R: Getting AIC/BIC/Likelihood from GLMNet

5
votes

I'm wondering if I can get AIC and BIC from GLMNet. I've found glmnet.cr that seems to be able to do it but my response is time, not ordinal. I could calculate it myself from likelihood but glmnet doesn't return that either.

Tangential: can I actually return the l1norm? I feel like it should just be 

fit$norm

but it doesn't seem to be. (I know it says don't pull the numbers out but I'm actually not using the R)

Thanks in advance for the help.

3
rstatisticsglmnet
The short answer is no but there might be a way around it depending what you're trying to do. I presume you are using the glmnet R package, but we need to know more about your model. For example, does it have a Gaussian response? There are some answers on Cross-Validated that might help. - Peter Ellis

3 Answers

4
votes

I was struggling a lot with a way how to calculate AIC and BIC for glmnet models. However, after quite a lot of searching, I found on the third page of google results the answer. It can be found here. I am posting it here for future readers as I believe I cannot be the only one.

In the end, I implemented the AIC and BIC in the following way:

fit <- glmnet(x, y, family = "multinomial") 

tLL <- fit$nulldev - deviance(fit)
k <- fit$df
n <- fit$nobs
AICc <- -tLL+2*k+2*k*(k+1)/(n-k-1)
AICc

BIC<-log(n)*k - tLL
BIC
1
votes

Based on @merten's answer, I fixed the formula. Now it matches the built-in function.

Summary,

  1. the original log-likelihood (tLL) was bias.
  2. AIC and AICc from the built-in functions were added for comparison.
BICAICglm=function(fit){
  #tLL <- fit$null.deviance - deviance(fit)  
  tLL <- -deviance(fit) # 2*log-likelihood
  k <- dim(model.matrix(fit))[2]
  n <- nobs(fit)
  AICc <- -tLL+2*k+2*k*(k+1)/(n-k-1)
  AIC_ <- -tLL+2*k

  BIC<-log(n)*k - tLL
  res=c(AIC_, BIC, AICc)
  names(res)=c("AIC", "BIC", "AICc")
  return(res)
}
#some data simulation to test
set.seed(123)
x=rnorm(20)
set.seed(231)
y=as.numeric(x+rnorm(20)<0)

#the model
glm1=glm(y~x, family="binomial")

Results

BICAICglm(glm1)
     AIC      BIC     AICc 
21.91018 23.90165 22.61607

Answers according to built-in functions

AIC(glm1)
[1] 21.91018
BIC(glm1)
[1] 23.90165

AICc correction for small sample sizes

AIC(glm1, k=2*nobs(glm1)/(nobs(glm1)-1-glm1$rank))
[1] 22.61607
0
votes

Unfortunatly I cannot reproduce the BIC using this formula for from a "normal" glm model (for which the built-in function BIC works as a correct reference)

I changed the code proposed above to make it work with a glm object:

    #BIC function for glm according to stackoverflow
    BICAICglm=function(fit){
      tLL <- fit$null.deviance - deviance(fit)
      k <- dim(model.matrix(fit))[2]
      n <- nobs(fit)
      AICc <- -tLL+2*k+2*k*(k+1)/(n-k-1)
      AICc

      BIC<-log(n)*k - tLL
      res=c(AICc, BIC)
      names(res)=c("AICc", "BIC")
      return(res)
    }

    #some data simulation to test
    set.seed(123)
    x=rnorm(20)
    set.seed(231)
    y=as.numeric(x+rnorm(20)<0)

    #the model
    glm1=glm(y~x, family="binomial")

now when we apply the standard BIC() function we get the "true" BIC of the model, that we then can compare with the function proposed here.

    BIC(glm1)
    [1] 23.68755

and the new one:

    BICAICglm(glm1)
    AICc       BIC 
    -4.518496 -3.232914

So the way of calculating BIC and AICc this way is not quite right.