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)
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
When gam.random is evaluated with an
xeval argument, it returns a vector of predictions.
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.
Written by Trevor Hastie, following closely the design in the "Generalized Additive Models" chapter (Hastie, 1992) in Chambers and Hastie (1992).
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
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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