R: Convergence issues with jagam (mgcv R package)

Question

I am trying to fit following model:

mod <- jagam(y_freq ~ 
           s(x, bs="cr", fx=FALSE, k=5) + 
           s(x, by=a, bs="cr", fx=FALSE, k=5) + 
           s(x, by=b, bs="cr", fx=FALSE, k=5) + 
           s(x, by=c, bs="cr", fx=FALSE, k=5),
         family = binomial(), data = dt, 
         file = "file.jags", 
         weights = dt$total)

where 'a' is a numeric variable with 0 and 1 as potential values, 'b' is another numeric variable with 0 and 1 as potential values, and 'c' is the interaction between 'a' and 'b'.

As I would like to correct for overdispersion, I update the jags file that gets created by the jagam function as follows:

model {
  eta <- X %*% b
  for (i in 1:n) {
    y[i] ~ dbin(p[i],w[i])
    p[i] ~ dbeta(alpha[i], beta[i]) T(0.001,0.999) 
    alpha[i] = phi[i] * mu[i]
    beta[i] = phi[i] * (1 - mu[i])  
    phi[i] ~ dexp(1/250)
    mu[i] <-  ilogit(eta[i])
  } 
#splines are defined below here
}

After updating the file, I use the functions jags.model, jags.sample (for parameters: b, rho and mu) with 100k iterations and 3 chains, and sim2jam. After I check for convergence with the coda package, I get for all three chains following results (only one shown here):

example plot for one chain for rho parameter

I get traces for 8 rho parameters, for which only two seem to converge. I cannot show the results for the other parameters (b and mu) as there are too many (40 for b) to show on a plot.

I would like to know which of these 8 parameters for rho correspond to the null-space parameters, and what the cause of the convergence issue could be (too many parameters, too many splines, ...) and how to fix it?

Thank you,

Kate