R: Contrast Matrices

contrast {base} | R Documentation

## Contrast Matrices

### Description

Return a matrix of contrasts.

### Usage

    contr.helmert(n, contrasts = TRUE)
    contr.poly(n, contrasts = TRUE)
    contr.sum(n, contrasts = TRUE)
    contr.treatment(n, base = 1, contrasts = TRUE)

### Arguments

`n` | a vector of levels for a factor, or the number of levels.
`contrasts` | a logical indicating whether contrasts should be computed.
`base` | an integer specifying which group is considered the baseline group. Ignored if `contrasts` is `FALSE`.

### Details

These functions are used for creating contrast matrices for use in fitting analysis of variance and regression models. The columns of the resulting matrices contain contrasts which can be used for coding a factor with `n` levels. The returned value contains the computed contrasts. If the argument `contrasts` is `FALSE` then a square indicator matrix is returned.

Note that as from R version 0.62.2, `contr.poly` returns contrasts based on orthogonal (rather than raw) polynomials.

### Value

A matrix with `n` rows and `k` columns, with `k=n-1` if `contrasts` is `TRUE` and `k=n` if `contrasts` is `FALSE`.

### See Also

`contrasts`, `C`, and `aov`, `glm`, `lm`.

### Examples

    (cH <- contr.helmert(4))
    apply(cH, 2,sum) # column sums are 0!
    crossprod(cH) # diagonal -- columns are orthogonal
    contr.helmert(4, contrasts = FALSE) # just the 4 x 4 identity matrix

    (cT <- contr.treatment(5))
    all(crossprod(cT) == diag(4)) # TRUE: even orthonormal

    (cP <- contr.poly(3)) # Linear and Quadratic
    zapsmall(crossprod(cP), dig=15) # orthonormal up to fuzz

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