Output of cv.glm vs. cv.glmnet - r

Question

I'm trying to do cross validation for a dataset that I want to fit a Poisson model to. I notice, however, that I get very different outputs from the functions cv.glm and cv.glmnet when I use lambda = 0. Below is my code for the basic Poisson model (the first part is setup of the data set):
game_soon <- function(game_type, hour){
ret_vec <- c()
len_game_type <- length(game_type)
for(i in 1:len_game_type){
if(game_type[i] == 'N' && hour[i] >= 16){
ret_vec <- c(ret_vec, 1)
}
else if(game_type[i] == 'D' && hour[i] >= 10 && hour[i] <= 17){
ret_vec <- c(ret_vec, 1)
}
else{
ret_vec <- c(ret_vec, 0)
}
}
return(ret_vec)
}
wrigley_agg <- read.csv("/Users/eweine/Desktop/myDivvy/export/EWEINE/WR/WRIGLEY_DIVVY/data", header=FALSE)
colnames(wrigley_agg) <- c("Checkouts", "Temp", "Humidity", "Rain_Intensity",
"Rain_Total", "Hour", "DOY", "Weekday", "Cubs_Game")
game_vec <- wrigley_agg$Cubs_Game
hour_vec <- wrigley_agg$Hour
new_column <- game_soon(game_vec, hour_vec)
wrigley_agg$Game_Soon <- new_column
require(glm)
require(boot)
basic_poisson <- glm(Checkouts ~ Weekday + Game_Soon + poly(Hour, 6) +
poly(Temp, 4) + poly(Rain_Intensity, 4), data=wrigley_agg, family=poisson)
cv_possion <- cv.glm(wrigley_agg, basic_poisson, K=10)
print(cv_possion)
My output is:
[1] 958.9232 958.5509
Below is my code for the cv.glmnet model:
x_pois <- model.matrix(Checkouts ~ Weekday + Game_Soon + poly(Hour, 6) + poly(Temp, 4) +
poly(Rain_Intensity, 4), data=wrigley_agg)
y_pois <- wrigley_agg$Checkouts
cv_lasso_pois <- cv.glmnet(x_pois, y_pois, family="poisson", alpha=1, lambda=seq(1, 0, -1))
no_penalty_cv <- cv_lasso_pois$cvm[cv_lasso_pois$lambda == 0]
print(no_penalty_cv)
And my output is:
[1] 13.41691
The data can be found here.
Why are these values so different?

Answer 1

This is an interesting question.
The difference between the mean cross-validated errors given by cv.glm and cv.glmnet (with lambda=0) is due to the different cost functions used by the two commands.
For poisson models, cv.glm uses by default the average squared error while cv.glmnet uses deviance.
Below I define a function devi that calculates deviance as required by cv.glm:
library(glmnet)
library(boot)
basic_poisson <- glm(Checkouts ~ Weekday + Game_Soon + poly(Hour, 6) +
poly(Temp, 4) + poly(Rain_Intensity, 4), data = wrigley_agg, family =
poisson)
devi <- function(y, eta) {
deveta = y * log(eta) - eta
devy = y * log(y) - y
devy[y == 0] = 0
mean(2 * (devy - deveta))
}
set.seed(1)
cv_poisson <- cv.glm(data=wrigley_agg, glmfit=basic_poisson, cost=devi, K = 10)
print(cv_poisson$delta)
The estimated (raw and adjusted) mean cross-validated errors now are:
[1] 13.42184 13.41605
They are very close to the error given by cv.glmnet.