MOST {rMOST}

MOST

Description

Optimizes 3 objectives with normal boundary intersection algorithm

Usage

MOST(optProb, Rx, Rxy1, Rxy2, Rxy3, sr, prop1, prop2, d1, d2, Spac = 10)

Arguments

optProb

Optimization problem. "3C" = no adverse impact objectives and three non-adverse impact objectives; "2C_1AI" = one adverse impact objective and two non-adverse impact objectives; "1C_2AI" = two adverse impact objectives and one non-adverse impact objective.

Rx

Predictor intercorrelation matrix

Rxy1

Needs to specify for all three types of optimization problems (optProb). Predictor criterion-related validity for non-adverse impact objective 1 (i.e., correlation between each predictor and non-adverse impact objective 1)

Rxy2

Only specify if optimization problem is "3C" or "2C_1AI". Predictor criterion-related validity for non-adverse impact objective 2 (i.e., correlation between each predictor and non-adverse impact objective 2)

Rxy3

Only specify if optimization problem is "3C". Predictor criterion-related validity for non-adverse impact objective 3 (i.e., correlation between each predictor and non-adverse impact objective 3)

sr

Only specify if optimization problem is "2C_1AI" or "1C_2AI". Overall selection ratio.

prop1

Only specify if optimization problem is "2C_1AI" or "1C_2AI". Proportion of minority1 in the applicant pool; prop1 = (# of minority1 applicants)/(total # of applicants)

prop2

Only specify if optimization problem is "1C_2AI". Proportion of minority2 in the applicant pool; prop2 = (# of minority2 applicants)/(total # of applicants)

d1

Only specify if optimization problem is "2C_1AI" or "1C_2AI". Vector of standardized group-mean differences between majority and minority 1 for each predictor; d1 = avg_majority - avg_minority1

d2

Only specify if optimization problem is "1C_2AI". Vector of standardized group-mean differences between majority and minority 2 for each predictor; d2 = avg_majority - avg_minority2

Spac

Determines the number of solutions.

Details

# Inputs required by optimization problems Different types of optimization problems require different input parameters: * optProb = "3C": MOST(optProb, Rx, Rxy1, Rxy2, Rxy3) * optProb = "2C_1AI": MOST(optProb, Rx, Rxy1, Rxy2, sr, prop1, d1) * optProb = "1C_2AI": MOST(optProb, Rx, Rxy1, sr, prop1, d1, prop2, d2)

# Notes regarding the inputs * For personnel selection applications, all predictor-intercorrelations and criterion-related validity inputs should be corrected for range restriction and criterion unreliability to reflect the relations in the applicant sample. * For optimization problems with 2 adverse impact objectives (i.e., optProb = "1C_2AI"), d1 and d2 should be the standardized mean difference between a minority group and the same reference group (e.g., Black-White and Hispanic-White, not Black-White and female-male)

# Optimization * Optimization may take several minutes to run. * Optimization may fail in some applications due to non-convergence.

For more details, please consult the vignette.

Value

Pareto-Optimal solutions with objective values (e.g., C1, AI1) and the corresponding predictor weights (e.g., P1, P2)

Examples

# A sample optimization problem with 3 non-adverse impact objectives and 3 predictors
# For more examples, please consult the vignette.

# Specify inputs
# Predictor inter-correlation matrix (Rx)
Rx <- matrix(c(1,  .50, .50,
               .50,  1, .50,
               .50, .50,  1), 3, 3)

# Predictor-objective relation vectors (Rxy1, Rxy2, Rxy3)
# Criterion-related validities
## Criterion 1
Rxy1 <- c(-.30, 0, .30)
## Criterion 2
Rxy2 <- c(0, .30, -.30)
## Criterion 3
Rxy3 <- c(.30, -.30, 0)

# Get Pareto-optimal solutions

out <- MOST(optProb = "3C", Rx = Rx, Rxy1 = Rxy1, Rxy2 = Rxy2, Rxy3 = Rxy3, Spac = 10)
out