Hi, I am really new to Stan and trying to fit Bass Model with hierarchical structure.

I succeeded in estimating all the coefficients in the model by MH algorithm using R before. However, I have some trouble now. In inference, I faced error codes like

Chain 1: Rejecting initial value:

Chain 1: Gradient evaluated at the initial value is not finite.

Chain 1: Stan can’t start sampling from this initial value.

Chain 1:

Chain 1: Initialization between (-2, 2) failed after 100 attempts.

Chain 1: Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.

[1] “Error in sampler$call_sampler(args_list[[i]]) : Initialization failed.”

[1] “error occurred during calling the sampler; sampling not done”

Because I use multiplicative error model, I evaluate likelihood in log-normal form, which could cause numerical issue such as log(0), I conjecture. However, I could not find any 0 in my simulated data. Also I added very very small number to the expected DV to avoid log(0) . Still I face the same problem. Do you have any nice idea to solve this problem? Thanks.

```
stancode <-
'
data {
int<lower=0> N; ##Num Total observation
int<lower=1> H; ##Num Firms
int<lower=1> ncoef; ##Num of Coefficients (p,q,m)
int<lower=1> nhier; ##Num of Firm level coefficients
int<lower=1> ntime; ##Time
vector[ntime] time;
row_vector[nhier] Z[H]; ## Firm level Covariates including intercept (H*nhier)
vector<lower=0>[N] sales; ## Sales of all firms (deprendent variable)
vector[ncoef] mu; ## Just 0,0,0
}
parameters {
corr_matrix[ncoef] C; ## prior correlation by Stan reference
vector<lower=0> [ncoef] tau; ## prior scale by Stan reference
real delta1; ## Coefficient1 for firm level covariate
real delta2; ## Coefficient2 for firm level covariate
real delta3; ## Coefficient3 for firm level covariate
real delta4; ## Coefficient4 for firm level covariate
real delta5; ## Coefficient5 for firm level covariate
real delta6; ## Coefficient6 for firm level covariate
real delta7; ## Coefficient7 for firm level covariate
real delta8; ## Coefficient8 for firm level covariate
real delta9; ## Coefficient9 for firm level covariate
real<lower=0> sigmasq; ## scale parameter
matrix [H,ncoef] eta; ## Firm level error term for p,q,m
}
transformed parameters{
real <lower=0> p[H]; ## each firm\'s p
real <lower=0> q[H]; ## each firm\'s q
real <lower=0> m[H]; ## each firm\'s r
vector<lower=0,upper=1> [ntime] F; ## Cumulative Dist of sales
vector<lower=0,upper=1> [ntime] lf; ## lag Cumulative Dist
vector<lower=0,upper=1> [ntime] f; ## Prob Dist
vector<lower=0> [N] mf; ## Expected Sales calculated by martket potential*Prob Dist
for(h in 1:H){
p[h]=exp(Z[h,1]*delta1+Z[h,2]*delta2+Z[h,3]*delta3)*exp(eta[h,1]); ## Multiplicative Error
q[h]=exp(Z[h,1]*delta4+Z[h,2]*delta5+Z[h,3]*delta6)*exp(eta[h,2]); ## Multiplicative Error
m[h]=exp(Z[h,1]*delta7+Z[h,2]*delta8+Z[h,3]*delta9)*exp(eta[h,3]); ## Multiplicative Error
for(t in 1:ntime){
F[t]=(1-exp(-(p[h]+q[h])*time[t]))/(1+(q[h]/p[h])*exp(-(p[h]+q[h])*time[t])) ; ## Formula for calculating Cum
}
lf[1]=0;
for(i in 2:ntime){
lf[i]=F[i-1];
f=F-lf;
}
mf[(ntime*(h-1)+1):(ntime*h)]=m[h]*f+0.00000000000000000000001; ### To avoid exact 0
}
}
model{
matrix[ncoef, ncoef] Sigma_beta;
tau ~ cauchy(0, 2.5); ## By Stan Manual
C ~ lkj_corr(2); ## By Stan Manual
delta1~normal(-1.7,5); ## Priod of deltas
delta2~normal(0,5);
delta3~normal(0,5);
delta4~normal(-1.73,5);
delta5~normal(0,5);
delta6~normal(0,5);
delta7~normal(13,5);
delta8~normal(0,5);
delta9~normal(0,5);
Sigma_beta = quad_form_diag(C, tau); ## By Stan Manual
for (h in 1:H){
eta[h]~multi_normal(mu, Sigma_beta); ### errors in p,q,m
}
log(sales)~normal(log(mf),sigmasq); ####Likelihood function
} '
initf <- function() list(delta1=delta1,delta2=delta2,delta3=delta3,delta4=delta4,delta5=delta5,delta6=delta6,delta7=delta7,delta8=delta8,delta9=delta9)
bassstan <- stan_model(model_code = stancode, verbose = TRUE)
```

Here my data generation code

```
library(dplyr)
options(scipen=999)
library(rstan)
library(tidybayes)
H<-2 #Number of Firms
ntime<-20 #Number of time
N=H*ntime #Number of total overvation
ncoef=3 #Number of coefficients (p,q,m)
nhier=3 #Number of coefficients for firm level covariates
mu=as.vector(rep(0,ncoef)) ###Just 0,0,0
sigsq=0.01
#prec=1/sigsq
z1=rnorm(H,0,0.1) ### Firm level covariates
z2=rnorm(H,0,0.1) ### Firm level covariates
Z=cbind(1,z1,z2) ### Firm level covariates matrix
delta1=-1.702585
delta2=0.0000005
delta3=-0.0000007
delta4=-1.731472
delta5=-0.0000001
delta6=0.00000009
delta7=13.81551
delta8=0.0000001
delta9=-0.0000001
deltamat=matrix(c(delta1,delta2,delta3,delta4,delta5,delta6,delta7,delta8,delta9),nrow=nhier,ncol=ncoef)
betabar=Z%*%deltamat
beta=matrix(0,H,ncoef)
###### Making beta matrix
sigeta=0.001
for(i in 1:H){
beta[i,]=exp(betabar[i,])%*%matrix(c(exp(rnorm(1,0,sigeta)),0,0,0,exp(rnorm(1,0,sigeta)),0,0,0,exp(rnorm(1,0,sigeta))),ncoef,ncoef )
}
time=1:(ntime) ####Time
sale=matrix(0,N,1) ####Dependent variable
for(i in 1:H){
u=rnorm(ntime,0,sd=sqrt(sigsq))
eps=exp(u)
F=((1-exp(-(beta[i,1]+beta[i,2])*time))/(1+(beta[i,2]/beta[i,1])*exp(-(beta[i,1]+beta[i,2])*time)))
lf=dplyr::lag(F,1)
lf[1]=0
f=F-lf
sale00=beta[i,3]*f
sale0=sale00*eps
sale[(ntime*(i-1)+1):(ntime*i)]=sale0
}
data=list(sales=as.vector(sale),time=as.vector(1:ntime),mu=mu,Z=Z,N=N,H=H,ntime=ntime,ncoef=ncoef,nhier=nhier)
```