Estimate ai and average criterion scores for majority and minority groups.

1 | ```
aiPuxComposite(r_mat, y_col, x_col, dX, dY, wt_x, wt_y, sr, pct_minority)
``` |

`r_mat` |
Super correlation matrix between the predictors and criteria. This argument assumes that the predictors come first in the matrix. |

`y_col` |
A vector of columns representing criterion variables. |

`x_col` |
A vector of columns representing predictor variables. |

`dX` |
A vector of d values for the predictors. These d values are expected to have been computed in the direction of Majority - Minority. |

`dY` |
A vector of d values for the criteria These d values are expected to have been computed in the direction of Majority - Minority. |

`wt_x` |
Weights for the predictors to form the overall composite predictor. |

`wt_y` |
Weights for the criteria to form the overall composite criterion. |

`sr` |
The percentage of the applicant population who are selected. |

`pct_minority` |
The percentage of the applicant population who are part of a given minority group. |

AIAdverse Impact

Overeall_srThe overall selection ratio set by the user

Majority_srMajority Selection Rate

Minority_srMinority Selection Rate

Majority_StandardizedPredicted composite criterion score relative to the majority population

Global_StandardizedPredicted composite criterion score relative to the overall population

Jeff Jones and Allen Goebl

De Corte, W., Lievens, F.(2003). A Practical procedure to estimate
the quality and the adverse impact of single-stage selection decisions.
*International Journal of Selection and Assessment.*, 11(1), 87-95.
De Corte, W. (2003). Caiqs user's guide. http://allserv.rug.ac.be/~wdecorte/software.html

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
# Example taken from De Corte, W. (2003)
R <- matrix(c(1.000, 0.170, 0.000, 0.100, 0.290, 0.160,
0.170, 1.000, 0.120, 0.160, 0.300, 0.260,
0.000, 0.120, 1.000, 0.470, 0.120, 0.200,
0.100, 0.160, 0.470, 1.000, 0.240, 0.250,
0.290, 0.300, 0.120, 0.240, 1.000, 0.170,
0.160, 0.260, 0.200, 0.250, 0.170, 1.000), 6, 6)
wt_x <- c(.244, .270, .039, .206)
wt_y <- c(6, 2)
sr <- 0.25
pct_minority <- .20
# Note that the d-values are reversed from what the CAIQS manual reports (see pg 4)
dX <- c(1, 0.09, 0.09, 0.20)
dY <- c(0.450, 0.0)
aiPuxComposite(R, 5:6, 1:4, dX, dY, wt_x, wt_y, sr, pct_minority)
# compare the output from predictAI with the output in the CAIQS manual on page 7 where SR = .250
``` |

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