I am wondering whether anyone could explain what'd be the difference between
running a 'generalized additive regression' versus 'generalized linear
regression' with splines.
The smooth terms in mgcv::gam are represented using *penalized*
regression splines, with the degree of penalization selected as part of
fitting. Using glm with ns the smooth terms are represented using
unpenalized regression splines with the smoothness controlled by how
many knots you chose (none in your example, so the ns terms were
actually straight lines).
best,
Simon
Are they same models theoretically? My apologies if this is a silly question.
Any comments or direction to references will be highly appreciated.
Thanks in advance,
Ehsan
#####################
set.seed(545)
require(mgcv)
n <- 200
x1 <- c(rnorm(n), 1+rnorm(n))
x2 <- sqrt(c(rnorm(n,4),rnorm(n,6)))
y <- c(rep(0,n), rep(1,n))
#####################
# GAM version
#####################
r1 <- gam(y~s(x1, bs = "cr")+s(x2, bs = "cr"),family=binomial)
pr1 <- predict(r1, type='response')
summary(pr1)
hist(pr1)
#####################
# GLM version
#####################
r2 <- glm(y~ns(x1)+ns(x2),family=binomial)
pr2 <- predict(r2, type='response')
summary(pr2)
hist(pr2)
#####################
# Results
#####################
summary(pr1)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000394 0.0550200 0.5027000 0.5000000 0.9322000 1.0000000
summary(pr2)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000403 0.0573300 0.5229000 0.5000000 0.9159000 0.9992000
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--
Simon Wood, Mathematical Science, University of Bath BA2 7AY UK
+44 (0)1225 386603 http://people.bath.ac.uk/sw283
______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
