Transform Parameter into logit form

Modeling
1

Hey there, I’m relativly new to stan and made some steps forward the last few weeks. I implemented a relativ simple cognitive model (code below). Since the parameter f should map individual differences, it is drawn from a normal distribution. However, the parameter should then be between 0 and 1, so I wanted to transform it with 1/1+exp(f) into the logit form, like this;

transformed parameters {
real Xsi[N] 
Xsi[N] = 1 / exp(f[N])
}

I tried to implement this, with different approaches, but failed. Do I have to declare a helper variable like this? Any tip is appreciated, since the Stan User guide was not that helpful

thanks

jan

Model:

data {
  int <lower=0> N;  // number of subjects
  int <lower=0> K;  // categories 
  int R[K];         // number of responses per category
  int count[N,K];   // observed data
  real scale_b;     // set scaling for background noise
}

parameters {
  // subject parameters
  real <lower=0> a[N];
  real <lower=0> c[N];
  real <lower=0> f[N];



  // Mu & Sigma for hyper distributions
  real <lower=0> mu_a;
  real <lower=0> sig_a;
  real <lower=0> mu_c;
  real <lower=0> sig_c;
  real <lower=0> mu_f;
  real <lower=0> sig_f;
}

transformed parameters{
  // activations
  vector[K] acts[N];
  real SummedActs[N];
  

  
  // probabilities
  
  vector[K] probs[N];
  
  // loop over subjects to compute activations and probabilites
  for (i in 1:N){
    acts[i,1] = scale_b + a[i] + c[i];
    acts[i,2] = scale_b + a[i];
    acts[i,3] = scale_b + f[i]*(a[i]+c[i]);
    acts[i,4] = scale_b + f[i] *a[i];
    acts[i,5] = scale_b;
    
    SummedActs[i] = R[1] * acts[i,1] + R[2] * acts[i,2] + R[3] * acts[i,3]+ R[4] * acts[i,4]+ R[5] * acts[i,5];
    
    probs[i,1] = (R[1] * acts[i,1]) ./ (SummedActs[i]);  
    probs[i,2] = (R[2] * acts[i,2]) ./ (SummedActs[i]);
    probs[i,3] = (R[3] * acts[i,3]) ./ (SummedActs[i]);
    probs[i,4] = (R[4] * acts[i,4]) ./ (SummedActs[i]);
    probs[i,5] = (R[5] * acts[i,5]) ./ (SummedActs[i]);
    

  }

}


model{
  // priors for hyper parameters
  mu_c ~ normal(10,10);
  sig_c ~ gamma(1,0.01);
  
  mu_a ~normal(10,10);
  sig_a ~ gamma(1,0.01);
  
  mu_f ~ normal(0,10);
  sig_f ~ gamma(1,0.01);
  
  // Loop over subjects
  for(i in 1:N){
    // Draw subject parameters from truncated normal
    c[i] ~ normal(mu_c, sig_c);
    a[i] ~ normal(mu_a, sig_a);
    f[i] ~ normal(mu_f, sig_f);


    // draw data from probabilities determined by MMM parms
    count[i,]  ~ multinomial(probs[i,]);
  }
}

****
2

Stan has a builtin logit function. Try this

Xsi = inv_logit(f); // Xsi = 1 / (1 + exp(-f))
3

hey, thanks I think that did the thing!

jan