Find Aliases (Dependencies) in a Model

Usage

alias(object, ...)

Arguments

object A fitted model object, for example from lm or aov, or a formula for alias.formula.
data Optionally, a data frame to search for the objects in the formula.
complete Should information on complete aliasing be included?
partial Should information on partial aliasing be included?
partial.pattern Should partial aliasing be presented in a schematic way? If this is done, the results are presented in a more compact way, usually giving the deciles of the coefficients.

Description

Although the main method is for class "lm", alias is most useful for experimental designs and so is used with fits from aov. Complete aliasing refers to effects in linear models that cannot be estimated independently of the terms which occur earlier in the model and so have their coefficients omitted from the fit. Partial aliasing refers to effects that can be estimated less precisely because of correlations induced by the design.

Value

A list (of class "listof") containing components
Model Description of the model; usually the formula.
Complete A matrix with columns corresponding to effects that are linearly dependent on the rows; may be of class "mtable" which has its own print method.
Partial The correlations of the estimable effects, with a zero diagonal.

Note

The aliasing pattern may depend on the contrasts in use: Helmert contrasts are probably most useful.

The defaults are different from those in S.

Author(s)

B.D. Ripley

Examples

## From Venables and Ripley (1997) p.210.
N <- c(0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0)
P <- c(1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0)
K <- c(1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0)
yield <- c(49.5,62.8,46.8,57.0,59.8,58.5,55.5,56.0,62.8,55.8,69.5,55.0,
           62.0,48.8,45.5,44.2,52.0,51.5,49.8,48.8,57.2,59.0,53.2,56.0)
npk <- data.frame(block=gl(6,4), N=factor(N), P=factor(P),
                  K=factor(K), yield=yield)

## The next line is optional (for fractions package which gives neater
## results.)
has.VR <- require(MASS, quietly = TRUE)

op <- options(contrasts=c("contr.helmert", "contr.poly"))
npk.aov <- aov(yield ~ block + N*P*K, npk)
alias(npk.aov)
if(has.VR) detach(package:MASS)
options(op)# reset

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