Multinomial Logit: probability of choice of a soccer action

Modeling
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2

Sounds like this is similar to your previous model but now you have a three-state outcome instead of a binary one.

The main change would be categorical_logit instead of bernoulli_logit.
Here’s an example of how that might look.

data {
    int<lower=0> Nobs; // number of observations
    int Nplayers; // number of players
    int Nzones; // number of zones
    
    int<lower=1,upper=Nplayers> player_id[Nobs];
    int<lower=1,upper=Nzones> zone_id[Nobs];

    int<lower=1,upper=3> action[Nobs];
}
parameters {
    vector[3] beta_player[Nplayers];
    vector[3] beta_zone[Nzones];
}
model {
    for (i in 1:Nplayers){
        beta_player[i] ~ normal(0,1);
    }
    for (i in 1:Nzones) {
        beta_zone[i] ~ normal(0,1);
    }
    for (i in 1:Nobs) {
        action[i] ~ categorical_logit(beta_player[player_id[i]] + beta_zone[zone_id[i]]);
    }
}

The above model has some nonidentifiability because only differences in beta values matter for prediction. Due to this betas will probably have very vague posterior distributions no matter how much data you have. Despite that the posterior predictive distribution should be sharp.
It’s possible to fix the nonidentifiability but I left it in to keep this starting point model simple.

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