glhpwr {hpower}R Documentation

Power Function for Tests of the General Linear Hypothesis

Description

Use a noncentral F approximation to compute the power of a test of the general linear hypothesis.

Usage

glhpwr(alpha, x, bt1, sigma, cc, u, th0, test=1, tol=1e-08)

Arguments

alpha type I error probability of the test.
x N-by-q design matrix.
bt1 q-by-p alternative hypothesis value of the regression coefficient.
sigma p-by-p variance matrix of a single observation.
cc a-by-q between-rows contrast matrix.
u p-by-b between-columns contrast matrix.
th0 a-by-b null value of cc%*%beta%*%u.
test test for which power is desired. test=1 (the default) is the Wilks lambda test; test=2 is the Hotelling-Lawley trace test; test=3 is the Pillai-Bartlett trace test. See Muller and Peterson (1984) for details.
tol tolerance for computing the rank of x (using qr()). The default is 1.e-8.

Value

the approximate power of a test of the general linear hypothesis cc%*%beta%*%u=th0 under the alternative beta=bt1. The model is y(Nxp)=x(Nxq)%*%beta(qxp)+e(Nxp), where x is the design, beta is the matrix of multivariate regression parameters, and e is the error matrix, whose rows are assumed to be independent draws from a multivariate normal with mean 0 and p-by-p variance matrix sigma.

NOTE

If the computed approximate degrees of freedom are negative, a power of 0 is returned; this may mean that the proposed design has no degrees of freedom for error.

Author(s)

Daniel F. Heitjan <dheitjan@peter.cpmc.columbia.edu>, R-port by Stefan Funke <funke@attglobal.net>

References

Muller, K.E. and Peterson, B.L. (1984). Practical methods for computing power in testing the multivariate general linear hypothesis. Computational Statistics and Data Analysis 2, 143–158.

See Also

pfnc, sscomp