 # Initial values in non-linear model on log scal (Location parameter is nan, but must be finite!)

Hi!

I’m trying to fit the non-linear von Bertalanffy growth equation to length-at-age data of fish:
L_t=L_{\infty}(1-e^{(-K(t-t_0))} using brms. I am experiencing some problems with initial values.

I have two sites with data from multiple years that I want to compare. I include site as a dummy coded variable, following this post. I also let parameters K and L_\infty vary between cohorts (birth_year).

Furthermore, exploratory analysis and QQ plots in particular made me want to fit it on log scale (commonly done for this model), and also utilise a Student-t likelihood to adress the tail situation that arises whith a gaussian likelihood on log data. I put the data on a repository. The model I’m fitting to that data is this:

library(readr)
library(brms)

# Informative priors to for convergence, chosen after sampling from the prior predictive distribution
prior <-
prior(normal(-0.5, 1), nlpar = "t0C") +
prior(normal(-0.5, 1), nlpar = "t0W") +
prior(normal(0.2, 0.1), nlpar = "KC") +
prior(normal(0.2, 0.1), nlpar = "KW") +
prior(normal(45, 20), nlpar = "LinfC") +
prior(normal(45, 20), nlpar = "LinfW")

# I use the following inits
inits <- list(
t0C = -0.5,
t0W = -0.5,
KC = 0.5,
KW = 0.5,
nu = 10,
mu = 10
)

m <-
brm(
bf(
log(length_cm) ~ areaW*log(LinfW*(1-exp(-KW*(age-t0W)))) +
areaC*log(LinfC*(1-exp(-KC*(age-t0C)))),
t0C ~ 1, t0W ~ 1, KC ~ 1 + (1|birth_year), KW ~ 1 + (1|birth_year),
LinfC ~ 1 + (1|birth_year), LinfW ~ 1 + (1|birth_year), nl = TRUE),

data = d, family = student(), prior = prior,
seed = 9, iter = 50, thin = 1, cores = 1, chains = 1,
inits = list(inits)
)


This works well, it samples and when I run for more chains the model diagnostics and fit quite good! However, when I want to use two chains:

# More chains
list_of_inits <- list(inits, inits)

m2 <-
brm(
bf(
log(length_cm) ~ areaW*log(LinfW*(1-exp(-KW*(age-t0W)))) +
areaC*log(LinfC*(1-exp(-KC*(age-t0C)))),
t0C ~ 1, t0W ~ 1, KC ~ 1 + (1|birth_year), KW ~ 1 + (1|birth_year),
LinfC ~ 1 + (1|birth_year), LinfW ~ 1 + (1|birth_year), nl = TRUE),

data = d, family = student(), prior = prior,
seed = 9, iter = 50, thin = 1, cores = 2, chains = 2,
inits = list_of_inits
)


I get the following error message:

...
Chain 2: Rejecting initial value:
Chain 2:   Error evaluating the log probability at the initial value.
Chain 2: Exception: student_t_lpdf: Location parameter is nan, but must be finite!  (in 'modeld9cc6691c6e7_dae435bc9f4399190964a8f3e866def5' at line 134)

Chain 2:
Chain 2: Initialization between (-2, 2) failed after 100 attempts.
Chain 2:  Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
 "Error in sampler\$call_sampler(args_list[[i]]) : Initialization failed."
error occurred during calling the sampler; sampling not done
Chain 1: Iteration: 15 / 50 [ 30%]  (Warmup)
Chain 1: Iteration: 20 / 50 [ 40%]  (Warmup)
....


Chain 1 works again, but chain 2 cannot find good initial values. Line 134 (which the error points me to) in my stancode is this one:

target += student_t_lpdf(Y | nu, mu, sigma).

(That’s why I set inits for mu, but I don’t think that’s correct…) My guess now is that I actually don’t set inits for the parameters I should, and therefore they are random which in my model can be problematic. But I’m not sure how to find which parameters get bad inits, and initis = "0" across the board of inits is not an option here…

Any advice on how to proceed from here is greatly appreciated!

Yes so please ignore the mu in the initis above, I did not think that through!

And regarding inits: is there a neat way to extract the inits from a model, pre fitting? It would be helpful to compare the inits of the two chains in m2, where one could sample and the other rejected.

It’s possible your initial values aren’t being used. brms needs initial values specified with the parameter names in the Stan code.

You can check those with stancode() or make_stancode()

Yes that must be the case. I extracted the inits from the chain that did sample and use that for chain 2 in the example with a minor random error multiplied to it. Still not fully understanding why (which parametersand why those specific inits make it sample) - will have to read up on it! Thanks @JLC!

Great!

It can be a little tricky in some cases where you have to set arrays of initial values. If you get dimension mismatches you can give something like this a try:

init_list <- list(
list(b_dv1 = array(data = 2),
b_dv2= array(data =  2),
b_dv3 = array(data = 2))