anova.glm {stats}

Analysis of Deviance for Generalized Linear Model Fits

Description

Compute an analysis of deviance table for one or more generalized linear model fits.

Usage

## S3 method for class 'glm'
anova(object, ..., dispersion = NULL, test = NULL)

Arguments

object, ...

objects of class glm, typically the result of a call to glm, or a list of objects for the "glmlist" method.

dispersion

the dispersion parameter for the fitting family. By default it is obtained from the object(s).

test

a character string, (partially) matching one of "Chisq", "LRT", "Rao", "F" or "Cp". See stat.anova. Or logical FALSE, which suppresses any test.

Details

Specifying a single object gives a sequential analysis of deviance table for that fit. That is, the reductions in the residual deviance as each term of the formula is added in turn are given in as the rows of a table, plus the residual deviances themselves.

If more than one object is specified, the table has a row for the residual degrees of freedom and deviance for each model. For all but the first model, the change in degrees of freedom and deviance is also given. (This only makes statistical sense if the models are nested.) It is conventional to list the models from smallest to largest, but this is up to the user.

The table will optionally contain test statistics (and P values) comparing the reduction in deviance for the row to the residuals. For models with known dispersion (e.g., binomial and Poisson fits) the chi-squared test is most appropriate, and for those with dispersion estimated by moments (e.g., gaussian, quasibinomial and quasipoisson fits) the F test is most appropriate. If anova.glm can determine which of these cases applies then by default it will use one of the above tests. If the dispersion argument is supplied, the dispersion is considered known and the chi-squared test will be used. Argument test=FALSE suppresses the test statistics and P values. Mallows' C_p statistic is the residual deviance plus twice the estimate of \sigma^2 times the residual degrees of freedom, which is closely related to AIC (and a multiple of it if the dispersion is known). You can also choose "LRT" and "Rao" for likelihood ratio tests and Rao's efficient score test. The former is synonymous with "Chisq" (although both have an asymptotic chi-square distribution).

The dispersion estimate will be taken from the largest model, using the value returned by summary.glm. As this will in most cases use a Chi-squared-based estimate, the F tests are not based on the residual deviance in the analysis of deviance table shown.

Value

An object of class "anova" inheriting from class "data.frame".

Warning

The comparison between two or more models will only be valid if they are fitted to the same dataset. This may be a problem if there are missing values and R's default of na.action = na.omit is used, and anova will detect this with an error.

References

Hastie, T. J. and Pregibon, D. (1992) Generalized linear models. Chapter 6 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

See Also

glm, anova.

drop1 for so-called ‘type II’ ANOVA where each term is dropped one at a time respecting their hierarchy.

Examples

## --- Continuing the Example from  '?glm':

anova(glm.D93, test = FALSE)
anova(glm.D93, test = "Cp")
anova(glm.D93, test = "Chisq")
glm.D93a <-
   update(glm.D93, ~treatment*outcome) # equivalent to Pearson Chi-square
anova(glm.D93, glm.D93a, test = "Rao")