Tools to Support Relative Importance Analysis

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The {domir} package supports the determination of the relative importance of the inputs (i.e., independent variables, predictors, or features) in a user’s statistical or machine learning model. The methodology used by {domir} is called Dominance Analysis which is based on a series of pairwise comparisons between the model fit values ascribed to elements in the model including comparing Shapley values.

The intention of this package is to provide a flexible user interface to dominance analysis—a relatively assumption-free methodology for comparing the value of model inputs to prediction. The user interface is structured such that {domir} automates the decomposition of the returned value and comparisons between model inputs and the user provides the model inputs, the predictive model into which they are entered, and returned value from the model to decompose.


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


{domir} is also used as the computational engine underlying the dominance_analysis() function for the {parameters} package from the {easystats} collection.

What {domir} Does

The primary dominance analysis function domir implements the most computationally intensive and programming heavy parts of dominance analysis for the user and has relatively few requirements on the predictive modeling functions with which it can work.

The flexibility of domir comes at the cost of more complexity for the user in terms of setting up a function that accepts the type of input domir will provide (currently only a ‘formula’) and and expects to receive (currently only a numeric scalar).

Below these ideas are outlined in greater detail in the context of a few examples. The next section begins the discussion with a more extensive comparison of domir with packages that implement similar methods.

Comparison with Existing Relative Importance Packages

The domir function implements the same method as the “lmg” type for the calc.relimpo function in the {relaimpo} package. domir can replicate the results produced by both the above package but, as will be seen, requires more user input.

To illustrate these points, consider the following example linear regression on which all three of the dominance analysis results to come are based:

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

Classic dominance analysis uses the variance explained \(R^2\) as fit statistic (i.e., as implemented by lm’s summary method) and so will this example.

{domir}’s domir

Implementing a ‘classic’ dominance analysis on this linear regression in domir can be inputted as:

lm_wrapper <-       
  function(formula, data) {
    lm(formula, data = data) |> 
      summary() |>

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:
##     Subset Size: 1 Subset Size: 2 Subset Size: 3
## am       0.3597989      0.1389842    0.033684441
## vs       0.4409477      0.1641982    0.002963748
## cyl      0.7261800      0.3432799    0.075894823
## Complete Dominance Designations:
##             Dmnated?am Dmnated?vs Dmnated?cyl
## Dmnates?am          NA         NA       FALSE
## Dmnates?vs          NA         NA       FALSE
## Dmnates?cyl       TRUE       TRUE          NA

In domir, the lm model is not submitted directly. Rather, it is wrapped into a function (i.e., lm_wrapper) that, in this case, accepts two arguments; formula or an R formula and data a data frame in which the independent variables in the formula are present. The result of the lm submitted into the summary function and the result is then filtered to just the r.squared element and returned.

What domir does automate taking subsets of the formula and submit them, repeatedly until all possible subsets have been submitted, to lm_wrapper (see this vignette for a conceptual discussion of dominance analysis). In this way, domir is a Map- or lapply-like function as it receives an object on which to operate (i.e., the formula) and a function to which to apply to it. domir expects a numeric scalar to be returned from the function.

Like lapply, other arguments (data = mtcars) can also be passed to each call of the function and must be explicitly built into the wrapper function.

What is important to note about domir that differs from other dominance analysis-oriented functions discussed below is that domir expects that the user will supply the analysis pipeline linking the formula it passes to the numeric scalar value that it expects. This ‘supply the pipeline’ approach makes domir far more flexible than other implementations but does require the user to think more carefully about how to structure the pipeline.

Note that the focus of domir’s print-ed results focuses on the numerical results from “General Dominance Values” and “Conditional Dominance Values” and, a logical matrix of “Complete Dominance Designations”.

See also the (now superseded) domir::domin function for another approach to structuring the input pipeline for dominance analysis.

{relaimpo}’s calc.relimp with type = "lmg"

{relaimpo} is not a dominance analysis software but does produce general dominance value decomposition for linear regression using the explained variance \(R^2\) in the calc.relimp function with the argument type = "lmg".

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

calc.relimp has a similar to structure to that of domir but does not require a pipeline function. This is because {relaimpo} is specialized and works only with lm models and the variance explained \(R^2\) as a fit statistic. calc.relimp also allows for multiple methods of submitting (i.e., correlation matrices, fitted lm object, a data.frame) given that it always implements the same model.

calc.relimp’s printed results provide relative importance metric values that match those obtained from domir (i.e., the general dominance values). In addition, calc.relimp reports the average lm coefficients across numbers of independent variables/\(X\)s in a way similar to the conditional dominance values reported by domir—an additional and useful result to show the impact of inclusion of different numbers of independent variables on obtained coefficients/predicted values.

Again, note that {relaimpo} is not dominance analysis-oriented and does not report on dominance designations or dominance values other than the general dominance values.

Further Examples

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