Analysis of Deviance for Generalized Linear Model Fits
Compute an analysis of deviance table for one or more generalized linear model fits.
"anova"(object, ..., dispersion = NULL, test = NULL)
- object, ...
- objects of class
glm, typically the result of a call to
glm, or a list of
- the dispersion parameter for the fitting family. By default it is obtained from the object(s).
- a character string, (partially) matching one of
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.,
quasipoisson fits) the F test is
most appropriate. Mallows' $Cp$ 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
"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 Chisquared-based estimate, the F tests are not based on
the residual deviance in the analysis of deviance table shown.
An object of class
"anova"inheriting from class
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,
anova will detect this with an error.
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.
so-called type II anova where each term is dropped one at a
time respecting their hierarchy.
## --- Continuing the Example from '?glm': anova(glm.D93) 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")