Hi all,

I’m trying to speed up a model that I am writing (*I’m aware this is a model that can be fitted already using existing code, however I’m writing this as a sub-model that will later be used as a block in the full model*).

I want to move the normally distributed zero mean random effects (labelled b2 and b3) from the parameters block to be local parameters in the model block - so that they are not recorded at each iteration which might speed up model fit?

However, when I move the random effects, the model cannot initialise (an error message is printed - “Chain 1: Rejecting initial value:

Chain 1: Error evaluating the log probability at the initial value.

Chain 1: Exception: normal_lpdf: Location parameter[1] is nan, but must be finite! (in ‘string’, line 71, column 2 to column 119)”

I’ve tried a few different specifications but get a similar message to this each time.

The model runs (slowly) if b2 and b3 are in the parameter block

Any tips on how to correctly move these matrices of random effects (b2 and b3) to be local only, so that they are not returned would be really helpful.

Aside - I have tried editing brms code to edit fast running code rather than writing from scratch, however I need the code to remain flexible in the number of possible random effects at each level, and the brms code seems tailored to a specific number of random effects?

Model below, moved lines have been commented out. I’m running the model using rstan.

```
functions{
}
data {
//dimensions of data
int<lower=1> M; //number of observations
int<lower=1> N; //number of individuals
int<lower=1> K; //number of studies
int<lower=1> pl; //number long fixed
int<lower=1> ql; //number long indrand
int<lower=0> rl; //number long studrand
//id variables
int<lower=1> idnum[M]; //long ind id variable
int<lower=1> studnum[M]; //long stud id variable
//longitudinal outcome information
vector[M] y1; //longitudinal outcome
//longitudinal fixed information
matrix[M,pl] X_l; //design matrix long fixed
real<lower=0> beta_l_sig; //sd for fixed effects prior
real<lower=0> sigma_e_sig; //involved in prior for sigma_e - sig for longerror
real<lower=0> sigma_e_nu; //involved in prior for sigma_e - sig for longerror
//longitudinal indrand information
matrix[M,ql] Z2_l; //design matrix long indrand
vector[ql] b2_ones; //vector of ones for use indrand
real<lower=0> tau_Dl_sig; //involved in prior for tau_Dl - sd for indrand
real<lower=0> tau_Dl_nu; //involved in prior for tau_Dl - sd for indrand
real Omega_Dl_eta; //involved in prior for Omega_Dl - corr mat for indrand
//longitudinal studrand information
matrix[M,rl] Z3_l; //design matrix long studrand
vector[rl] b3_ones; //vector of ones for use studrand
real<lower=0> tau_Al_sig; //involved in prior for tau_Al - sd for studrand
real<lower=0> tau_Al_nu; //involved in prior for tau_Al - sd for studrand
real Omega_Al_eta; //involved in prior for Omega_Al - corr mat for indrand
}
transformed data{
vector[ql] mu_b2; //mean vector for longindrand
vector[rl] mu_b3; //mean vector for longstudrand
mu_b2 = rep_vector(0,ql); //used for mean vector for long indrand
mu_b3 = rep_vector(0,rl); //used for mean vector for long studrand
}
parameters{
vector[pl] beta_l; //fixed effects for longitudinal component
real<lower=0> sigma_e; //longitudinal error term (sd)
//matrix[N,ql] b2; //longitudinal indrand effects
cholesky_factor_corr[ql] Omega_Dl; //Correlation Matrix long indrand
vector<lower=0>[ql] tau_Dl; //variance terms long indrand
//matrix[K,rl] b3; //longitudinal studrand effects
cholesky_factor_corr[rl] Omega_Al; //Correlation Matrix long indrand
vector<lower=0>[rl] tau_Al; //variance terms long indrand
}
transformed parameters{
//vector[M] linpred_y1; //longitudinal linear predictor
//matrix[ql,ql] Dl; //covariance matrix for long indrand
//matrix[rl,rl] Al; //covariance matrix for long studrand
//linpred_y1 = X_l*beta_l + (Z2_l .* to_matrix(b2[idnum,]))*b2_ones+ (Z3_l .* to_matrix(b3[studnum,]))*b3_ones;
//Dl = diag_pre_multiply(tau_Dl, Omega_Dl);
//Al = diag_pre_multiply(tau_Al, Omega_Al);
}
model{
matrix[ql,ql] Dl = diag_pre_multiply(tau_Dl, Omega_Dl);
matrix[rl,rl] Al = diag_pre_multiply(tau_Al, Omega_Al);
matrix[N,ql] b2;
matrix[K,rl] b3;
//Priors
tau_Dl ~ student_t(tau_Dl_nu,0,tau_Dl_sig); //prior for sig for long indrand
Omega_Dl~ lkj_corr_cholesky(Omega_Dl_eta); //prior for corr matrix for long indrand
tau_Al ~ student_t(tau_Al_nu,0,tau_Al_sig); //prior for sig for long studrand
Omega_Al~ lkj_corr_cholesky(Omega_Al_eta); //prior for corr matrix for long studrand
beta_l ~ normal(0,beta_l_sig); //prior for fixed effects
sigma_e ~ student_t(sigma_e_nu,0,sigma_e_sig); //prior for longitudinal error term
//Likelihood
y1 ~ normal(X_l*beta_l + (Z2_l .* to_matrix(b2[idnum,]))*b2_ones+ (Z3_l .* to_matrix(b3[studnum,]))*b3_ones,sigma_e); //update longitudinal outcome
for(i in 1:N){
b2[i] ~ multi_normal_cholesky(mu_b2, Dl); //update long indrand
}
for(j in 1:K){
b3[i] ~ multi_normal_cholesky(mu_b3, Al); //update long studrand
}
}
//generated quantities{
//}
```

Any advice greatly appreciated