| anova.mlm {stats} | R Documentation |
Compute gereralized analysis of variance table for a list of multivariate linear models. At least two models must be given.
## 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)))
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 |
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.
An object of class "anova" inheriting from class "data.frame"
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.
Hand, D. J. and Taylor, C. C. (1987) Multivariate Analysis of Variance and Repeated Measures. Chapman and Hall.
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))