# bothsidesmodel.lrt: Test subsets of beta are zero. In msos: Data Sets and Functions Used in Multivariate Statistics: Old School by John Marden

## Description

Tests the null hypothesis that an arbitrary subset of the β _{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

 ```1 2 3 4 5 6 7``` ```bothsidesmodel.lrt( x, y, z, pattern0, patternA = matrix(1, nrow = ncol(x), ncol = ncol(z)) ) ```

## Arguments

 `x` An N x P design matrix. `y` The N x Q matrix of observations. `z` A Q x L design matrix. `pattern0` An N x P matrix of 0's and 1's specifying `patternA` An optional N x 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.

`bothsidesmodel.chisquare`, `bothsidesmodel.df`, `bothsidesmodel.hotelling`, `bothsidesmodel`, and `bothsidesmodel.mle`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# 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) ```