anova.gam {mgcv} | R Documentation

## 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. The tests are usually approximate, unless the models are un-penalized.

### Usage

    anova.gam(object, ..., dispersion = NULL, test = NULL)
    print.anova.gam(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"`.
`digits` | number of digits to use when printing output.

### Details

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 under the null. 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.) Note however that tests can have low power if the estimated rank of the test statistic is much higher than the EDF, so that p-values can also be too low in some cases.

If it is important to have p-values that are as accurate as possible, then, at least in the single model case, it is probably advisable to perform tests using unpenalized smooths (i.e. `s(...,fx=TRUE)`) with the basis dimension, `k`, left at what would have been used with penalization. Such tests are not as powerful, of course, but the p-values are more accurate under the null. Whether or not extra accuracy is required will usually depend on whether or not hypothesis testing is a key objective of the analysis.

### 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

P-values are only approximate, particularly as a result of ignoring smoothing parameter uncertainty.

### Author(s)

Simon N. Wood simon.wood@r-project.org with substantial improvements by Henric Nilsson.

### See Also

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

### Examples

    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")

[Package mgcv version 1.3-17 Index]