# fungible: Generate Fungible Regression Weights In fungible: Psychometric Functions from the Waller Lab

## Description

Generate fungible weights for OLS Regression Models.

## Usage

 `1` ```fungible(R.X, rxy, r.yhata.yhatb, sets, print = TRUE) ```

## Arguments

 `R.X` p x p Predictor correlation matrix. `rxy` p x 1 Vector of predictor-criterion correlations. `r.yhata.yhatb` Correlation between least squares (yhatb) and alternate-weight (yhata) composites. `sets` Number of returned sets of fungible weights. `print` Logical, if TRUE then print 5-point summaries of alternative weights.

## Value

 `a` Number of sets x p matrix of fungible weights. `k` Number of sets x p matrix of k weights. `b` p x 1 vector of LS weights. `u` p x 1 vector of u weights. `r.yhata.yhatb` Correlation between yhata and yhatb. `r.y.yhatb` Correlation between y and yhatb. `cov.a` Expected covariance matrix for a. `cor.a` Expected correlation matrix for a.

Niels Waller

## References

Waller, N. (2008). Fungible weights in multiple regression. Psychometrika, 73, 69–703.

## 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``` ```## Predictor correlation matrix R.X <- matrix(c(1.00, .56, .77, .56, 1.00, .73, .77, .73, 1.00), 3, 3) ## vector of predictor-criterion correlations rxy <- c(.39, .34, .38) ## OLS standardized regression coefficients b <- solve(R.X) %*% rxy ## Coefficient of determination (Rsq) OLSRSQ <- t(b) %*% R.X %*% b ## theta controls the correlation between ## yhatb: predicted criterion scores using OLS coefficients ## yhata: predicted criterion scores using alternate weights theta <- .01 ## desired correlation between yhata and yhatb r.yhata.yhatb <- sqrt( 1 - (theta)/OLSRSQ) ## number of returned sets of fungible weight vectors Nsets <- 50 output <- fungible(R.X, rxy, r.yhata.yhatb, sets = Nsets, print = TRUE) ```

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