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.
dominance(model, print = c("all", "gen", "cond", "comp"), digits = 3,
write = NULL, append = TRUE, check = TRUE, output = TRUE)Returns an object of class misty.object, which is a list with following
entries:
callfunction call
typetype of analysis
modelmodel specified in model
argsspecification of function arguments
resultlist 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
a fitted model of class lm.
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.
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.
a character string naming a file for writing the output into
either a text file with file extension ".txt" (e.g.,
"Output.txt") or Excel file with file extension
".xlsx" (e.g., "Output.xlsx"). If the file
name does not contain any file extension, an Excel file will
be written.
logical: if TRUE (default), output will be appended
to an existing text file with extension .txt specified
in write, if FALSE existing text file will be
overwritten.
logical: if TRUE (default), argument specification is checked.
logical: if TRUE (default), output is shown.
Takuya Yanagida takuya.yanagida@univie.ac.at
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:
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
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.
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.
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.
dominance.manual, std.coef, write.result
#----------------------------------------------------------------------------
# Example 1: Dominance analysis for a linear model
mod <- lm(mpg ~ cyl + disp + hp, data = mtcars)
dominance(mod)
# Print all results
dominance(mod, print = "all")
if (FALSE) {
#----------------------------------------------------------------------------
# Example 2: Write results into a text file
dominance(mod, write = "Dominance.txt", output = FALSE)
#----------------------------------------------------------------------------
# Example 3: Write results into an Excel file
dominance(mod, write = "Dominance.xlsx", output = FALSE)
result <- dominance(mod, print = "all", output = FALSE)
write.result(result, "Dominance.xlsx")
}
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