Test blocks of \(\beta\) are zero.

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

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)

Wilks

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

. .

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)
#> $Hotelling
#> $Hotelling$T2
#> [1] 2.903177
#> 
#> $Hotelling$F
#> [1] 0.6967626
#> 
#> $Hotelling$df
#> [1]  4 24
#> 
#> $Hotelling$pvalue
#> [1] 0.6016391
#> 
#> 
#> $Wilks
#> $Wilks$Lambda
#> [1] 0.8959089
#> 
#> $Wilks$Chisq
#> [1] 2.692955
#> 
#> $Wilks$df
#> [1] 4
#> 
#> $Wilks$pvalue
#> [1] 0.610448
#> 
#>