random(x, df, sigma)
sigma
can be viewed as a shrinkage parameter.
x
is returned with class
"smooth"
, with an attribute named
"call"
which is to be evaluated in
all.wam()
by
gam()
This is an experimental
smootherfor use with factors in
gam()
. It allows the fitted mean for a factor predictor to be shrunk towards the overall mean, where the amount of shrinking depends either on
sigma
, or on the equivalent
df
. Similar in spirit to smoothing splines, this fitting method can be justified on Bayesian grounds or by a random effects model.
Since factors are coded by
model.matrix()
into a set of contrasts, care has been taken to add an appropriate
"contrast"
attribute to the output of
random()
.
This zero contrast results in a column of zeros in the model matrix, which is
aliased with any column and is hence ignored.
gam(y ~ random(f1) + random(f2, df = 3) + x) # fit a random effects model using gam()