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))