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.
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