mauchly.test {stats} | R Documentation |
Tests whether a Wishart-distributed covariance matrix (or transformation thereof) is proportional to a given matrix.
mauchly.test(object, 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 |
object of class SSD or mlm . |
Sigma |
matrix to be proportional to. |
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. |
... |
arguments to be passed to or from other methods. |
Mauchly's test test for whether a covariance matrix can be assumed to be proportional to a given matrix.
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
).
The common use of this test is in repeated measurements designs, with
X=~1
. This is almost, but not quite the same as testing for
compund symmetry in the untransformed covariance matrix.
This is a generic function with methods for classes "mlm"
and
"SSD"
.
An object of class "htest"
The p-value differs slightly from that of SAS because a second order term is included in the asymptotic approximation in R.
T. W. Anderson (1958). An Introduction to Multivariate Statistical Analysis. Wiley.
example(SSD) # Brings in the mlmfit and reacttime objects ### traditional test of intrasubj. contrasts mauchly.test(mlmfit, X=~1) ### 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"))) mauchly.test(mlmfit, X = ~ deg + noise, idata = idata) mauchly.test(mlmfit, M = ~ deg + noise, X = ~ noise, idata=idata)