bartlett.cortest: Bartlett's test that a correlation matrix is an identity matrix
Description
Bartlett (1951) proposed that -ln(det(R)*(N-1 - (2p+5)/6) was distributed as chi square if R were an identity matrix. A useful test that residuals correlations are all zero.
Usage
bartlett.cortest(R, n = NULL)
Arguments
R
A correlation matrix. (If R is not square, correlations are found and a warning is issued.
n
Sample size (if not specified, 100 is assumed.
Value
chisqAssymptotically chisquare
p.valueOf chi square
dfThe degrees of freedom
Details
More useful for pedagogical purposes than actual applications. The Bartlett test is asymptotically chi square distributed.
References
Bartlett, M. S., (1951), The Effect of Standardization on a $^2$ Approximation in Factor Analysis, Biometrika, 38, 337-344.
[object Object]
mat.cortest, normal.cortest, jennrich.cortestset.seed(42)
x <- matrix(rnorm(1000),ncol=10)
r <- cor(x)
bartlett.cortest(r) #random data don't differ from an identity matrix
data(bfi)
bartlett.cortest(bfi) #not an identity matrixmultivariate