Hottelling T^2 test for multivariate regression

Hottelling T^2 test compares estimated regression coefficients to specified values under the null. This tests a global hypothesis for all specified coefficients. It uses the F-distribution as the null for the test statistic which is exact under finite sample size.

Usage

hotelling(beta, Sigma, n, mu_null = rep(0, length(beta)))

Arguments

beta: regressioin coefficients
Sigma: covariance matrix of regression coefficients
n: sample size used for estimation
mu_null: the values of the regression coefficients under the null hypothesis. Defaults to all zeros

Details

The Hotelling T2 test is not defined when n - p < 1. Returns data.frame with stat = pvalue = NA.

Examples

library(clusterGeneration)
library(mvtnorm)

# sample size
n = 30

# number of response variables
m = 2

# Error covariance
Sigma = genPositiveDefMat(m)$Sigma

# regression parameters
beta = matrix(.6, 1, m)

# covariates
X = matrix(rnorm(n), ncol=1)

# Simulate response variables
Y = X %*% beta + rmvnorm(n, sigma = Sigma)

# Multivariate regression
fit = lm(Y ~ X)

# extract coefficients and covariance
# corresponding to the x variable
beta = coef(fit)['X',]
S = vcov(fit)[c(2,4), c(2,4)]

# perform Hotelling test
hotelling(beta, S, n)
#>    n p     tsq     stat    p.value
#> 1 30 2 9.54848 4.609611 0.01859817