# enhancement: Find OLS Regression Coefficients that Exhibit Enhancement In fungible: Psychometric Functions from the Waller Lab

## Description

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

## Usage

 `1` ```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.

Niels Waller

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ```## 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) ```

fungible documentation built on Sept. 29, 2021, 1:06 a.m.