Specify a Random Effects Fit in a GAM Formula
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)
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 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. |
intercept |
if |
xeval |
If this argument is present, then |
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.
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) Degrees-of-freedom tests for smoothing splines, Biometrika 89(2), 251-263
# 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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