anova.zlm: ANOVA for Complex Linear Fits

Description

A very simple adaptation of stats::anova.lm which can handle fits of complex variables. The only change was to take the absolute value of squared residuals, and eliminate quantile based features. Note that this function uses the variance, not the pseudo-variance. An analysis of pseudo-variance (ANOPVA) is also possible (and maybe useful), but not yet implemented.

Usage

# S3 method for zlm
anova(object, ...)
# S3 method for zlmlist
anova(object, ..., scale = 0, test = "F")

Value

An object of class "anova", which inherits from class "data.frame". Contains a analysis of variance table, except for those components that rely on quantiles.

Arguments

object: objects of class "zlm", usually produced by lm.
...: Other arguments.
scale: numeric. An estimate of the noise variance \(\sigma^2\). If zero this will be estimated from the largest model considered.
test: a character string specifying the test statistic to be used. Can be one of "F", "Chisq" or "Cp", with partial matching allowed, or NULL for no test.

Functions

anova.zlmlist: s3 method for class 'zlmlist'

Details

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. If 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.

References

Chambers, J. M. (1992) Linear models. Chapter 4 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

Examples

Run this code

set.seed(4242)
n <- 8
slop <- complex(real = 4.23, imaginary = 2.323)
interc <- complex(real = 1.4, imaginary = 1.804)
err <- complex(real = rnorm(n)/16, imaginary = rnorm(n)/16)
tframe <- data.frame(x= x <- complex(real=rnorm(n), imaginary= rnorm(n)), y=slop*x + interc+err)
fit <- lm(y ~ x, data = tframe, weights = rep(1,n))
anova(fit)
robfit <- rlm(y ~ x, data = tframe)
anova(fit, robfit)

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