AIC and BIC calculations for the brnn method Recently I got a recommendation from a reviewer of my article to calculate AIC (or BIC) for the brnn model. However, there is no straightforward way of doing that. Could anyone suggest how to do it?
alligator = data.frame(
  lnLength = c(3.87, 3.61, 4.33, 3.43, 3.81, 3.83, 3.46, 3.76,
               3.50, 3.58, 4.19, 3.78, 3.71, 3.73, 3.78),
  lnWeight = c(4.87, 3.93, 6.46, 3.33, 4.38, 4.70, 3.50, 4.50,
               3.58, 3.64, 5.90, 4.43, 4.38, 4.42, 4.25))

library(brnn)
model_brnn = brnn(lnWeight ~ lnLength, data = alligator)

 A: This is not a package I'm very familiar with, so I'll describe my thought process generally -
To calculate AIC, you need to specify a likelihood function - likelihood functions using sum-of-squares are pretty common, and the residuals sum-of-squares is included in the output as out$Ed (according to ?brnn). The also include "effective number of parameters" as out$gamma. If you used weights or other features, you should take those in to account.
In R, if you implement a logLik method for brnn,  AIC will use it automatically:
logLik.brnn <- function(object) structure(
  -(object$n / 2) * log(object$Ed),
  nobs = object$n,
  df = object$gamma,
  class = 'logLik'
)

Then you can compare two models using AIC, etc:
model_brnn2 = brnn(lnWeight ~ lnLength, data = alligator, neurons=2)
model_brnn4 = brnn(lnWeight ~ lnLength, data = alligator, neurons=4)

AIC(model_brnn2)
AIC(model_brnn4)

This is probably good enough for a random revise-and-resubmit, but could probably use some deeper thought - you could incorporate the coefficients in the likelihood, etc. 
Also be sure to set the RNG seed, I get slightly different results each run otherwise.
A: Typically, reviewers ask for AIC and BIC without caring whether or not it is meaningful. What I do in those situations is provide meaningful analysis as an answer to the reviewer's request without elaboration. For example,
Reviewer 1: Please provide AIC (BIC) to show model comparison.
Author response: Adjusted $R^2$ of the logarithms of the data were compared between methods. Significance testing showed blah blah blah...
