams; int<lower=1> n_matches; int<lower=1, upper=n_teams> home_team[n_matches]; int<lower=1, upper=n_teams> away_team[n_matches]; int<lower=0> home_goals[n_matches]; int<lower=0> away_goals[n_matches]; } parameters { real home; real mu_att; real mu_def; real<lower=0> tau_att; real<lower=0> tau_def; vector[n_teams - 1] raw_att; vector[n_teams - 1] raw_def; } transformed parameters { vector[n_teams] att; vector[n_teams] def; vector[n_matches] home_log_theta; vector[n_matches] away_log_theta; for (team in 1:(n_teams - 1)) { att[team] = raw_att[team]; def[team] = raw_def[team]; } att[n_teams] = -sum(raw_att); def[n_teams] = -sum(raw_def); home_log_theta = exp(home + att[home_team] + def[away_team]); away_log_theta = exp(att[away_team] + def[home_team]); } model { // priors home ~ normal(0, 100); mu_att ~ normal(0, 10); mu_def ~ normal(0, 10); tau_att ~ gamma(0.01, 0.01); tau_def ~ gamma(0.01, 0.01); raw_att ~ normal(mu_att, tau_att); raw_def ~ normal(mu_def, tau_def); home_goals ~ poisson(home_log_theta); away_goals ~ poisson(away_log_theta); }`

Now, I would like to make my model on a *player*-level. I assume that for each team:

- the attack parameter is equal to exp(sum(attack parameters of each player of team))
- the defense parameter is equal to exp(sum(defense parameters of each player of team))

Visually:

In the graph I only draw the player-lines for the home team, but the same method applies for the away team.

My code looks as follows:

```
data {
int<lower=1> n_teams;
int<lower=1> n_games;
int<lower=1> n_players
int<lower=1, upper=n_teams> home_team_id[n_games];
int<lower=1, upper=n_teams> away_team_id[n_games];
int<lower=1, upper=n_players> player_id[n_games];
int<lower=0> home_goals[n_games];
int<lower=0> away_goals[n_games];
}
parameters {
real home_advantage;
real player_att_mu;
real player_att_tau;
real player_def_mu;
real player_def_tau;
real team_att_raw[n_teams - 1];
real team_def_raw[n_teams - 1];
real player_att_raw[n_players - 1];
real player_def_raw[n_players - 1];
}
transformed parameters {
// Enforce sum-to-zero constraint
real team_att[n_teams];
real team_def[n_teams];
real player_att[n_players];
real player_def[n_players];
vector[n_games] home_expected_goals;
vector[n_games] away_expected_goals;
for (team in 1:(n_teams-1)) {
team_att[team] = team_att_raw[team];
team_def[team] = team_def_raw[team];
}
team_att[n_teams] = -sum(team_att_raw);
team_def[n_teams] = -sum(team_def_raw);
for (player in 1:(n_players-1)) {
player_att[player] = player_att_raw[player]
player_def[player] = player_def_raw[player]
}
player_att[n_players] = -sum(player_att_raw);
player_def[n_players] = -sum(player_def_raw);
for (game in 1:n_games) {
team_att[home_team_id[game]] = exp(sum(player_att[player_id[game]])); // problem
team_def[home_team_id[game]] = exp(sum(player_def[player_id[game]])); // problem
team_att[away_team_id[game]] = exp(sum(player_att[player_id[game]])); // problem
team_def[away_team_id[game]] = exp(sum(player_def[player_id[game]])); // problem
home_expected_goals[game] = exp(team_att[home_team_id[game]] + team_def[away_team_id[game]] + home_advantage);
away_expected_goals[game] = exp(team_att[away_team_id[game]] + team_def[home_team_id[game]]);
}
}
model {
// Priors (uninformative)
player_att_mu ~ normal(0, 10);
player_def_mu ~ normal(0, 10);
player_att_tau ~ gamma(0.1, 0.1);
player_def_tau ~ gamma(0.1, 0.1);
home_advantage ~ normal(0, 100);
home_goals ~ poisson(home_expected_goals);
away_goals ~ poisson(away_expected_goals);
}
```

How can I make sure that my code knows for each game which players belonged to the home team and which players belonged to the away team. I need to specify somewhere a vector with the player_ids of each team. But I donâ€™t see how this can be done. Please advice! Help is much appreciated