msos (version 1.2.0)

bothsidesmodel.hotelling: 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

# NOT RUN {
# 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)
# }