Find Aliases (Dependencies) in a Model

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Description

Find aliases (linearly dependent terms) in a linear model specified by a formula.

Usage

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alias(object, ...)

## S3 method for class 'formula'
alias(object, data, ...)

## S3 method for class 'lm'
alias(object, complete = TRUE, partial = FALSE,
      partial.pattern = FALSE, ...)

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.

...

further arguments passed to or from other methods.

Details

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.

Some parts of the "lm" method require recommended package MASS to be installed.

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.

Partial

The correlations of the estimable effects, with a zero diagonal. An object of class "mtable" which has its own print method.

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)

The design was inspired by the S function of the same name described in Chambers et al (1992).

References

Chambers, J. M., Freeny, A and Heiberger, R. M. (1992) Analysis of variance; designed experiments. Chapter 5 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

Examples

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

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