bothsidesmodel.hotelling {msos}

Test blocks of \beta are zero.

Description

Performs tests of the null hypothesis H0 : \beta^* = 0, where \beta^* is a block submatrix of \beta as in Section 7.2.

Usage

bothsidesmodel.hotelling(x, y, z, rows, cols)

Arguments

x

An N \times P design matrix.

y

The N \times Q matrix of observations.

z

A Q \times L design matrix

rows

The vector of rows to be tested.

cols

The vector of columns to be tested.

Value

A list with the following components:

Hotelling

A list with the components of the Lawley-Hotelling T^2 test (7.22)

T2

The T^2 statistic (7.19).

F

The F version (7.22) of the T^2 statistic.

df

The degrees of freedom for the F.

pvalue

The p-value of the F.

Wilks

A list with the components of the Wilks \Lambda test (7.37)

lambda

The \Lambda statistic (7.35).

Chisq

The \chi ^2 version (7.37) of the \Lambda statistic, using Bartlett's correction.

df

The degrees of freedom for the \chi ^2

.

pvalue

The p-value of the \chi ^2

.

See Also

bothsidesmodel, bothsidesmodel.chisquare, bothsidesmodel.df, bothsidesmodel.lrt, and bothsidesmodel.mle.

Examples

# Finds the Hotelling values for example 7.3.1
data(mouths)
x <- cbind(1, mouths[, 5])
y <- mouths[, 1:4]
z <- cbind(c(1, 1, 1, 1), c(-3, -1, 1, 3), c(1, -1, -1, 1), c(-1, 3, -3, 1))
bothsidesmodel.hotelling(x, y, z, 1:2, 3:4)