gam.random  R Documentation 
A symbolic wrapper for a factor term, to specify a random effect term in a formula argument to gam
gam.random(f, y, w, df = sum(non.zero), lambda = 0, intercept = TRUE, xeval)
random(f, df = NULL, lambda = 0, intercept = TRUE)
f 
factor variable, or expression that evaluates to a factor. 
y 
a response variable passed to 
w 
weights 
df 
the target equivalent degrees of freedom, used as a smoothing
parameter. The real smoothing parameter ( 
lambda 
the nonnegative penalty parameter. This is interpreted as a variance ratio in a mixed effects model  namely the ratio of the noise variance to the randomeffect variance. 
intercept 
if 
xeval 
If this argument is present, then 
This "smoother" takes a factor as input and returns a shrunkenmean 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 mixedeffect
model by generalized least squares.
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
residuals 
The residuals from the smooth fit. 
nl.df 
the degrees of freedom 
var 
the pointwise variance for the fit 
lambda 
the value of

When gam.random
is evaluated with an
xeval
argument, it returns a vector of predictions.
Written by Trevor Hastie, following closely the design in the "Generalized Additive Models" chapter (Hastie, 1992) in Chambers and Hastie (1992).
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) Degreesoffreedom tests for smoothing splines, Biometrika 89(2), 251263
lo
, s
, bs
,
ns
, poly
# 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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