mgcv (version 1.7-17)

anova.gam: Approximate hypothesis tests related to GAM fits

Description

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: this latter approach should not be use to test the significance of terms which can be penalized to zero. See details.

Usage

## S3 method for class 'gam':
anova(object, ..., dispersion = NULL, test = NULL,
                    freq = TRUE,p.type=0)
## S3 method for class 'anova.gam':
print(x, digits = max(3, getOption("digits") - 3),...)

Arguments

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".

freq

whether to use frequentist or Bayesian approximations for parametric term p-values. See summary.gam for details.

p.type

selects exact test statistic to use for single smooth term p-values. See summary.gam for details.

digits

number of digits to use when printing output.

Value

• 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.

WARNING

If models 'a' and 'b' differ only in terms with no un-penalized components then p values from anova(a,b) are unreliable, and usually much too low.

Details

If more than one fitted model is provided than anova.glm is used, with the difference in model degrees of freedom being taken as the difference in effective degress of freedom. The p-values resulting from this are only approximate, and must be used with care. The approximation is most accurate when the comparison relates to unpenalized terms, or smoothers with a null space of dimension greater than zero. (Basically we require that the difference terms could be well approximated by unpenalized terms with degrees of freedom approximately the effective degrees of freedom). In simualtions the p-values are usually slightly to low. For terms with a zero-dimensional null space (i.e. those which can be penalized to zero) the approximation is often very poor, and significance can be greatly overstated: i.e. p-values are often substantially too low. This case applies to random effect terms.

Note also that in the multi-model call to anova.gam, it is quite possible for a model with more terms to end up with lower effective degrees of freedom, but better fit, than the notionally null model with fewer terms. In such cases it is very rare that it makes sense to perform any sort of test, since there is then no basis on which to accept the notional null model.

If only one model is provided then the significance of each model term is assessed using Wald tests: see summary.gam for details. The p-values provided here are better justified than in the multi model case, and have close to the correct distribution under the null for smooths with a non-zero dimensional null space (i.e. terms that can-not be penalized to zero). ML or REML smoothing parameter selection leads to the best results in simulations as they tend to avoid occasional severe undersmoothing. In the single model case print.anova.gam is used as the printing method.

See Also

gam, predict.gam, gam.check, summary.gam

Examples

library(mgcv)
set.seed(0)
dat <- gamSim(5,n=200,scale=2)

b<-gam(y ~ x0 + s(x1) + s(x2) + s(x3),data=dat)
anova(b)
b1<-gam(y ~ x0 + s(x1) + s(x2),data=dat)
anova(b,b1,test="F")