Hiya folks! First post, so apologies if this isn’t articulated well. I’m working with a Cormack-Jolly-Seber model using the marginalization method outlined in Yackulic et al. (2020). I’ve adapted it to include a predictor of the survival rates (e.g. some climatic variable). Additionally, I’ve added some code to set the detection probablity of unsampled years to 0. However, I’m uncertain of how to extract the point-wise log-likelihood values for use in loo. I suppose I need some vector in a generated quantity block that is the likelihood of each capture history given my estimates for the survival and detection probabilities. Then, I think I would append this vector with the likelihood of these survival estimates given the values of my predictor variable, but I am less sure about this. Overall, I’m a bit stumped and am wondering if others have done anything similar or have ideas. My code without this generated quantity is below.

```
// CJS Model with time varying survival (s) and capture probability (p)
data{
int<lower = 1> NsumCH; // number of capture histories
int<lower = 1> n_occasions; // number of capture occasions
int<lower = 1, upper = 2> sumCH[NsumCH, n_occasions]; // capture histories
int<lower = 1> sumf[NsumCH]; // first capture occasion
int<lower = 1> sumFR[NsumCH]; // frequency of each capture history
int<lower = 1> n_missing; // number of unsampled years
int<lower = 1> missing[n_missing]; // unsampled years
int<lower = 1> n_observed; // number of sampled years
int<lower = 1> observed[n_observed]; // sampled years
vector[n_occasions-1] pred; // predictor variable each year
}
parameters{
real<lower = 0, upper = 1> free_p[n_occasions - 1]; // detection probability for all years
real<lower = 0, upper = 1> logit_phi[n_occasions - 1]; // logit survival probability
real phi_0; // intercept for survival model
real phi_pred; // effect of pred on survival
}
transformed parameters{
simplex[2] tr[2,n_occasions - 1]; // survival likelihoods for marginalization
simplex[2] pmat[2,n_occasions - 1]; // detection likelihoods for marginalization
// real mu[n_occasions-1];
real<lower = 0, upper = 1> p[n_occasions - 1]; // detection probability with unsampled years = 0
real<lower=0,upper=1> phi[n_occasions-1]; // survival probability
for(i in missing){
p[i] = 0; // set unsampled p to 0
}
for(i in observed){
p[i] = free_p[i]; // fill in sampled p with a real estimate
}
for(i in 1:n_occasions - 1){
phi[i] = inv_logit(phi_0+pred[i]*phi_pred); // survival is a function of predictor vars
}
for(k in 1:n_occasions - 1){
tr[1,k,1] = phi[k];
tr[1,k,2] = (1 - phi[k]);
tr[2,k,1] = 0;
tr[2,k,2] = 1;
pmat[1,k,1] = p[k];
pmat[1,k,2] = (1 - p[k]);
pmat[2,k,1] = 0;
pmat[2,k,2] = 1;
}
}
model{
vector[2] pz[n_occasions]; // marginalized likelihoods
free_p ~ uniform(0,1);
for(i in 1:NsumCH){
pz[sumf[i],1] = 1;
pz[sumf[i],2] = 0;
for(k in (sumf[i] + 1):n_occasions){
pz[k,1] = pz[k-1,1] * tr[1,k-1,1] * pmat[1,k-1,sumCH[i,(k)]];
pz[k,2] = (pz[k-1, 1] * tr[1,k-1,2] + pz[k-1, 2]) * pmat[2,k-1,sumCH[i,(k)]];
}
target += sumFR[i] * log(sum(pz[n_occasions]));
}
// for(i in 1:n_occasions-1){
// target += normal_lpdf(logit_phi[i] | mu[i], 10);
// }
}
```

Any help would be great! Let me know if I’m missing important information in this post or if I’m demonstrating a misconception or gap in my knowledge. Thanks in advance!