Solve one Taylor-Russell parameter from the other three — tr

Solves for one missing Taylor-Russell parameter among base rate, selection ratio, validity, and PPV. Exactly one of the four arguments must be NULL. The default validity interval is non-negative to match the classical Taylor-Russell table convention and the defensive behavior of the TaylorRussell::TR() implementation.

Usage

tr_solve(
  base_rate = NULL,
  selection_ratio = NULL,
  validity = NULL,
  ppv = NULL,
  interval = NULL,
  tol = 1e-08,
  allow_negative_validity = FALSE
)

Arguments

base_rate: Population proportion of successful applicants.
selection_ratio: Proportion selected.
validity: Predictor-criterion correlation.
ppv: Positive predictive value / success ratio among selected applicants.
interval: Search interval for the missing parameter.
tol: Numerical tolerance passed to optimize().
allow_negative_validity: Logical. Should the solver allow negative validity when validity = NULL? Defaults to FALSE.

Value

A psu_tr object containing the solved parameter and the resulting Taylor-Russell table.

References

Taylor, H. C., & Russell, J. T. (1939). The relationship of validity coefficients to the practical effectiveness of tests in selection. Journal of Applied Psychology, 23, 565-578.

Waller, N. G. (2024). TaylorRussell: A Taylor-Russell function for multiple predictors (R package version 1.2.1). CRAN.

Examples

# Literature: Taylor and Russell (1939); Waller (2024).
# Use the first call as a minimal example; the longer block illustrates
# how to interpret the function in the substantive setting discussed in the literature.
# Minimal example: solve validity from desired PPV.
tr_solve(base_rate = .50, selection_ratio = .20, validity = NULL, ppv = .70)
#> <psu_tr>
#>   base_rate: 0.5
#>   selection_ratio: 0.2
#>   validity: 0.356075
#>   predictor_cutoff_z: 0.841621
#>   criterion_cutoff_z: 0
#>   true_positive: 0.14
#>   false_positive: 0.06
#>   false_negative: 0.36
#>   true_negative: 0.44
#>   ppv: 0.7
#>   success_ratio: 0.7
#>   incremental_success: 0.2
#>   sensitivity: 0.28
#>   specificity: 0.88
#>   digits: 3
#>   target_ppv: 0.7

# Substantive example (Taylor and Russell, 1939; Waller, 2024).
# Solve the selection ratio needed for a desired PPV.
tr_solve(base_rate = .50, selection_ratio = NULL, validity = .35, ppv = .70)
#> <psu_tr>
#>   base_rate: 0.5
#>   selection_ratio: 0.190709
#>   validity: 0.35
#>   predictor_cutoff_z: 0.875286
#>   criterion_cutoff_z: 0
#>   true_positive: 0.133496
#>   false_positive: 0.0572127
#>   false_negative: 0.366504
#>   true_negative: 0.442787
#>   ppv: 0.7
#>   success_ratio: 0.7
#>   incremental_success: 0.2
#>   sensitivity: 0.266993
#>   specificity: 0.885575
#>   digits: 3
#>   target_ppv: 0.7