ANOVA for Linear Model Fits
Compute an analysis of variance table for one or more linear model fits.
# S3 method for lm anova(object, …)
# S3 method for lmlist anova(object, …, scale = 0, test = "F")
- object, …
objects of class
lm, usually, a result of a call to
a character string specifying the test statistic to be used. Can be one of
"Cp", with partial matching allowed, or
NULLfor no test.
numeric. An estimate of the noise variance \(\sigma^2\). If zero this will be estimated from the largest model considered.
Specifying a single object gives a sequential analysis of variance table for that fit. That is, the reductions in the residual sum of squares as each term of the formula is added in turn are given in as the rows of a table, plus the residual sum of squares.
The table will contain F statistics (and P values) comparing the mean square for the row to the residual mean square.
If more than one object is specified, the table has a row for the residual degrees of freedom and sum of squares for each model. For all but the first model, the change in degrees of freedom and sum of squares is also given. (This only make 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.
Optionally the table can include test statistics. Normally the
F statistic is most appropriate, which compares the mean square for a
row to the residual sum of squares for the largest model considered.
scale is specified chi-squared tests can be used. Mallows'
\(C_p\) statistic is the residual sum of squares plus twice the
estimate of \(\sigma^2\) times the residual degrees of freedom.
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.lmlist will detect this with an error.
Chambers, J. M. (1992) Linear models. Chapter 4 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.
## sequential table fit <- lm(sr ~ ., data = LifeCycleSavings) anova(fit) ## same effect via separate models fit0 <- lm(sr ~ 1, data = LifeCycleSavings) fit1 <- update(fit0, . ~ . + pop15) fit2 <- update(fit1, . ~ . + pop75) fit3 <- update(fit2, . ~ . + dpi) fit4 <- update(fit3, . ~ . + ddpi) anova(fit0, fit1, fit2, fit3, fit4, test = "F") anova(fit4, fit2, fit0, test = "F") # unconventional order