alias {stats} | R Documentation

## Find Aliases (Dependencies) in a Model

### Description

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

### Usage

    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.

### 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)

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

    had.VR <- "package:MASS" %in% search()
    ## The next line is for fractions() which gives neater results
    if(!had.VR) res <- require(MASS)
    ## From Venables and Ripley (2002) p.165.
    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)

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

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