fungible | R Documentation |

Generate fungible weights for OLS Regression Models.

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

`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. |

`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

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

```
## 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)
```

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