acX_to_rho {ciuupi}R Documentation

Computes the known correlation ρ\rho between θ^\widehat{\theta} and τ^\widehat{\tau} from the pp-vectors aa and cc and the design matrix XX

Description

Computes the known correlation ρ\rho between θ^\widehat{\theta} and τ^\widehat{\tau}. This correlation is computed from the pp-vectors aa and cc and the n×pn \times p design matrix XX, with linearly independent columns, using the formula ρ=a(XX)1c/(vθvτ)1/2\rho=a^{\top}(X^{\top} X)^{-1} c /(v_{\theta} \, v_{\tau})^{1/2}, where vθ=a(XX)1av_{\theta} =a^{\top}(X^{\top} X)^{-1}a and vτ=c(XX)1cv_{\tau} =c^{\top}(X^{\top} X)^{-1}c.

Usage

acX_to_rho(a, c, X)

Arguments

a

The pp-vector aa that specifies the parameter of interest θ=aβ\theta =a^{\top}\beta

c

The pp-vector cc used in the specification of the parameter τ=cβt\tau=c^{\top} \beta-t. The uncertain prior information is that τ=0\tau=0

X

The n×pn \times p design matrix XX, with linearly independent columns

Value

The known correlation ρ\rho between θ^\widehat{\theta} and τ^\widehat{\tau}.

Examples

a <- c(0, 2, 0, -2)
c <- c(0, 0, 0, 1)
x1 <- c(-1, 1, -1, 1)
x2 <- c(-1, -1, 1, 1)
X <- cbind(rep(1, 4), x1, x2, x1*x2)
rho <- acX_to_rho(a, c, X)
print(rho)


[Package ciuupi version 1.2.3 Index]