anova.mlm {stats}R Documentation

Comparisons between multivariate linear models

Description

Compute gereralized analysis of variance table for a list of multivariate linear models. At least two models must be given.

Usage

## S3 method for class 'mlm'
anova.mlm(object, ...,
   test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy", " Spherical"),
   Sigma = diag(nrow = p),
   T = Thin.row(proj(M) - proj(X)), M = diag(nrow = p), X = ~0,
   idata = data.frame(index = seq(length = p)))

Arguments

object An object of class mlm
... Further objects of class mlm
test Choice of test statistic (se below)
Sigma (Only relevant if test=="Spherical"). Covariance matrix assumed proportional to Sigma
T Transformation matrix. By default computed from M and X
M Formula or matrix describing the outer projection (see below)
X Formula or matrix describing the inner projection (see below)
idata Data frame describing intra-block design

Details

The anova.mlm method uses either a multivariate test statistic for the summary table, or a test based on sphericity assumptions (i.e. that the covariance is proportional to a given matrix).

For the multivariate test, Wilks' statistic is most popular in the literature, but the default Pillai-Bartlett statistic is recommended by Hand and Taylor (1987).

For the "Spherical" test, proportionality is usually with the identity matrix but a different matrix can be specified using Sigma). Corrections for asphericity known as the Greenhouse-Geisser, respectively Huynh-Feldt, epsilons are given and adjusted F tests are performed.

It is common to transform the observations prior to testing. This typically involves transformation to intra-block differences, but more complicated within-block designs can be encountered, making more elaborate transformations necessary. A transformation matrix T can be given directly or specified as the difference between two projections onto the spaces spanned by M and X, which in turn can be given as matrices or as model formulas with respect to idata (the tests will be invariant to parametrization of the quotient space M/X).

Similar to anova.lm all test statistics use the SSD matrix from the largest model considered as the (generalized) denominator.

Value

An object of class "anova" inheriting from class "data.frame"

Note

The Huynh-Feldt epsilon differs from that calculated by SAS (as of v. 8.2) except when the DF is equal to the number of observations minus one. This is believed to be a bug in SAS, not in R.

References

Hand, D. J. and Taylor, C. C. (1987) Multivariate Analysis of Variance and Repeated Measures. Chapman and Hall.

See Also

summary.manova

Examples

example(SSD) # Brings in the mlmfit and reacttime objects

mlmfit0 <- update(mlmfit,~0)

### Traditional tests of intrasubj. contrasts
## Using MANOVA techniques on contrasts:
anova(mlmfit, mlmfit0, X=~1)

## Assuming sphericity
anova(mlmfit, mlmfit0, X=~1, test="Spherical") 

### tests using intra-subject 3x2 design
idata <- data.frame(deg=gl(3,1,6,labels=c(0,4,8)),
                    noise=gl(2,3,6,labels=c("A","P")))

anova(mlmfit, mlmfit0, X = ~ deg + noise, idata = idata, test = "Spherical")
anova(mlmfit, mlmfit0, M = ~ deg + noise, X = ~ noise, idata = idata,
          test="Spherical" )
anova(mlmfit, mlmfit0, M = ~ deg + noise, X = ~ deg, idata = idata,
          test="Spherical" )

### There seems to be a strong interaction in these data
plot(colMeans(reacttime))

[Package stats version 2.1.0 Index]