anova.gam {mgcv} | R Documentation |
Performs hypothesis tests relating to one or more fitted
gam
objects. For a single fitted gam
object, Wald tests of
the significance of each parametric and smooth term are performed. Otherwise
the fitted models are compared using an analysis of deviance table. The tests
are usually approximate, unless the models are un-penalized.
anova.gam(object, ..., dispersion = NULL, test = NULL) print.anova.gam(x,...)
object,... |
fitted model objects of class gam as produced by gam() . |
x |
an anova.gam object produced by a single model call to anova.gam() . |
dispersion |
a value for the dispersion parameter: not normally used. |
test |
what sort of test to perform for a multi-model call. One of
"Chisq" , "F" or "Cp" . |
If more than one fitted model is provided than anova.glm
is
used. If only one model is provided then the significance of each model term
is assessed using Wald tests: see summary.gam
for details of the
actual computations. In the latter case print.anova.gam
is used as the
printing method.
P-values are usually reliable if the smoothing parameters are known, or the model is unpenalized. If smoothing parameters have been estimated then the p-values are typically somewhat too low. i.e. terms that appear `not significant' really are not, while terms that are significant, may in fact be non-significant if the p-value is close to whatever significance level you are choosing to operate at. This occurs because the uncertainty associated with the smoothing parameters is neglected in the calculations of the distributions under the null, which tends to lead to underdispersion in these distributions, and in turn to p-value estimates that are too low. (In simulations where the null is correct, I have seen p-values that are as low as half of what they should be.)
In the multi-model case anova.gam
produces output identical to
anova.glm
, which it in fact uses.
In the single model case an object of class anova.gam
is produced,
which is in fact an object returned from summary.gam
.
print.anova.gam
simply produces tabulated output.
P-values may be under-estimates, as a result of ignoring smoothing parameter uncertainty.
Simon N. Wood simon.wood@r-project.org
gam
, predict.gam
,
gam.check
, summary.gam
library(mgcv) set.seed(0) n<-200 sig<-2 x0 <- rep(1:4,50) x1 <- runif(n, 0, 1) x2 <- runif(n, 0, 1) x3 <- runif(n, 0, 1) y <- 2 * x0 y <- y + exp(2 * x1) y <- y + 0.2 * x2^11 * (10 * (1 - x2))^6 + 10 * (10 * x2)^3 * (1 - x2)^10 e <- rnorm(n, 0, sig) y <- y + e x0<-as.factor(x0) b<-gam(y~x0+s(x1)+s(x2)+s(x3)) anova(b) b1<-gam(y~x0+s(x1)+s(x2)) anova(b,b1,test="F")