Dominance Analysis Methods

domir

Overview

domir implements several methods to compute dominance analysis¹. Dominance analysis is a relative importance analysis approach that derives conceptually from Shapley values in that it ascribes ‘values’ from some function to inputs (known as ‘names’ in the package) to that function.

When applied to predictive models, the method compares components of a fit metric ascribed to each ‘name’ (i.e., independent variable, predictor, feature, or parameter estimate) to each other ‘name’ in a pairwise fashion to determine a hierarchy of dominance or relative importance.

Installation

To install the most recent version of domir from CRAN use:

install.packages("domir")

domir is also used as the computational engine underlying the dominance_analysis() function for the parameters package in easystats.

What domir Does

domir computes dominance analysis results based on a set of inputs/names and the values returned from a function like this linear regression model.

lm(mpg ~ am + vs + cyl, data = mtcars)

Using the variance explained \(R^2\) as fit statistic as implemented by lm’s summary method as the returned value, domir produces:

lm_wrapper <-       
  function(formula, data) {
    lm(formula, data = data) |> 
      summary() |>
      _[["r.squared"]]
  }

domir(mpg ~ am + vs + cyl, lm_wrapper, data = mtcars)

## 
## Overall Value:      0.7619773 
## 
## General Dominance Values:
##     General Dominance Standardized Ranks
## am          0.1774892    0.2329324     3
## vs          0.2027032    0.2660226     2
## cyl         0.3817849    0.5010450     1
## 
## Conditional Dominance Values:
##     Include At: 1 Include At: 2 Include At: 3
## am      0.3597989     0.1389842   0.033684441
## vs      0.4409477     0.1641982   0.002963748
## cyl     0.7261800     0.3432799   0.075894823
## 
## Complete Dominance Proportions:
##       > am > vs > cyl
## am >    NA  0.5     0
## vs >   0.5   NA     0
## cyl >  1.0  1.0    NA

domir requires a set of inputs/names, submitted as a formula or a specialized formula_list object, and a function that accepts the input/names and returns a single, numeric value.

The function supplied to domir must then be a full ‘analysis pipeline’ function and is necessary for the effective use of domir. In fact, domir’s value is in that it allows the use of such pipelines as the user can define them to apply to almost any predictive model. This example uses wrapper function, lm_wrapper, that accepts a formula and returns the \(R^2\). A user could use an anonymous function defined within the domir call that has a similar format as an alternative.

Comparison with Existing Relative Importance Packages

Several other relative importance packages can produce results identical to domir under specific circumstances. I will focus on discussing two of the most relevant comparison packages below.

The calc.relimpo function in the relaimpo package with type = "lmg" produces the general dominance values for lm as in the example below:

relaimpo::calc.relimp(mpg ~ am + vs + cyl, data = mtcars, type = "lmg")

## Response variable: mpg 
## Total response variance: 36.3241 
## Analysis based on 32 observations 
## 
## 3 Regressors: 
## am vs cyl 
## Proportion of variance explained by model: 76.2%
## Metrics are not normalized (rela=FALSE). 
## 
## Relative importance metrics: 
## 
##           lmg
## am  0.1774892
## vs  0.2027032
## cyl 0.3817849
## 
## Average coefficients for different model sizes: 
## 
##            1X       2Xs       3Xs
## am   7.244939  4.316851  3.026480
## vs   7.940476  2.995142  1.294614
## cyl -2.875790 -2.795816 -2.137632

relaimpo is for importance analysis with linear regression with variance explained \(R^2\) as a fit statistic and is optimized to analyze that model-fit statistic pairing across multiple ways of submitting data (i.e., correlation matrices, fitted lm object, a data.frame).

The dominanceAnalysis function in dominanceAnalysis produces many of the same statistics as domir as in the example below:

dominanceanalysis::dominanceAnalysis(lm(mpg ~ am + vs + cyl, data = mtcars))

## 
## Dominance analysis
## Predictors: am, vs, cyl 
## Fit-indices: r2 
## 
## * Fit index:  r2 
##     complete conditional general
## am                              
## vs                            am
## cyl    am,vs       am,vs   am,vs
## 
## Average contribution:
##   cyl    vs    am 
## 0.382 0.203 0.177

dominanceAnalysis is for the relative importance of specific model-fit statistic pairs as it is implemented using S3 methods focused on model types to implement similar to how parameters::dominance_analysis works but using a custom implementation not dependent on the insight package to parse model components and implement the methodology.

Further Examples

Further examples of domirs functionality will be populated on the domir wiki.