A symbolic wrapper for a factor term, to specify a random effect term in a formula argument to gam
random(f, df = NULL, lambda = 0, intercept = TRUE)
gam.random(f, y, w, df = sum(non.zero), lambda = 0, intercept=TRUE, xeval)
factor variable, or expression that evaluates to a factor.
a response variable passed to gam.random
during backfitting
weights
the target equivalent degrees of freedom, used as a smoothing
parameter. The real smoothing parameter (lambda
below) is found
such that df=tr(S)
, where S
is the implicit smoother
matrix. Values for df
should be greater than 0
and less
than the number of levels of f
. If both df
and lambda
are
supplied, the latter takes precedence. Note that df
is not
necessarily an integer.
the non-negative penalty parameter. This is interpreted as a variance ratio in a mixed effects model - namely the ratio of the noise variance to the random-effect variance.
if intercept=TRUE
(the default) then the estimated level effects
are centered to average zero, otherwise they are left alone.
If this argument is present, then gam.random
produces a
prediction at xeval
.
random
returns the vector f
, endowed with a number of
attributes. The vector itself is used in computing the means in backfitting,
while the attributes are needed for the backfitting algorithms
general.wam
.
Note that random
itself does no smoothing; it simply sets things up
for gam
.
One important attribute is named call
. For example,
random(f, lambda=2)
has a call component
gam.random(data[["random(f, lambda = 2)"]], z, w, df = NULL, lambda = 2, intercept = TRUE)
.
This is an expression that gets evaluated repeatedly in general.wam
(the backfitting algorithm).
gam.random
returns an object with components
The residuals from the smooth fit.
the degrees of freedom
the pointwise variance for the fit
the value of lambda
used in the fit
This "smoother" takes a factor as input and returns a shrunken-mean fit.
If lambda=0
, it simply computes the mean of the response at
each level of f
. With lambda>0
, it returns a shrunken
mean, where the j'th level is shrunk by nj/(nj+lambda)
, with
nj
being the number of observations (or sum of their weights)
at level j
. Using such smoother(s) in gam is formally
equivalent to fitting a mixed-effect model by generalized least squares.
Hastie, T. J. (1992) Generalized additive models. Chapter 7 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth \& Brooks/Cole.
Hastie, T. and Tibshirani, R. (1990) Generalized Additive Models. London: Chapman and Hall.
Cantoni, E. and hastie, T. (2002) Degrees-of-freedom tests for smoothing splines, Biometrika 89(2), 251-263
# NOT RUN {
# fit a model with a linear term in Age and a random effect in the factor Level
y ~ Age + random(Level, lambda=1)
# }
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