R: Standard Errors for Contrasts in Model Terms

se.contrast {stats} | R Documentation

## Standard Errors for Contrasts in Model Terms

### Description

Returns the standard errors for one or more contrasts in an `aov` object.

### Usage

    se.contrast(object, ...)
    ## S3 method for class 'aov'
    se.contrast(object, contrast.obj,
               coef = contr.helmert(ncol(contrast))[, 1],
               data = NULL, ...)

### Arguments

`object` | A suitable fit, usually from `aov`.
`contrast.obj` | The contrasts for which standard errors are requested. This can be specified via a list or via a matrix. A single contrast can be specified by a list of logical vectors giving the cells to be contrasted. Multiple contrasts should be specified by a matrix, each column of which is a numerical contrast vector (summing to zero).
`coef` | used when `contrast.obj` is a list; it should be a vector of the same length as the list with zero sum. The default value is the first Helmert contrast, which contrasts the first and second cell means specified by the list.
`data` | The data frame used to evaluate `contrast.obj`.
`...` | further arguments passed to or from other methods.

### Details

Contrasts are usually used to test if certain means are significantly different; it can be easier to use `se.contrast` than compute them directly from the coefficients.

In multistratum models, the contrasts can appear in more than one stratum, in which case the standard errors are computed in the lowest stratum and adjusted for efficiencies and comparisons between strata. (See the comments in the note in the help for `aov` about using orthogonal contrasts.) Such standard errors are often conservative.

Suitable matrices for use with `coef` can be found by calling `contrasts` and indexing the columns by a factor.

### Value

A vector giving the standard errors for each contrast.

### See Also

`contrasts`, `model.tables`

### Examples

    ## 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)
    ## Set suitable contrasts.
    options(contrasts = c("contr.helmert", "contr.poly"))
    npk.aov1 <- aov(yield ~ block + N + K, data = npk)
    se.contrast(npk.aov1, list(N == "0", N == "1"), data = npk)
    # or via a matrix
    cont <- matrix(c(-1,1), 2, 1, dimnames = list(NULL, "N"))
    se.contrast(npk.aov1, cont[N, , drop = FALSE]/12, data = npk)

    ## test a multi-stratum model
    npk.aov2 <- aov(yield ~ N + K + Error(block/(N + K)), data = npk)
    se.contrast(npk.aov2, list(N == "0", N == "1"))

    ## an example looking at an interaction contrast
    ## Dataset from R.E. Kirk (1995)
    ## 'Experimental Design: procedures for the behavioral sciences'
    score <- c(12, 8,10, 6, 8, 4,10,12, 8, 6,10,14, 9, 7, 9, 5,11,12,
                7,13, 9, 9, 5,11, 8, 7, 3, 8,12,10,13,14,19, 9,16,14)
    A <- gl(2, 18, labels = c("a1", "a2"))
    B <- rep(gl(3, 6, labels = c("b1", "b2", "b3")), 2)
    fit <- aov(score ~ A*B)
    cont <- c(1, -1)[A] * c(1, -1, 0)[B]
    sum(cont)       # 0
    sum(cont*score) # value of the contrast
    se.contrast(fit, as.matrix(cont))
    (t.stat <- sum(cont*score)/se.contrast(fit, as.matrix(cont)))
    summary(fit, split = list(B = 1:2), expand.split = TRUE)
    ## t.stat^2 is the F value on the A:B: C1 line (with Helmert contrasts)
    ## Now look at all three interaction contrasts
    cont <- c(1, -1)[A] * cbind(c(1, -1, 0), c(1, 0, -1), c(0, 1, -1))[B,]
    se.contrast(fit, cont)  # same, due to balance.
    rm(A, B, score)

    ## multi-stratum example where efficiencies play a role
    utils::example(eff.aovlist)
    fit <- aov(Yield ~ A + B * C + Error(Block), data = aovdat)
    cont1 <- c(-1, 1)[A]/32  # Helmert contrasts
    cont2 <- c(-1, 1)[B] * c(-1, 1)[C]/32
    cont <- cbind(A = cont1, BC = cont2)
    colSums(cont*Yield) # values of the contrasts
    se.contrast(fit, as.matrix(cont))
    # comparison with lme
    library(nlme)
    fit2 <- lme(Yield ~ A + B*C, random = ~1 | Block, data = aovdat)
    summary(fit2)$tTable # same estimates, similar (but smaller) se's.

[Package stats version 3.1.2 Index]