bothsidesmodel.lrt {msos}

Test subsets of \beta are zero.

Description

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.

Usage

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)