dominance: Dominance Analysis

Description

This function conducts dominance analysis (Budescu, 1993; Azen & Budescu, 2003) for linear models estimated by using the lm() function to determine the relative importance of predictor variables. By default, the function reports general dominance, but conditional and complete dominance can be requested by specifying the argument print.

Usage

dominance(model, print = c("all", "gen", "cond", "comp"), digits = 3,
          write = NULL, check = TRUE, output = TRUE)

Value

Returns an object of class misty.object, which is a list with following entries:

call: function call
type: type of analysis
model: model specified in model
args: specification of function arguments
result: list with results, i.e., gen for general dominance, cond for conditional dominance, comp for complete dominance, and condtsat for the statistics of the conditional dominance

Arguments

model: a fitted model of class lm.
print: a character string or character vector indicating which results to show on the console, i.e. "all" for all results, "gen" for general dominance, "cond" for conditional dominance, and "comp" for complete dominance.
digits: an integer value indicating the number of decimal places to be used for displaying results. Note that the percentage relative importance of predictors are printed with digits minus 1 decimal places.
write: a character string for writing the results into a Excel file naming a file with or without file extension '.xlsx', e.g., "Results.xlsx" or "Results".
check: logical: if TRUE, argument specification is checked.
output: logical: if TRUE, output is shown.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

Details

Dominance analysis (Budescu, 1993; Azen & Budescu, 2003) is used to determine the relative importance of predictor variables in a statistical model by examining the additional contribution of predictors in R-squared relative to each other in all of the possible $2^{(p - 2)}$ subset models with $p$ being the number of predictors. Three levels of dominance can be established through pairwise comparison of all predictors in a regression model:

Complete Dominance: A predictor completely dominates another predictor if its additional contribution in R-Squared is higher than that of the other predictor across all possible subset models that do not include both predictors. For example, in a regression model with four predictors, $X_{1}$ completely dominates $X_{2}$ if the additional contribution in R-squared for $X_{1}$ is higher compared to $X_{2}$ in (1) the null model without any predictors, (2) the model including $X_{3}$ , (3) the model including $X_{4}$ , and (4) the model including both $X_{3}$ and $X_{4}$ . Note that complete dominance cannot be established if one predictor's additional contribution is greater than the other's for some, but not all of the subset models. In this case, dominance is undetermined and the result will be NA
Conditional Dominance: A predictor conditionally dominates another predictor if its average additional contribution in R-squared is higher within each model size than that of the other predictor. For example, in a regression model with four predictors, $X_{1}$ conditionally dominates $X_{2}$ if the average additional contribution in R-squared is higher compared to $X_{2}$ in (1) the null model without any predictors, (2) the four models including one predictor, (3) the six models including two predictors, and (4) the four models including three predictors.
General Dominance: A predictor generally dominates another predictor if its overall averaged additional contribution in R-squared is higher than that of the other predictor. For example, in a regression model with four predictors, $X_{1}$ generally dominates $X_{2}$ if the average across the four conditional values (i.e., null model, model with one predictor, model with two predictors, and model with three predictors) is higher than that of $X_{2}$ . Note that the general dominance measures represent the proportional contribution that each predictor makes to the R-squared since their sum across all predictors equals the R-squared of the full model.

The three levels of dominance are related to each other in a hierarchical fashion: Complete dominance implies conditional dominance, which in turn implies general dominance. However, the converse may not hold for more than three predictors. That is, general dominance does not imply conditional dominance, and conditional dominance does not necessarily imply complete dominance.

References

Azen, R., & Budescu, D. V. (2003). The dominance analysis approach for comparing predictors in multiple regression. Psychological Methods, 8(2), 129–148. https://doi.org/10.1037/1082-989X.8.2.129

Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. Psychological Bulletin, 114(3), 542–551. https://doi.org/10.1037/0033-2909.114.3.542

Luchman J (2023). domir: Tools to support relative importance analysis. R package version 1.0.1, https://CRAN.R-project.org/package=domir.

Examples

Run this code

dat <- data.frame(x1 = c(3, 2, 4, 9, 5, 3, 6, 4, 5, 6, 3, 5),
                  x2 = c(1, 4, 3, 1, 2, 4, 3, 5, 1, 7, 8, 7),
                  x3 = c(0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1),
                  y  = c(0, 1, 0, 2, 0, 1, 0, 0, 1, 2, 1, 0))

#----------------------------
# Dominance analysis for a linear model

mod <- lm(y ~ x1 + x2 + x3, data = dat)
dominance(mod)

# Print all results
dominance(mod, print = "all")

if (FALSE) {
#----------------------------
# Write Results into a Excel file

mod <- lm(y ~ x1 + x2 + x3, data = dat)

dominance(mod, write = "Dominance.xlsx", output = FALSE)

result <- dominance(mod, print = "all", output = FALSE)
write.result(result, "Dominance.xlsx")
}

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