Multigroup multivariate Taylor-Russell summaries — group_tr_multivariate • personnelSelectionUtility

Applies tr_multivariate() separately by group. This is useful for sensitivity analyses in which base rates or correlation matrices differ across demographic groups. It does not by itself establish legal compliance or fairness.

Usage

group_tr_multivariate(
  selection_ratios,
  base_rates,
  R_list,
  group_names = NULL,
  group_proportions = NULL
)

Arguments

selection_ratios: Vector of marginal selection ratios, common to all groups, or a list of group-specific vectors.
base_rates: Numeric vector of group-specific base rates.
R_list: List of group-specific correlation matrices.
group_names: Optional group labels.
group_proportions: Optional population proportions. If supplied, they are normalized and used to compute overall weighted summaries.

Value

A list with group-level Taylor-Russell summaries and optional weighted overall metrics.

References

De Corte, W., Lievens, F., & Sackett, P. R. (2007). Combining predictors to achieve optimal trade-offs between selection quality and adverse impact. Journal of Applied Psychology, 92, 1380-1393.

Thomas, J. G., Owen, D. B., & Gunst, R. F. (1977). Improving the use of educational tests as selection tools. Journal of Educational Statistics, 2(1), 55-77.

Examples

# Literature: Thomas, Owen, and Gunst (1977); De Corte et al. (2007).
R <- matrix(c(1, .30, .40, .30, 1, .35, .40, .35, 1), 3, 3)
group_tr_multivariate(c(.50, .50), base_rates = c(.50, .40),
                      R_list = list(R, R), group_names = c("A", "B"))
#> $groups
#> $groups$A
#> <psu_tr>
#>   base_rate: 0.5
#>   joint_selection_ratio: 0.298507
#>   criterion_cutoff_z: 0
#>   true_positive: 0.210473
#>   false_positive: 0.0880345
#>   false_negative: 0.289527
#>   true_negative: 0.411966
#>   ppv: 0.705084
#>   success_ratio: 0.705084
#>   incremental_success: 0.205084
#>   sensitivity: 0.420945
#>   specificity: 0.823931
#>   digits: 3
#> 
#> $groups$B
#> <psu_tr>
#>   base_rate: 0.4
#>   joint_selection_ratio: 0.298512
#>   criterion_cutoff_z: 0.253347
#>   true_positive: 0.180407
#>   false_positive: 0.118105
#>   false_negative: 0.219593
#>   true_negative: 0.481895
#>   ppv: 0.604354
#>   success_ratio: 0.604354
#>   incremental_success: 0.204354
#>   sensitivity: 0.451018
#>   specificity: 0.803158
#>   digits: 3
#> 
#> 
#> $summary
#>   group base_rate joint_selection_ratio       ppv sensitivity specificity
#> A     A       0.5             0.2985072 0.7050843   0.4209455   0.8239311
#> B     B       0.4             0.2985122 0.6043542   0.4510177   0.8031582
#> 
#> $overall
#> NULL
#>