bothsidesmodel.chisquare: 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, based on the least squares estimates, using the \chi^2 test as in Section 7.1. 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.chisquare(
  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 the null hypothesis.
patternA	An optional N \times P matrix of 0's and 1's specifying the alternative hypothesis.

Value

A 'list' with the following components:

Theta

The vector of estimated parameters of interest.

Covtheta

The estimated covariance matrix of the estimated parameter vector.

df

The degrees of freedom in the test.

chisq

T^2 statistic in (7.4).

pvalue

The p-value for the test.

See Also

bothsidesmodel, bothsidesmodel.df, bothsidesmodel.hotelling, bothsidesmodel.lrt, and bothsidesmodel.mle.

Examples

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