bothsidesmodel.lrt: Test subsets of beta are zero.

In coatless/msos: Data Sets and Functions Used in Multivariate Statistics: Old School by John Marden

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)

coatless/msos documentation built on Nov. 16, 2023, 5:31 a.m.