Last chance! 50% off unlimited learning
Sale ends in
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.
rellipsoid(R, Rsq, Npoints)A p x Npoints matrix of regression coefficients
A p x p predictor correlation matrix.
A user-supplied R-squared value.
Desired number of generated regression vectors.
Niels Waller and Jeff Jones.
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.
## 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,])
Run the code above in your browser using DataLab