Dominance analysis for predictor importance

Implements Budescu's (1993) dominance analysis to decompose the coefficient of determination of a multiple regression into contributions attributable to each predictor. Three dominance summaries are returned:

Usage

dominance_analysis(predictor_cor, predictor_criterion_cor)

Arguments

predictor_cor

Predictor correlation matrix R_xx.

predictor_criterion_cor

Vector of predictor-criterion correlations r_xy (length p).

Value

A list with components:

r_squared_full

The full-model R^2.

general_dominance

Vector of length p whose entries sum to r_squared_full.

conditional_dominance

p x p matrix; row i gives the average contribution of predictor i at subset sizes 0, 1, ..., p-1.

complete_dominance

p x p logical matrix where entry [i,j] is TRUE if i completely dominates j, FALSE if j completely dominates i, NA otherwise.

Details

• Complete dominance: predictor i completely dominates j if R^2(S \cup {i}) > R^2(S \cup {j}) for every subset S not containing i or j. Reported as a pairwise dominance matrix.

• Conditional dominance: average increment of predictor i to R^2 across subsets of size k, for k = 0, ..., p-1.

• General dominance: the average of conditional dominance values; equivalent to the Shapley value of R^2.

References

Azen, R., & Budescu, D. V. (2003). The dominance analysis approach for comparing predictors in multiple regression. Psychological Methods, 8, 129-148.

Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. Psychological Bulletin, 114, 542-551.

Examples

Rxx <- matrix(c(1, .30, .20,
                .30, 1, .25,
                .20, .25, 1), 3, 3)
rxy <- c(.40, .30, .25)
dominance_analysis(Rxx, rxy)
#> <psu_dominance>
#>   r_squared_full: 0.214657