Restricted canonical validity for a fixed criterion composite — restricted_canonical

Computes Sturman-style restricted canonical validity. Predictor weights are optimized, but criterion weights are fixed by the analyst.

Usage

restricted_canonical_validity(
  predictor_cor,
  predictor_criterion_cor,
  criterion_cor,
  criterion_weights
)

Arguments

predictor_cor: Predictor correlation matrix, Sigma_11.
predictor_criterion_cor: Matrix of predictor-criterion correlations, Sigma_12, with predictors in rows and criteria in columns.
criterion_cor: Criterion correlation matrix, Sigma_22.
criterion_weights: Fixed criterion weights, b.

Value

A psu_incremental_validity object with restricted canonical validity and optimized standardized predictor weights.

References

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

# Literature: Sturman (2001).
# 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 (Sturman (2001)).
S11 <- matrix(c(1, .30, .30, 1), 2, 2)
S12 <- matrix(c(.30, .20, .25, .15), 2, 2)
S22 <- matrix(c(1, .40, .40, 1), 2, 2)
restricted_canonical_validity(S11, S12, S22, criterion_weights = c(.6, .4))
#> <psu_incremental_validity>
#>   validity: 0.352614

# Substantive example (Sturman (2001)): change criterion weights and compare restricted validity.
task_weighted <- restricted_canonical_validity(S11, S12, S22, c(.8, .2))
balanced <- restricted_canonical_validity(S11, S12, S22, c(.5, .5))
c(task_weighted = task_weighted$validity, balanced = balanced$validity)
#> task_weighted      balanced 
#>     0.3442567     0.3485223