# [R] glmnet: converting coefficients back to original scale

Mark Seeto markseeto at gmail.com
Sat Apr 4 12:09:49 CEST 2015

```Thanks for your reply Mehmet. I've found that the problem was that I
didn't scale the lambda value. My original example did not follow the
instruction not to give a single lambda value, but that in itself
wasn't the problem. Example shown below.

library(glmnet)
library(MASS)

set.seed(1)
n <- 20

d <- data.frame(x1 = rnorm(n, 1, 1),
x2 = rnorm(n, 10, 2),
y = rnorm(n, 1, 2))

# Sample means
mx1 <- mean(d\$x1)
mx2 <- mean(d\$x2)
my <- mean(d\$y)

# Scaling factors
sx1 <- sd(d\$x1)*sqrt((n-1)/n)
sx2 <- sd(d\$x2)*sqrt((n-1)/n)
sy <- sd(d\$y)*sqrt((n-1)/n)

# Scaled variables
d\$x1s <- (d\$x1 - mx1)/sx1
d\$x2s <- (d\$x2 - mx2)/sx2
d\$ys <- (d\$y - my)/sy

# Centred y
d\$yc <- d\$y - my

lam <- 1  # lambda value for lm.ridge

lmr1 <- lm.ridge(y ~ x1 + x2, data=d, lambda=lam)
lmr2 <- lm.ridge(yc ~ x1s + x2s, data=d, lambda=lam)

coef(lmr1)

my - coef(lmr2)["x1s"]*mx1/sx1 - coef(lmr2)["x2s"]*mx2/sx2
# same as coef(lmr1)

coef(lmr2)["x1s"]/sx1  # same as coef(lmr1)["x1"]
coef(lmr2)["x2s"]/sx2  # same as coef(lmr1)["x2"]

glmnet1 <- glmnet(as.matrix(d[, c("x1", "x2")]), d[, "y"], alpha=0)
glmnet2 <- glmnet(as.matrix(d[, c("x1s", "x2s")]), d[, "ys"], alpha=0)

# Note: glmnet1\$lambda is glmnet2\$lambda*sy

ind <- 80  # index of lambda values to look at

coef(glmnet1)[, ind]

my - coef(glmnet2)["x1s", ind]*mx1*sy/sx1 -
coef(glmnet2)["x2s", ind]*mx2*sy/sx2
# same as coef(glmnet1)["(Intercept)", ind]

coef(glmnet2)["x1s", ind]*sy/sx1
# same as coef(glmnet1)["x1", ind]

coef(glmnet2)["x2s", ind]*sy/sx2
# same as coef(glmnet1)["x2", ind]

On Sat, Apr 4, 2015 at 6:03 AM, Suzen, Mehmet <mehmet.suzen at physics.org> wrote:
> This is interesting, can you post your lm.ridge solution as well?  I
> suspect in glmnet, you need to use model.matrix with intercept, that
> could be the reason.
>
> -m

```