rellipsoid: Generate Uniformly Spaced OLS Regression Coefficients that...

In fungible: Psychometric Functions from the Waller Lab

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)

Arguments

R	A p x p predictor correlation matrix.
Rsq	A user-supplied R-squared value.
Npoints	Desired number of generated regression vectors.

Value

b	A p x Npoints matrix of regression coefficients

Author(s)

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,])

fungible documentation built on March 31, 2023, 5:47 p.m.