ParetoR

Pareto-Optimization via Normal Boundary Intersection Method in Diversity Hiring
Developer: Q. Chelsea Song
Contact: qianqisong@gmail.com
Last Update: 04/22/2017

Objective

The current R program provides a set of Pareto-optimal solutions that simultaneously optimize both diversity and criterion validity in a personnel selection scenario [see Song, Wee & Newman (provisionally accepted); adapted from De Corte, Lievens & Sackett (2007); also see Wee, Newman & Joseph (2014) for more details]. Pareto-optimal solutions are estimated using the Normal-Boundary Intersection method (Das & Dennis, 1998).

Instructions

1. Open an R console or RStudio window. (R can be downloaded for free from https://cran.r-project.org; RStudio can be downloaded for free from https://www.rstudio.com/)
2. Install R package "ParetoR" through Github by pasting and running the following commands in R console or RStudio: install.packages("devtools")
   library("devtools")
   install_github("Diversity-ParetoOptimal/ParetoR")
   library("ParetoR")
   
3. Specify four inputs (example from DeCorte, Lievens & Sackett (2007) is given below):
     # (1) Proportion of minority applicants (prop) = (# of minority applicants)/(total # of applicants)
     ## Example:
           prop <- 1/4
     # (2) Selection ratio (sr) = (# of selected applicants)/(total # of applicants)
     ## Example:
           sr <- 0.10
     # (3) Subgroup differences (d): standardized mean differences between minority and majority subgroups, on each predictor (in applicant pool)
     ## Example:
           d <- c(1.00, 0.23, 0.09, 0.33)
     # (4) Correlation matrix (R) = criterion & predictor inter-correlation matrix (in applicant pool) <br >   ## Example:
           # Format: Predictor_1, ..., Predictor_n, Criterion
           R <- matrix(c(1, .24, .00, .19, .30,
                                 .24, 1, .12, .16, .30,
                                 .00, .12, 1, .51, .18,
                                 .19, .16, .51, 1, .28,
                                 .30, .30, .18, .28, 1),
                                 (length(d)+1),(length(d)+1))
   
4. Paste and run the following command in R console or RStudio: <br >         out = ParetoR(prop, sr, d, R)

Output Description

1. Pareto Optimal solutions (i.e., 21 equally-spaced solutions that characterize the Criterion validity – AI ratio tradeoff curve, and Predictor Weights at each point along tradeoff curve).
2. Plots (i.e., Criterion validity – AI ratio tradeoff curve, Predictor weights across trade-off points).

Note

The program is modeled after DeCorte's (2006) TROFSS Fortran program and Zhou's (2006) NBI Matlab program (version 0.1.3). The current version only supports scenarios where AI ratio and one other criterion are being optimized.

References

Song, Q. C., Wee, S., & Newman, D. (provisionally accepted). Diversity Shrinkage: Cross-Validating Pareto-Optimal Weights to Enhance Diversity via Hiring Practices. Journal of Applied Psychology.
Das, I., & Dennis, J. E. (1998). Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization, 8, 631-657.
De Corte, W. (2006). TROFSS User's Guide.
De Corte, W., Lievens, F., & Sackett, P. (2007). Combining predictors to achieve optimal trade-offs between selection quality and adverse impact. Journal of Applied Psychology, 92, 1380-1393.
Wee, S., Newman, D. A., & Joseph, D. L. (2014). More than g: Selection quality and adverse impact implications of considering second-stratum cognitive abilities. Journal of Applied Psychology, 99, 547-563.

Acknowledgements

Great appreciation to Dr. Serena Wee, Dr. Dan Newman and Dr. Wilfried De Corte for guidance and feedback on development of the program.

Web Application

We also developed a user-friendly web application to implement the Pareto-Optimal technique described in the current package (https://qchelseasong.shinyapps.io/ParetoR/). The web application (like the ParetoR package) uses only a correlation matrix, selection ratio, proportion of applicants from the minority group, and subgroup d values as input. It then provides a full set of Pareto solutions and their corresponding predictor weights.