Thanks for replying @Bob_Carpenter!
For context, the model is for the UK government assessment of fish catches. There is a wide variety of catch numbers between different species, with a few species caught far more than any others. I felt that a Student-t prior on the species random effect would capture this variety in scale better than a normal prior. Does this sound like a situation where a normal prior might be sufficient?
Please find below the Stan code that brms compiles for m2. Perhaps this will help a broader group of people in this forum identify where the initialisation error may be coming from.
// generated with brms 2.16.1
functions {
/* zero-inflated negative binomial log-PDF of a single response
* Args:
* y: the response value
* mu: mean parameter of negative binomial distribution
* phi: shape parameter of negative binomial distribution
* zi: zero-inflation probability
* Returns:
* a scalar to be added to the log posterior
*/
real zero_inflated_neg_binomial_lpmf(int y, real mu, real phi,
real zi) {
if (y == 0) {
return log_sum_exp(bernoulli_lpmf(1 | zi),
bernoulli_lpmf(0 | zi) +
neg_binomial_2_lpmf(0 | mu, phi));
} else {
return bernoulli_lpmf(0 | zi) +
neg_binomial_2_lpmf(y | mu, phi);
}
}
/* zero-inflated negative binomial log-PDF of a single response
* logit parameterization of the zero-inflation part
* Args:
* y: the response value
* mu: mean parameter of negative binomial distribution
* phi: shape parameter of negative binomial distribution
* zi: linear predictor for zero-inflation part
* Returns:
* a scalar to be added to the log posterior
*/
real zero_inflated_neg_binomial_logit_lpmf(int y, real mu,
real phi, real zi) {
if (y == 0) {
return log_sum_exp(bernoulli_logit_lpmf(1 | zi),
bernoulli_logit_lpmf(0 | zi) +
neg_binomial_2_lpmf(0 | mu, phi));
} else {
return bernoulli_logit_lpmf(0 | zi) +
neg_binomial_2_lpmf(y | mu, phi);
}
}
/* zero-inflated negative binomial log-PDF of a single response
* log parameterization for the negative binomial part
* Args:
* y: the response value
* eta: linear predictor for negative binomial distribution
* phi: shape parameter of negative binomial distribution
* zi: zero-inflation probability
* Returns:
* a scalar to be added to the log posterior
*/
real zero_inflated_neg_binomial_log_lpmf(int y, real eta,
real phi, real zi) {
if (y == 0) {
return log_sum_exp(bernoulli_lpmf(1 | zi),
bernoulli_lpmf(0 | zi) +
neg_binomial_2_log_lpmf(0 | eta, phi));
} else {
return bernoulli_lpmf(0 | zi) +
neg_binomial_2_log_lpmf(y | eta, phi);
}
}
/* zero-inflated negative binomial log-PDF of a single response
* log parameterization for the negative binomial part
* logit parameterization of the zero-inflation part
* Args:
* y: the response value
* eta: linear predictor for negative binomial distribution
* phi: shape parameter of negative binomial distribution
* zi: linear predictor for zero-inflation part
* Returns:
* a scalar to be added to the log posterior
*/
real zero_inflated_neg_binomial_log_logit_lpmf(int y, real eta,
real phi, real zi) {
if (y == 0) {
return log_sum_exp(bernoulli_logit_lpmf(1 | zi),
bernoulli_logit_lpmf(0 | zi) +
neg_binomial_2_log_lpmf(0 | eta, phi));
} else {
return bernoulli_logit_lpmf(0 | zi) +
neg_binomial_2_log_lpmf(y | eta, phi);
}
}
// zero_inflated negative binomial log-CCDF and log-CDF functions
real zero_inflated_neg_binomial_lccdf(int y, real mu, real phi, real hu) {
return bernoulli_lpmf(0 | hu) + neg_binomial_2_lccdf(y | mu, phi);
}
real zero_inflated_neg_binomial_lcdf(int y, real mu, real phi, real hu) {
return log1m_exp(zero_inflated_neg_binomial_lccdf(y | mu, phi, hu));
}
}
data {
int<lower=1> N; // total number of observations
int Y[N]; // response variable
// data for group-level effects of ID 1
int<lower=1> N_1; // number of grouping levels
int<lower=1> M_1; // number of coefficients per level
int<lower=1> J_1[N]; // grouping indicator per observation
// group-level predictor values
vector[N] Z_1_1;
int prior_only; // should the likelihood be ignored?
}
transformed data {
}
parameters {
real Intercept; // temporary intercept for centered predictors
real<lower=0> shape; // shape parameter
real<lower=0,upper=1> zi; // zero-inflation probability
vector<lower=0>[M_1] sd_1; // group-level standard deviations
vector[N_1] z_1[M_1]; // standardized group-level effects
real<lower = 0> sigma;
}
transformed parameters {
vector[N_1] r_1_1; // actual group-level effects
r_1_1 = (sd_1[1] * (z_1[1]));
}
model {
// likelihood including constants
if (!prior_only) {
// initialize linear predictor term
vector[N] mu = Intercept + rep_vector(0.0, N);
for (n in 1:N) {
// add more terms to the linear predictor
mu[n] += r_1_1[J_1[n]] * Z_1_1[n];
}
for (n in 1:N) {
target += zero_inflated_neg_binomial_log_lpmf(Y[n] | mu[n], shape, zi);
}
}
// priors including constants
target += student_t_lpdf(Intercept | 3, -2.3, 2.5);
target += gamma_lpdf(shape | 0.01, 0.01);
target += beta_lpdf(zi | 1, 1);
target += student_t_lpdf(sd_1 | 3, 0, sigma)
- 1 * student_t_lccdf(0 | 3, 0, sigma);
target += std_normal_lpdf(z_1[1]);
target += exponential_lpdf(sigma | 1);
}
generated quantities {
// actual population-level intercept
real b_Intercept = Intercept;
}