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

 enhancement R Documentation

## 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.

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)

``````

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