Find OLS regression coefficients that exhibit a specified degree of enhancement.
enhancement(R, br, rr)Vector of standardized regression coefficients.
Vector of predictor-criterion correlations.
Predictor correlation matrix.
Model R-squared = b' r. That is, br is the model coefficient of determination: b'Rb= Rsq = br
Sum of squared predictor-criterion correlations (rxy). That is, rr = r'r = Sum(rxy^2)
Niels Waller
Waller, N. G. (2011). The geometry of enhancement in multiple regression. Psychometrika, 76, 634--649.
## Example: For a given predictor correlation matrix (R) generate
## regression coefficient vectors that produce enhancement (br - rr > 0)
## Predictor correlation matrix
R <- matrix(c( 1, .5, .25,
.5, 1, .30,
.25, .30, 1), 3, 3)
## Model coefficient of determination
Rsq <- .60
output<-enhancement(R, br = Rsq, rr =.40)
r <- output$r
b <- output$b
##Standardized regression coefficients
print(t(b))
##Predictor-criterion correlations
print(t(r))
##Coefficient of determinations (b'r)
print(t(b) %*% r)
##Sum of squared correlations (r'r)
print(t(r) %*% r)
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