Aggregated logistic lasso regression in glmnet

Question

In glm() it is possible to model bernoulli [0,1] outcomes with a logistic regression using the following sort of syntax.

glm(bin ~ x, df, family = "binomial")

However you can also perform aggregated binomial regression, where each observation represents a count of target events from a certain fixed number of bernoulli trials. For example see the following data:

set.seed(1)
n <- 50
cov <- 10
x <- c(rep(0,n/2), rep(1, n/2))
p <- 0.4 + 0.2*x
y <- rbinom(n, cov, p)

With these sort of data you use slightly different syntax in glm()

mod <- glm(cbind(y, cov-y) ~ x, family="binomial")
mod

# output

# Call:  glm(formula = cbind(y, cov - y) ~ x, family = "binomial")
# 
# Coefficients:
#   (Intercept)            x  
# -0.3064       0.6786  
# 
# Degrees of Freedom: 49 Total (i.e. Null);  48 Residual
# Null Deviance:        53.72 
# Residual Deviance: 39.54  AIC: 178

I was wondering is it possible to model this type of aggregated binomial data in the glmnet package? If so, what is the syntax?

smiling4ever smiling4ever · Accepted Answer · 2020-07-16T20:30:27

Yes you can do it as the following

set.seed(1)
n <- 50
cov <- 10
x <- c(rep(0,n/2), rep(1, n/2))
x = cbind(x, xx = c(rep(0.5,20), rep(0.7, 20), rep(1,10)))
p <- 0.4 + 0.2*x
y <- rbinom(n, cov, p)

I added another covariate here called xx as glmnet accepts minimum of two covariates

In glm as you have it in your post

mod <- glm(cbind(y, cov-y) ~ x, family="binomial")
mod

# output
# Call:  glm(formula = cbind(y, cov - y) ~ x, family = "binomial")

# Coefficients:
# (Intercept)           xx          xxx  
# 0.04366      0.86126     -0.64862  

# Degrees of Freedom: 49 Total (i.e. Null);  47 Residual
# Null Deviance:        53.72 
# Residual Deviance: 38.82  AIC: 179.3

In glmnet, without regularization (lambda=0) to reproduce similar results as in glm

library(glmnet)
fit = glmnet(x, cbind(cov-y,y), family="binomial", lambda=0)
coef(fit)
# output
# 3 x 1 sparse Matrix of class "dgCMatrix"
#                     s0
# (Intercept)  0.04352689
# x            0.86111234
# xx          -0.64831806

Aggregated logistic lasso regression in glmnet

1 Answers