rcone {fungible}

Generate a Cone of Regression Coefficient Vectors

Description

Compute a cone of regression vectors with a constant R-squared around a target vector.

Usage

rcone(R, Rsq, b, axis1, axis2, deg, Npoints = 360)

Arguments

R

Predictor correlation matrix.

Rsq

Coefficient of determination.

b

Target vector of OLS regression coefficients.

axis1

1st axis of rotation plane.

axis2

2nd axis of rotation plane.

deg

All vectors b.i will be ‘deg’ degrees from b.

Npoints

Number of rotation vectors, default = 360.

Value

b.i

Npoints values of b.i

Author(s)

Niels Waller and Jeff Jones

References

Waller, N. G. & Jones, J. A. (2011). Investigating the performance of alternate regression weights by studying all possible criteria in regression models with a fixed set of predictors. Psychometrika, 76, 410-439.

Examples

R <- matrix(.5, 4, 4)
diag(R) <- 1

Npoints <- 1000
Rsq <- .40
NumDeg <- 20
V <- eigen(R)$vectors

## create b parallel to v[,3]
## rotate in the 2 - 4 plane
b <- V[,3]
bsq <- t(b) %*% R %*% b 
b <- b * sqrt(Rsq/bsq)                
b.i <- rcone(R, Rsq,b, V[,2], V[,4], deg = NumDeg, Npoints)

t(b.i[,1]) %*% R %*% b.i[,1]
t(b.i[,25]) %*% R %*% b.i[,25]