fungible (version 2.4.4)

rellipsoid: Generate Uniformly Spaced OLS Regression Coefficients that Yield a User-Supplied R-Squared Value

Description

Given predictor matrix R, generate OLS regression coefficients that yield a user-supplied R-Squared value. These regression coefficient vectors will be uniformly spaced on the surface of a (hyper) ellipsoid.

Usage

rellipsoid(R, Rsq, Npoints)

Value

b

A p x Npoints matrix of regression coefficients

Arguments

R

A p x p predictor correlation matrix.

Rsq

A user-supplied R-squared value.

Npoints

Desired number of generated regression vectors.

Author

Niels Waller and Jeff Jones.

References

Waller, N. G. and 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

## generate uniformly distributed regression vectors
## on the surface of a 14-dimensional ellipsoid 
N <- 10000
Rsq <- .21

# Correlations from page 224 WAIS-III manual 
# The Psychological Corporation (1997).
wais3 <- matrix(
 c(1, .76, .58, .43, .75, .75, .42, .54, .41, .57, .64, .54, .50, .53,
 .76,   1, .57, .36, .69, .71, .45, .52, .36, .63, .68, .51, .47, .54,
 .58, .57,   1, .45, .65, .60, .47, .48, .43, .59, .60, .49, .56, .47,
 .43, .36, .45,   1, .37, .40, .60, .30, .32, .34, .35, .28, .35, .29,
 .75, .69, .65, .37,   1, .70, .44, .54, .34, .59, .62, .54, .45, .50,
 .75, .71, .60, .40, .70,   1, .42, .51, .44, .53, .60, .50, .52, .44,
 .42, .45, .47, .60, .44, .42,   1, .46, .49, .47, .43, .27, .50, .42,
 .54, .52, .48, .30, .54, .51, .46,   1, .45, .50, .58, .55, .53, .56,
 .41, .36, .43, .32, .34, .44, .49, .45,   1, .47, .49, .41, .70, .38,
 .57, .63, .59, .34, .59, .53, .47, .50, .47,   1, .63, .62, .58, .66,
 .64, .68, .60, .35, .62, .60, .43, .58, .49, .63,   1, .59, .50, .59,
 .54, .51, .49, .28, .54, .50, .27, .55, .41, .62, .59,   1, .48, .53,
 .50, .47, .56, .35, .45, .52, .50, .53, .70, .58, .50, .48,   1, .51,
 .53, .54, .47, .29, .50, .44, .42, .56, .38, .66, .59, .53, .51,   1),
 nrow = 14, ncol = 14)

R <- wais3[1:6,1:6]             
b <- rellipsoid(R, Rsq, Npoints = N)
b <- b$b
# 
plot(b[1,],b[2,])