enhancement {fungible}

Find OLS Regression Coefficients that Exhibit Enhancement

Description

Find OLS regression coefficients that exhibit a specified degree of enhancement.

Usage

enhancement(R, br, rr)

Arguments

R

Predictor correlation matrix.

br

Model R-squared = b' r. That is, br is the model coefficient of determination: b'Rb= Rsq = br

rr

Sum of squared predictor-criterion correlations (rxy). That is, rr = r'r = Sum(rxy^2)

Value

b

Vector of standardized regression coefficients.

r

Vector of predictor-criterion correlations.

Author(s)

Niels Waller

References

Waller, N. G. (2011). The geometry of enhancement in multiple regression. Psychometrika, 76, 634–649.

Examples

## 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)