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How do I compare cv.glmnet models with AIC?

Cross Validated Asked by Thomas on August 20, 2020

I am using the glmnet package in R, and not(!) the caret package for my binary ElasticNet regression. I have come to the point where I would like to compare models (e.g. lambda set to lambda.1se or lambda.min, and models where k-fold is set to 5 or 10). But, I have not yet achieved to compute the AICc or BIC for my models. How do I do that? I tried this and this but it did not work for me, I only get an empty list.
Code:

set.seed(123)
foldid <- sample(rep(seq(10), length.out = nrow(x.train)))
list.of.fits.df <- list()
for (i in 0:10){
     fit.name <- paste0("alpha", i/10) 
     list.of.fits.df[[fit.name]] <- cv.glmnet(x.train, y.train, type.measure = c("auc"), alpha = i/10, family = "binomial", nfolds = 10, foldid = foldid, parallel = TRUE)
 }
best.fit <- coef(list.of.fits.df[[fit.name]], s = list.of.fits.df[[fit.name]]$lambda.1se)
best.fit.min <- coef(list.of.fits.df[[fit.name]], s = list.of.fits.df[[fit.name]]$lambda.min)

#AICc & BIC
#???

How do I find an AIC and/or BIC value from my list.of.fits[[fit.name]]$lambda.min?

One Answer

Create a function

cv_aicc <- function(fit, lambda = 'lambda.1se'){
  whlm <- which(fit$lambda == fit[[lambda]])
  with(fit$glmnet.fit,
       {
         tLL <- nulldev - nulldev * (1 - dev.ratio)[whlm]
         k <- df[whlm]
         n <- nobs
         return(list('AICc' = - tLL + 2 * k + 2 * k * (k + 1) / (n - k - 1),
                     'BIC' = log(n) * k - tLL))
       })
}

Plug in the lists now.

AICc <- cv_aicc(list.of.fits.df[[fit.name]])
AICc.min <- cv_aicc(list.of.fits.df[[fit.name]], 'lambda.min')

Correct answer by Thomas on August 20, 2020

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