Sturman's (2001) comprehensive utility analysis

Composes the six adjustments of Sturman's (2001) comprehensive model (§15 of the package's accompanying review) into a single call. The returned object includes both the integrated comprehensive estimate and a stepwise cascade that documents the contribution of each adjustment.

Usage

sturman_comprehensive(
  validity,
  baseline_validity = 0,
  selection_ratio,
  sdy,
  n_year_one,
  tenure = 5,
  fixed_cost = 0,
  hires_per_period = NULL,
  losses_per_period = NULL,
  tax_rate = 0,
  discount_rate = 0,
  variable_value = 0,
  maintenance_cost_per_period = NULL,
  predictor_cor = NULL,
  predictor_criterion_cor = NULL,
  criterion_cor = NULL,
  criterion_weights = NULL,
  probation_cutoff_z = NULL,
  acceptance_rate = 1,
  quality_acceptance_correlation = 0
)

Arguments

validity

Focal-system validity (used directly when predictor_cor is NULL; replaced by the restricted canonical validity otherwise).

baseline_validity

Operating-system baseline validity. Default 0 collapses to a random-baseline analysis, which the function will warn about.

selection_ratio

Selection ratio.

sdy

Standard deviation of job performance in monetary units.

n_year_one

Number of hires in year 1.

tenure

Horizon in years (>= 1).

fixed_cost

Year-1 selection cost (currency).

hires_per_period, losses_per_period

Optional vectors of length tenure for replacement hires and turnover losses; if NULL a steady state with n_year_one per year is used.

tax_rate, discount_rate, variable_value

Boudreau parameters.

maintenance_cost_per_period

Optional cost vector of length tenure.

predictor_cor, predictor_criterion_cor, criterion_cor, criterion_weights

If supplied, the function computes the restricted canonical validity from this multidimensional criterion specification and substitutes it for validity.

probation_cutoff_z

Standardized cutoff for the probation rule (default NULL skips this adjustment).

acceptance_rate, quality_acceptance_correlation

Murphy's (1986) offer-rejection adjustment. If acceptance_rate < 1, the function adjusts the year-1 expected criterion mean and headcount accordingly.

Value

Object of class c("psu_sturman", "psu_utility") with components: net_utility (final comprehensive estimate), cascade (a data frame documenting each step), effective_validity, effective_baseline_validity, and the relevant intermediate objects.

Details

The six adjustments combined here are: (1) baseline correction (Sturman, 2000, 2001), (2) restricted canonical validity for a multidimensional criterion, (3) multi-period employee flows, (4) Boudreau-style economic adjustments (taxes, variable costs, discount rate), (5) De Corte (1994) probation-period truncation, and optionally (6) Murphy's (1986) offer-rejection adjustment. See bcg_utility(), boudreau_utility(), restricted_canonical_validity(), probation_adjustment(), employee_flow(), and offer_rejection_adjustment() for the underlying components.

References

De Corte, W. (1994). Utility analysis for the one-cohort selection-retention decision with a probationary period. Journal of Applied Psychology, 79, 402-411.

Murphy, K. R. (1986). When your top choice turns you down: Effect of rejected offers on the utility of selection tests. Psychological Bulletin, 99, 133-138.

Sturman, M. C. (2000). Implications of utility analysis adjustments for estimates of human resource intervention value. Journal of Management, 26, 281-299.

Sturman, M. C. (2001). Utility analysis for multiple selection devices and multiple outcomes. Journal of Human Resource Costing and Accounting, 6(2), 9-28.

Examples

Rxx <- matrix(c(1, .30, .30, 1), 2, 2)
Rxy <- matrix(c(.30, .10, .15, .25), 2, 2, byrow = TRUE)
Ryy <- matrix(c(1, .40, .40, 1), 2, 2)

sturman_comprehensive(
  validity = .35, baseline_validity = .20, selection_ratio = .20,
  sdy = 50000, n_year_one = 100, tenure = 5, fixed_cost = 75000,
  tax_rate = .25, discount_rate = .08,
  predictor_cor = Rxx, predictor_criterion_cor = Rxy,
  criterion_cor = Ryy, criterion_weights = c(.7, .3),
  probation_cutoff_z = -1,
  acceptance_rate = 0.70, quality_acceptance_correlation = -0.20
)
#> <psu_sturman: Sturman (2001) comprehensive utility>
#>   Comprehensive net utility: 12219500 
#>   Effective validity: 0.3068  (baseline: 0.2 )
#> 
#>   Cascade:
#>                            step net_utility pct_of_naive
#>  1. Naive BCG (random baseline)    12173334    100.00000
#>         2. + operating baseline     5174286     42.50509
#>  3. + multidim. criterion (RCV)     3663342     30.09317
#>     4. + flows + tax + discount     6303570     51.78179
#>                  5. + probation    17562257    144.26826
#>            6. + offer rejection    12219496    100.37921