Compare compensatory and conjunctive multiple-hurdle selection systems — compare_selection

Computes analytic compensatory expected performance and simulated multiple-hurdle expected performance using the same predictor/criterion correlation structure.

Usage

compare_selection_systems(
  predictor_cor,
  validities,
  compensatory_weights = NULL,
  compensatory_selection_ratio,
  hurdle_selection_ratios,
  n_sim = 1e+05,
  seed = NULL,
  n_applicants = NA_real_,
  compensatory_cost_per_applicant = 0,
  hurdle_cost_per_stage = 0,
  sdy = NULL,
  applicant_n = NULL
)

Arguments

predictor_cor: Predictor intercorrelation matrix.
validities: Vector of predictor-criterion correlations.
compensatory_weights: Weights for the compensatory composite.
compensatory_selection_ratio: Overall compensatory selection ratio.
hurdle_selection_ratios: Marginal selection ratios for hurdle stages.
n_sim: Number of simulated applicants for the hurdle system.
seed: Optional random seed.
n_applicants: Optional number of real applicants.
compensatory_cost_per_applicant: Cost per applicant for the compensatory system.
hurdle_cost_per_stage: Cost per applicant assessed at each hurdle.
sdy: Optional monetary value of one criterion standard deviation.
applicant_n: Legacy alias for n_applicants.

Value

A list with compensatory, multiple-hurdle, and difference summaries.

References

Ock, J., & Oswald, F. L. (2018). The utility of personnel selection decisions: Comparing compensatory and multiple-hurdle selection models. Journal of Personnel Psychology, 17(4), 172-182.

Examples

# Literature: Ock and Oswald (2018).
# Minimal example (Ock and Oswald (2018)).
Rxx <- matrix(c(1, .30, .30, 1), 2, 2)
compare_selection_systems(Rxx, c(.40, .30), hurdle_selection_ratios = c(.50, .50),
                          compensatory_selection_ratio = .25, n_sim = 1000, seed = 1)
#> <psu_comparison>
#>   Model: Compensatory versus conjunctive multiple-hurdle comparison
#>   expected_criterion_z_difference: -0.024615
#>   selection_ratio_difference: -0.037
#>   net_utility_difference: NA
#> 
#>   Compensatory subsystem:
#>     composite_validity: 0.440567
#>     selection_ratio: 0.25
#>     selected_mean_z: 1.27111
#>     expected_criterion_z: 0.560008
#>     n_applicants: NA
#>     applicant_n: NA
#>     n_selected: NA
#>     cost_per_applicant: 0
#>     total_cost: NA
#>     net_utility: NA
#> 
#>   Multiple-hurdle subsystem:
#>     joint_selection_ratio: 0.287
#>     expected_criterion_z: 0.584623
#>     n_sim: 1000
#>     selected_simulated: 287
#>     n_applicants: NA
#>     applicant_n: NA
#>     n_selected: NA
#>     total_cost: NA
#>     net_utility: NA

# Substantive example with monetary utility.
compare_selection_systems(
  predictor_cor = Rxx,
  validities = c(.40, .30),
  compensatory_selection_ratio = .25,
  hurdle_selection_ratios = c(.50, .50),
  n_sim = 5000,
  seed = 123,
  n_applicants = 400,
  compensatory_cost_per_applicant = 800,
  hurdle_cost_per_stage = c(100, 300),
  sdy = 50000
)
#> <psu_comparison>
#>   Model: Compensatory versus conjunctive multiple-hurdle comparison
#>   expected_criterion_z_difference: 0.0550903
#>   selection_ratio_difference: -0.0442
#>   net_utility_difference: -391184
#> 
#>   Compensatory subsystem:
#>     composite_validity: 0.440567
#>     selection_ratio: 0.25
#>     selected_mean_z: 1.27111
#>     expected_criterion_z: 0.560008
#>     n_applicants: 400
#>     applicant_n: 400
#>     n_selected: 100
#>     cost_per_applicant: 800
#>     total_cost: 320000
#>     sdy: 50000
#>     net_utility: 2480040
#> 
#>   Multiple-hurdle subsystem:
#>     joint_selection_ratio: 0.2942
#>     expected_criterion_z: 0.504917
#>     n_sim: 5000
#>     selected_simulated: 1471
#>     n_applicants: 400
#>     applicant_n: 400
#>     n_selected: 117.68
#>     total_cost: 99712
#>     sdy: 50000
#>     net_utility: 2871220