How can one specify link functions in glmnet for lasso / ridge / elastic net regression?
I have found the following post but not sure this helps me when I need to specify a cloglog link.
How to specify log link in glmnet?
I have a survey data set with binary response 0/1 (disease no/yes) and several predictor variables, which are mostly binary categorical (yes/no, male/female), some are counts (herd size), and a few are categorical with several levels.
I previously ran a generalized linear mixed model using glmer() function with binomial family and link = cloglog as doing so created the exact interpretation of the resulting intercept that I wanted (in disease study the intercept from this setup is equivalent to the mean value 'force of infection' - the rate at which susceptibles become infected - among the variation specified in the random effect (in my case the geographic unit (village or subvillage or household).
As there are several survey variables now available to me, I wanted to try a lasso and a ridge regression using glmnet. It is my understanding that I should best do this by putting in the glmm formula into the glmnet. However, I cannot find any documentation about how to add a link. I did so, in the syntax I thought would work, and it did run. But it also ran with nonsense entered in the link function.
Here is a reproducible example:
library(msm)
library(glmnet)
set.seed(1)
N = 1000
X = cbind( rbinom(n=N,size=1,prob=0.5), rnorm(n=N) )
beta = c(-0.1,0.1)
phi.true = exp( X%*%beta )
p = 1 - exp(-phi.true)
y = rbinom(n=N,size=1,prob = p)
dat <- data.frame(x=X,y=y)
x <- model.matrix(y~., dat)
glmnet(x, y, family="binomial", link="logit", alpha = 1, lambda = 2)
I get the same output whether I put in 'logit', 'cloglog' or even a name 'adam'. And cannot use same syntax as GLMM as in glmnet must be a character vector.
OUTPUT:
> glmnet(x, y, family="binomial"(link="logit"), alpha = 1, lambda = 2)
Error in match.arg(family) : 'arg' must be NULL or a character vector
> glmnet(x, y, family="binomial", link="logit", alpha = 1, lambda = 2)
Call: glmnet(x = x, y = y, family = "binomial", alpha = 1, lambda = 2, link = "logit")
Df %Dev Lambda
1 0 -7.12e-15 2
> glmnet(x, y, family="binomial", link="cloglog", alpha = 1, lambda = 2)
Call: glmnet(x = x, y = y, family = "binomial", alpha = 1, lambda = 2, link = "cloglog")
Df %Dev Lambda
1 0 -7.12e-15 2
> glmnet(x, y, family="binomial", link="adam", alpha = 1, lambda = 2)
Call: glmnet(x = x, y = y, family = "binomial", alpha = 1, lambda = 2, link = "adam")
Df %Dev Lambda
1 0 -7.12e-15 2
Is it not possible to change the default link function for binomial family in glmnet?
