Stan error: require unconstrained variable declaration. found simplex

Question

In Stan, I get the following error:

SYNTAX ERROR, MESSAGE(S) FROM PARSER:
require unconstrained variable declaration. found simplex.

ERROR at line 48
 46:    for (j in 1:records) {  
 47:            real phenology_predictor;
 48:            simplex[7] pi;
                        ^

I don't quite understand what is the problem. When I used real pi[7] instead of simplex[7] pi, I got different error:

SYNTAX ERROR, MESSAGE(S) FROM PARSER:
no matches for function name="categorical_log"
    arg 0 type=int
    arg 1 type=real[1]
available function signatures for categorical_log:
0.  categorical_log(int, vector) : real
1.  categorical_log(int[1], vector) : real
unknown distribution=categorical

ERROR at line 63
 62:    
 63:                    Y[j] ~ categorical(pi);
                                      ^
 64:    

which I don't understand either... My whole code:

data {
    int sites;
    int records;
    int Y[records];
    vector[records] yday;
    int site[records];
}
transformed data {
    int M[sites];
}
parameters {
    real<lower=0,upper=1> psi;
    real<lower=0,upper=1000> phi_phen_scale;
    real phi_alpha;
    real q_date;
    real q_date2;
    real q_site[sites];
}
model {
    real p[records];
    real q[records];

// priors
phi_phen_scale ~ normal(0, 10);
phi_alpha ~ normal(0, 10);
q_date ~ normal(0, 10);
q_date2 ~ normal(0, 10);

// vectorized
M ~ bernoulli(psi);
q_site ~ normal(0, 10);

for (j in 1:records) {  
    real phenology_predictor;
    simplex[7] pi;

    phenology_predictor <- q_date * yday[j] + q_date2 * yday[j]^2;
    p[j] <- M[site[j]] * inv_logit(phi_alpha + phi_phen_scale * phenology_predictor);
    q[j] <- inv_logit(q_site[site[j]] + phenology_predictor);

    pi[1] <- 1-p[j] + p[j]*(1-q[j])^6; 
    pi[2] <- p[j]*q[j]  ;   
    pi[3] <- p[j]*(1-q[j])*q[j];
    pi[4] <- p[j]*(1-q[j])^2*q[j];
    pi[5] <- p[j]*(1-q[j])^3*q[j];
    pi[6] <- p[j]*(1-q[j])^4*q[j];
    pi[7] <- p[j]*(1-q[j])^5*q[j];

    Y[j] ~ categorical(pi);

}

}

Answer 1

Constrained local parameters, such as simplexes, cannot be declared inside the model block because they are not checked. So, you should just declare pi to be a plain vector of length 7, like vector[7] pi;. Nevertheless, pi needs to be on the simplex in order to be an admissible argument to the categorical function.

If it is the case that symbolically pi is non-negative and sums to 1, then it is a question of making sure that numerically they are sufficiently close to non-negative and sum to something that is sufficiently close to 1. I'm not sure what the numerical tolerance is for a simplex in Stan but there is some wiggle room. If numerical error is the problem then doing pi <- pi / sum(pi); before passing pi to the categorical function may help.