I am trying to fit non-linear models with brms. My model is:
y = intercept + b1 * (x1 * mean(x2^b2))
where:
x1 is a measured continuous variable,x2 is also a continuous variable nested in x1. For more context, x1 is a population size and x2 is the mass of a subset of individuals of that population.intercept, b1 and b2 are parameters to be estimatedA colleague of mine coded it in rjags this way:
y1[i] <- x1[i]*(mean(x2_matrix[1:no_per_site[i],i]^b2))
y2[i] <- intercept + y1[i]*b1
Where i is the site index, x2_matrix has one row per individual mass (x2) values and one column per site, and where no_per_site is the number of x2 measured in each site.
Is there a way to fit this model in brms? How do I manage the x2 matrix?
Here is the structure of the data:
'data.frame': 31 obs. of 3 variables:
$ population: chr "p1" "p2" "p3" "p4" ...`
$ y2 : num 592 551 1720 5135 3710 ...
$ x1 : int 145 145 72 3173 3173 1262 1262 504 504 777 ...
$ no_per_site: num 104 55 187 102 ...
and the x2 matrix:
num [1:187, 1:31] 530 600 460 510 325 420 490 430 450 350 ...
Thank you!
The solution I fond is to use taylor expansions for the first moment of functions of random variables. The details can be found here: vignette_taylor_series