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

Tests the null hypothesis that an arbitrary subset of the \(\beta _{ij}\)'s is zero, using the likelihood ratio test as in Section 9.4. The null and alternative are specified by pattern matrices \(P_0\) and \(P_A\), respectively. If the \(P_A\) is omitted, then the alternative will be taken to be the unrestricted model.

bothsidesmodel.lrt(
  x,
  y,
  z,
  pattern0,
  patternA = matrix(1, nrow = ncol(x), ncol = ncol(z))
)

Arguments

x

An \(N \times P\) design matrix.

y

The \(N \times Q\) matrix of observations.

z

A \(Q \times L\) design matrix.

pattern0

An \(N \times P\) matrix of 0's and 1's specifying

patternA

An optional \(N \times P\) matrix of 0's and 1's specifying the alternative hypothesis.

Value

A list with the following components:

chisq

The likelihood ratio statistic in (9.44).

df

The degrees of freedom in the test.

pvalue

The \(p\)-value for the test.

See also

bothsidesmodel.chisquare, bothsidesmodel.df, bothsidesmodel.hotelling, bothsidesmodel, and bothsidesmodel.mle.

Examples

# Load data
data(caffeine)

# Matrices
x <- cbind(
  rep(1, 28),
  c(rep(-1, 9), rep(0, 10), rep(1, 9)),
  c(rep(1, 9), rep(-1.8, 10), rep(1, 9))
)
y <- caffeine[, -1]
z <- cbind(c(1, 1), c(1, -1))
pattern <- cbind(c(rep(1, 3)), 1)

# Fit model
bsm <- bothsidesmodel.lrt(x, y, z, pattern)