Hi all,

I’m trying to fit a non-linear growth model to some data with Stan (R code below). It seems pretty straightforward but I can’t get reasonable parameter estimates. Also I’m getting warning messages about divergent transitions and exceedance of the tree-depth.

I would greatly appreciate some advice.

Thanks,

Maarten

```
library(rstan)
dat <- list(
"N" = 14,
"x" = c(18, 19, 33, 39, 41, 41, 42, 44, 48, 57, 80, 81, 88, 93),
"Y" = c(0.80, 1.16, 1.55, 2.22, 2.76, 4.63, 5.41, 6.93, 4.55, 5.17, 6.42, 6.78, 8.92, 5.99)
)
nlm <- nls(Y ~ a*(1-exp(-b*x))^c, data = dat,
start = list(a = 1, b = 0.01, c = 1))
plot(dat$x, dat$Y)
lines(dat$x, predict(nlm))
print(nlm)
stanmodel <- "
data {
int<lower=0> N;
real<lower=0> x[N];
real<lower=0> Y[N];
}
parameters {
real alpha;
real beta;
real gamma;
real<lower=0> tau;
}
transformed parameters {
real<lower=0> sigma;
real<lower=0> m[N];
real<lower=0> a;
real<lower=0> b;
real<lower=0> c;
a = exp(alpha);
b = exp(beta);
c = exp(gamma);
for (i in 1:N)
m[i] = a*(1-exp(-b*x[i]))^c;
sigma = 1 / sqrt(tau);
}
model {
// priors
alpha ~ normal(0.0, 1000);
beta ~ normal(0.0, 1000);
gamma ~ normal(0.0, 1000);
tau ~ gamma(.0001, .0001);
Y ~ normal(m, sigma); // likelihood
}
generated quantities{
real Y_mean[N];
real Y_pred[N];
for(i in 1:N){
Y_mean[i] = a*(1-exp(-b*x[i]))^c; // Posterior parameter distribution of the mean
Y_pred[i] = normal_rng(Y_mean[i], sigma); // Posterior predictive distribution
}
}
"
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
fit <- stan(model_code = stanmodel,
model_name = "GrowthCurve",
data = dat)
print(fit)
```