Title: Tools to Support Relative Importance Analysis
Version: 1.2.0
Date: 2024-5-4
Description: Methods to apply decomposition-based relative importance analysis for R functions. This package supports the application of decomposition methods by providing 'lapply'- or 'Map'-like meta-functions that compute dominance analysis (Azen, R., & Budescu, D. V. (2003) <doi:10.1037/1082-989X.8.2.129>; Grömping, U. (2007) <doi:10.1198/000313007X188252>) an extension of Shapley value regression (Lipovetsky, S., & Conklin, M. (2001) <doi:10.1002/asmb.446>) based on the values returned from other functions.
Imports: parallel, stats, utils
Suggests: dplyr, dominanceanalysis, forcats, Formula, ggplot2, knitr, lme4, parameters, performance, pscl, purrr, relaimpo, rlang, rmarkdown, stringr, systemfit, testthat (≥ 3.0.0), tidyr
License: GPL (≥ 3)
URL: https://github.com/jluchman/domir, https://jluchman.github.io/domir/
BugReports: https://github.com/jluchman/domir/issues
Encoding: UTF-8
RoxygenNote: 7.3.1
Config/testthat/edition: 3
VignetteBuilder: knitr
Language: en-US
NeedsCompilation: no
Packaged: 2024-05-04 23:09:05 UTC; josephluchman
Author: Joseph Luchman ORCID iD [aut, cre]
Maintainer: Joseph Luchman <jluchman@gmail.com>
Repository: CRAN
Date/Publication: 2024-05-04 23:20:02 UTC

Tools to Support Relative Importance Analysis

Description

Methods to apply dominance analysis-based relative importance analysis for predictive modeling functions.

Details

This package supports the determination of importance for inputs (i.e., independent variables, predictors, features, parameter estimates; called 'names' in the package) using dominance analysis (Azen & Budescu, 2004; Budescu, 1993).

Dominance analysis resolves the indeterminancy of ascribing the value returned by a predictive modeling function to inputs/names when it is not possible to do so analytically. The most common use case for the application of dominance analysis is in comparing inputs/names in terms of their contribution to a predictive model's fit statistic or metric.

Dominance analysis is a common, and generally well accepted, method for determining the relative importance of inputs/names that is, in part, a conceptual extension of the well-known Shapley value decomposition (e.g., Grömping, 2007; Lipovetsky & Conklin, 2001).

Author(s)

Joseph Luchman jluchman@gmail.com

References

Dominance analysis supporting formula-based modeling functions

Description

Computes dominance statistics for predictive modeling functions that accept a formula.

Usage

domin(
  formula_overall,
  reg,
  fitstat,
  sets = NULL,
  all = NULL,
  conditional = TRUE,
  complete = TRUE,
  consmodel = NULL,
  reverse = FALSE,
  ...
)

Arguments

formula_overall

An object of class formula or that can be coerced to class formula for use in the modeling function in reg. The terms on the right hand side of this formula are used as separate entries to the dominance analysis.

A valid formula_overall entry is necessary, even if only submitting entries in sets, to define a valid left hand side of the prediction equation (see examples). The function called in reg must accept one or more responses on the left hand side.

reg

A function implementing the predictive (or "reg"ression) model called.

String function names (e.g., "lm"), function names (e.g., lm), or anonymous functions (e.g., function(x) lm(x)) are acceptable entries. This argument's contents are passed to do.call and thus any function call do.call would accept is valid.

The predictive model in reg must accept a formula object as its first argument or must be adapted to do so with a wrapper function.

fitstat

List providing arguments to call a fit statistic extracting function (see details). The fitstat list must be of at least length two.

The first element of fitstat must be a function implementing the fit statistic extraction. String function names (e.g., "summary"), function names (e.g., summary), or anonymous functions (e.g., function(x) summary(x)) are acceptable entries. This element's contents are passed to do.call and thus any function call do.call would accept is valid.

The second element of fitstat must be the named element of the list or vector produced by the fit extractor function called in the first element of fitstat. This element must be a string (e.g., "r.squared").

All list elements beyond the second are submitted as additional arguments to the fit extractor function call.

The fit statistic extractor function in the first list element of fitstat must accept the model object produced by the predictive modeling function in reg as its first argument or be adapted to do so with a wrapper function.

The fit statistic produced must be scalar valued (i.e., vector of length 1).

sets

A list with each element comprised of vectors containing variable/factor names or formula coercible strings.

Each separate list element-vector in sets is concatenated (when the list element-vector is of length > 1) and used as an entry to the dominance analysis along with the terms in formula_overall.

all

A vector of variable/factor names or formula coercible strings. The entries in this vector are concatenated (when of length > 1) but are not used in the dominance analysis. Rather the value of the fit statistic associated with these terms is removed from the dominance analysis; this vector is used like a set of covariates.

The entries in all are removed from and considered an additional component that explains the fit metric. As a result, the general dominance statistics will no longer sum to the overall fit metric and the standardized vector will no longer sum to 1.

conditional

Logical. If FALSE then conditional dominance matrix is not computed.

If conditional dominance is not desired as an importance criterion, avoiding computing the conditional dominance matrix can save computation time.

complete

Logical. If FALSE then complete dominance matrix is not computed.

If complete dominance is not desired as an importance criterion, avoiding computing complete dominance designations can save computation time.

consmodel

A vector of variable/factor names, formula coercible strings, or other formula terms (i.e., 1 to indicate an intercept). The entries in this vector are concatenated (when of length > 1) and, like the entries of all, are not used in the dominance analysis; this vector is used as an adjustment to the baseline value of the overall fit statistic.

The use of consmodel changes the interpretation of the the general and conditional dominance statistics. When consmodel is used, the general and conditional dominance statistics are reflect the difference between the constant model and the overall fit statistic values.

Typical usage of consmodel is to pass "1" to set the intercept as the baseline and control for its value when the baseline model's fit statistic value is not 0 (e.g., if using the AIC or BIC as a fit statistic; see examples).

As such, this vector is used to set a baseline for the fit statistic when it is non-0.

reverse

Logical. If TRUE then standardized vector, ranks, and complete dominance designations are reversed in their interpretation.

This argument should be changed to TRUE if the fit statistic used decreases with better fit to the data (e.g., AIC, BIC).

...

Additional arguments passed to the function call in the reg argument.

Details

domin automates the computation of all possible combination of entries to the dominance analysis (DA), the creation of formula objects based on those entries, the modeling calls/fit statistic capture, and the computation of all the dominance statistics for the user.

domin accepts only a "deconstructed" set of inputs and "reconstructs" them prior to formulating a coherent predictive modeling call.

One specific instance of this deconstruction is in generating the number of entries to the DA. The number of entries is taken as all the terms from formula_overall and the separate list element vectors from sets. The entries themselves are concatenated into a single formula, combined with the entries in all, and submitted to the predictive modeling function in reg. Each different combination of entries to the DA forms a different formula and thus a different model to estimate.

For example, consider this domin call:

domin(y ~ x1 + x2, lm, list(summary, "r.squared"), sets = list(c("x3", "x4")), all = c("c1", "c2"), data = mydata))

This call records three entries and results in seven (i.e., 2^3 - 1) different combinations:

  1. x1

  2. x2

  3. x3, x4

  4. x1, x2

  5. x1, x3, x4

  6. x2, x3, x4

  7. x1, x2, x3, x4

domin parses formula_overall to obtain all the terms in it and combines them with sets. When parsing formula_overall, only the processing that is available in the stats package is applied. Note that domin is not programmed to process terms of order > 1 (i.e., interactions/products) appropriately (i.e., only include in the presence of lower order component terms). domin also does not allow offset terms.

From these combinations, the predictive models are constructed and called. The predictive model call includes the entries in all, applies the appropriate formula, and reconstructs the function itself. The seven combinations above imply the following series of predictive model calls:

  1. lm(y ~ x1 + c1 + c2, data = mydata)

  2. lm(y ~ x2 + c1 + c2, data = mydata)

  3. lm(y ~ x3 + x4 + c1 + c2, data = mydata)

  4. lm(y ~ x1 + x2 + c1 + c2, data = mydata)

  5. lm(y ~ x1 + x3 + x4 + c1 + c2, data = mydata)

  6. lm(y ~ x2 + x3 + x4 + c1 + c2, data = mydata)

  7. lm(y ~ x1 + x2 + x3 + x4 + c1 + c2, data = mydata)

It is possible to use a domin with only sets (i.e., no IVs in formula_overall; see examples below). There must be at least two entries to the DA for domin to run.

All the called predictive models are submitted to the fit extractor function implied by the entries in fitstat. Again applying the example above, all seven predictive models' objects would be individually passed as follows:

summary(lm_obj)["r.squared"]

where lm_obj is the model object returned by lm.

The entries to fitstat must be as a list and follow a specific structure: list(fit_function, element_name, ...)

fit_function

First element and function to be applied to the object produced by the reg function

element_name

Second element and name of the element from the object returned by fit_function to be used as a fit statistic. The fit statistic must be scalar-valued/length 1

...

Subsequent elements and are additional arguments passed to fit_function

In the case that the model object returned by reg includes its own fit statistic without the need for an extractor function, the user can apply an anonymous function following the required format to extract it.

Value

Returns an object of class "domin". An object of class "domin" is a list composed of the following elements:

General_Dominance

Vector of general dominance statistics.

Standardized

Vector of general dominance statistics normalized to sum to 1.

Ranks

Vector of ranks applied to the general dominance statistics.

Conditional_Dominance

Matrix of conditional dominance statistics. Each row represents a term; each column represents an order of terms.

Complete_Dominance

Logical matrix of complete dominance designations. The term represented in each row indicates dominance status; the terms represented in each columns indicates dominated-by status.

Fit_Statistic_Overall

Value of fit statistic for the full model.

Fit_Statistic_All_Subsets

Value of fit statistic associated with terms in all.

Fit_Statistic_Constant_Model

Value of fit statistic associated with terms in consmodel.

Call

The matched call.

Subset_Details

List containing the full model and descriptions of terms in the full model by source.

Notes

domin is an R port of the Stata command with the same name (see Luchman, 2021).

domin has been superseded by domir.

References

Luchman, J. N. (2021). Relative importance analysis in Stata using dominance analysis: domin and domme. The Stata Journal, 21, 2. doi: 10.1177/1536867X211025837.

Examples

## Basic linear model with r-square

domin(mpg ~ am + vs + cyl, 
  lm, 
  list("summary", "r.squared"), 
  data = mtcars)


## Linear model including sets

domin(mpg ~ am + vs + cyl, 
  lm, 
  list("summary", "r.squared"), 
  data = mtcars, 
  sets = list(c("carb", "gear"), c("disp", "wt")))


## Multivariate linear model with custom multivariate r-square function 
## and all subsets variable

Rxy <- function(obj, names, data) {
   return(list("r2" = cancor(predict(obj), 
       as.data.frame(mget(names, as.environment(data))))[["cor"]][1]^2)) 
       }
       
domin(cbind(wt, mpg) ~ vs + cyl + am, 
  lm, 
  list(Rxy, "r2", c("mpg", "wt"), mtcars), 
  data = mtcars, 
  all = c("carb"))


## Sets only

domin(mpg ~ 1, 
  lm, 
  list("summary", "r.squared"), 
  data = mtcars, 
  sets = list(c("am", "vs"), c("cyl", "disp"), c("qsec", "carb")))
  
## Constant model using AIC

domin(mpg ~ am + carb + cyl, 
  lm, 
  list(function(x) list(aic = extractAIC(x)[[2]]), "aic"), 
  data = mtcars, 
  reverse = TRUE, consmodel = "1")

Dominance analysis meta-function that returns scalar

Description

Internal dominance analysis computation function assuming scalar or vector of length 1 returned value.

Not intended to be called by the user.

Usage

dominance_scalar(
  function2call,
  args_list,
  value_w_all_names,
  do_cdl,
  do_cpt,
  reverse,
  cluster,
  progress
)

Dominance analysis methods

Description

Parses input object to obtain list of names, determines all required combinations of subsets of the name list, submits name list subsets to a function as the input type, and computes dominance decomposition statistics based on the returned values from the function.

Usage

domir(.obj, ...)

## S3 method for class 'formula'
domir(
  .obj,
  .fct,
  .set = NULL,
  .wst = NULL,
  .all = NULL,
  .adj = FALSE,
  .cdl = TRUE,
  .cpt = TRUE,
  .rev = FALSE,
  .cst = NULL,
  .prg = FALSE,
  ...
)

## S3 method for class 'formula_list'
domir(
  .obj,
  .fct,
  .set = NULL,
  .wst = NULL,
  .all = NULL,
  .adj = FALSE,
  .cdl = TRUE,
  .cpt = TRUE,
  .rev = FALSE,
  .cst = NULL,
  .prg = FALSE,
  ...
)

Arguments

.obj

A formula or formula_list.

Parsed to produce list of names. Combinations of subsets the name list are sapply-ed to .fct.

The name list subsets submitted to .fct are formatted to be of the same class as .obj and are submitted to .fct as the first, unnamed argument.

...

Passes arguments to other methods during method dispatch; passes arguments to the function in .fct during function execution.

.fct

A function or string function name.

Applied to all subsets of elements as received from .obj. Must return a length 1/scalar, numeric, atomic vector.

.set

A list.

Must be comprised of elements of the same class as .obj. Elements of the list can be named.

.wst

Not yet used.

.all

A formula or formula_list.

Must be the same class as .obj.

.adj

Logical.

If TRUE then a model including only an intercept is submitted to .fct and the value returned is subtracted from the values returned from all subsets in the dominance analysis.

.cdl

Logical.

If FALSE then conditional dominance matrix is not computed.

.cpt

Logical.

If FALSE then complete dominance matrix is not computed.

.rev

Logical.

If TRUE then standardized vector, ranks, and complete dominance designations are reversed in their interpretation.

.cst

Object of class c("SOCKcluster", "cluster") from parallel-package.

When non-NULL, will alter the method for collecting values from all combinations of names from using sapply to parallel::parSapply.

.prg

Logical.

If TRUE then a progress bar is displayed during collection of values to indicate progress.

Details

Element Parsing

.objs is parsed into a name list that is used to determine the required number of combinations of subsets of the name list included the dominance analysis. How the name list is obtained depends on .obj's class.

formula

The formula creates a name list using all terms in the formula. The terms are obtained using terms.formula. All processing that is normally applied to the right hand side of a formula is implemented (see formula).

A response/left hand side is not required but, if present, is included in all formulas passed to .fct.

formula_list

The formula_list creates a name list out of response-term pairs. The terms are obtained using terms.formula applied to each individual formula in the list.

Additional Details

By default, names obtained from .obj are all considered separate 'value-generating names' with the same priority. Each value-generating name will be a separate element when computing combination subsets and will be compared to all other value-generating names.

formulas and formula_list elements are assumed to have an intercept except if explicitly removed with a - 1 in the formula(s) in .obj. If removed, the intercept will be removed in all formula(s) in each sapply-ed subset to .fct.

If offsets are included, they are passed, like intercepts, while sapply-ing subsets to .fct.

Changing Element Parsing

All methods' default behavior that considers all value-generating names to be of equal priority can be overriden using .set and .all arguments.

Names in .set and .all must also be present in .obj.

.set

.set binds together value-generating names such that they are of equal priority and are never separated when submitted to .fct. Thus, the elements in .set bound together contribute jointly to the returned value and are considered, effectively, a single value-generating name.

If list elements in .set are named, this name will be used in all returned results as the name of the set of value-generating names bound together.

.set thus considers the value-generating names an 'inseparable set' in the dominance analysis and are always included or excluded together.

.all

.all gives immediate priority to value-generating names. The value-generating names in .all are bound together, are ascribed their full amount of the returned value from .fct, and are not adjusted for contribution of other value-generating names.

The value of .fct ascribed to the value-generating names bound together in .all is returned separately from, and not directly compared to, the other value-generating names.

The formula method for .all does not allowthe submitted formula to have a left hand side.

.all includes the value-generating names in 'all subsets' submitted to the dominance analysis which effectively removes the value associated with this set of names.

.adj

.adj indicates that an intercept-only model should be supplied to .fct. This intercept-only subset is given most immediate priority and the value of .fct ascribed to it is removed from all other value-generating names and sets including those in .all.

The formula method will submit an intercept-only formula to .fct. The formula_list method creates a separate, intercept-only subset for each of the formulas in the list. Both the formula and formula_list methods will respect the user's removal of an intercept and or inclusion of an offset.

.adj then 'adjusts' the returned value for a non-0 value-returning null model when no value generating names are included. This is often useful when a predictive model's fit metric is not 0 when no predictive factors are included in the model.

Additional Details

All methods submit combinations of names as an object of the same class as .obj. A formula in .obj will submit all combinations of names as formulas to .fct. A formula_list in .obj will submit all combinations of subsets of names as formula_lists to .fct. In the case that .fct requires a different class (e.g., a character vector of names, a Formula::Formula see fmllst2Fml) the subsets of names will have to be processed in .fct to obtain the correct class.

The all subsets of names will be submitted to .fct as the first, unnamed argument.

.fct as Analysis Pipeline

.fct is expected to be a complete analysis pipeline that receives a subset of names of the same class as .obj and uses these names in the class as submitted to generate a returned value of the appropriate type to dominance analyze. Typically, the returned value is a scalar fit statistic/metric extracted from a predictive model.

At current, only atomic (i.e., non-list), numeric scalars (i.e., vectors of length 1) are allowed as returned values.

The .fct argument is strict about names submitted and returned value requirements for functions used. A series of checks to ensure the submitted names and returned value adhere to these requirements. The checks include whether the .obj can be submitted to .fct without producing an error and whether the returned value from .fct is a length 1, atomic, numeric vector. In most circumstances, the user will have to make their own named or anonymous function to supply as .fct to satisfy the checks.

Value

Returns an object of class "domir" composed of:

General_Dominance

Vector of general dominance values.

Standardized

Vector of general dominance values normalized to sum to 1.

Ranks

Vector of ranks applied to the general dominance values.

Conditional_Dominance

Matrix of conditional dominance values. Each row represents an element in .obj; each column represents a number of elements from .obj in a subset.

Complete_Dominance

Matrix of proportions of subsets where the name in the row has a larger value than the name in the column. The se proportions determine complete dominance when a value of 1 or 0.

Value

Value returned by .fct with all elements (i.e., from .obj, .all, and .adj.

Value_All

Value of .fct associated with elements included in .all; when elements are in .adj, will be adjusted for Value_Adjust.

Value_Adjust

Value of .fct associated with elements in .adj.

Call

The matched call.

Notes

formula method

Prior to version 1.1.0, the formula method allowed a formula to be submitted to .adj. Submitting an intercept-only formula as opposed to a logical has been depreciated and submitting a formula with more than an intercept is defunct.

The formula and formula_list methods can be used to pass responses, intercepts, and offsets to all combinations of names. If the user seeks to include other model components integral to estimation (i.e., a random effect term in lme4::glmer()) include them as update to the submitted formula or formula_list imbedded in .fct.

Second-order or higher terms (i.e., interactions like ~ a*b) are parsed by default but not used differently from first-order terms for producing subsets. The values ascribed to such terms may not be valid unless the user ensures that second-order and higher terms are used appropriately in .fct.

Examples

## Linear model returning r-square
lm_r2 <-
  function(fml, data) {
    lm_res <- lm(fml, data = data)
    summary(lm_res)[["r.squared"]]
 }

domir(mpg ~ am + vs + cyl, lm_r2, data = mtcars)


## Linear model including set
domir(
  mpg ~ am + vs + cyl + carb + gear + disp + wt,
  lm_r2,
  .set = list(~ carb + gear, ~ disp + wt),
  data = mtcars
)


## Multivariate regression with multivariate r-square and
## all subsets variable
mlm_rxy <-
  function(fml, data, dvnames) {
    mlm_res <- lm(fml, data = data)
    mlm_pred <- predict(mlm_res)
    cancor(mlm_pred, data[dvnames])$cor[[1]]^2
  }

domir(
  cbind(wt, mpg) ~ vs + cyl + am + carb,
  mlm_rxy,
  .all = ~ carb,
  data = mtcars,
  dvnames = c("wt", "mpg")
)


## Named sets
domir(
  mpg ~ am + gear + cyl + vs + qsec + drat,
  lm_r2,
  data = mtcars,
  .set =
    list( 
      trns = ~ am + gear,
      eng = ~ cyl + vs, 
      misc = ~ qsec + drat
    )
)


## Linear model returning AIC
lm_aic <-
  function(fml, data) {
    lm_res <- lm(fml, data = data)
    AIC(lm_res)
 }

domir(
  mpg ~ am + carb + cyl,
  lm_aic,
  .adj = TRUE,
  .rev = TRUE,
  data = mtcars
 )


## 'systemfit' with 'formula_list' method returning AIC
if (requireNamespace("systemfit", quietly = TRUE)) {
  domir(
    formula_list(mpg ~ am + cyl + carb, qsec ~ wt + cyl + carb),
    function(fml) {
      res <- systemfit::systemfit(fml, data = mtcars)
      AIC(res)
    },
    .adj = TRUE, .rev = TRUE
  )
}

Translate formula_list into Formula::Formula

Description

Translates formula_list objects into a Formula::Formula

Usage

fmllst2Fml(fmllst, drop_lhs = NULL)

Arguments

fmllst

A formula_list classed object.

drop_lhs

An integer vector.

Used as a selection vector to remove left hand side names prior to generating the Formula object. This vector must be composed of integers (e.g., 1L and not 1).

This is useful for some Formulas that do not have a separate LHS for each LHS model part (e.g., pscl::zeroinfl) but are required to have separte LHS parts by formula_list.

Value

A Formula::Formula object.

A list composed of formulas

Description

Defines a list object composed of formulas. The purpose of this class of object is to impose structure of the list to ensure that it can be used to obtain RHS-LHS pairs and will be able to be parsed in domir.

Usage

formula_list(...)

Arguments

...

formulas, possibly named

Details

The formula_list requires that each element of the list is a formula and that each formula is unique with a different, non-NULL dependent variable/response.

Value

A list of class formula_list.

Internal formula parsing function

Description

Internal formula parsing function to facilitate re-construction of a formula using reformulate()

Not intended to be called by the user.

Usage

formula_parse(.obj)

Print method for domin

Description

Reports formatted results from domin class object.

Usage

## S3 method for class 'domin'
print(x, ...)

Arguments

x

an object of class "domin".

...

further arguments passed to or from other methods. Not used currently.

Details

The print method for class domin objects reports out the following results:

The domin print method alters dimension names for readability and they do not display as stored in the original domin object.

Value

The "domin" object with altered column and row names for conditional and complete dominance results as displayed in the console.

Print method for domir

Description

Reports formatted results from domir class object.

Usage

## S3 method for class 'domir'
print(x, ...)

Arguments

x

an object of class "domir".

...

further arguments passed to print.default.

Details

The print method for class domir objects reports out the following results:

The domir print method alters dimension names for readability and they do not display as stored in the domir object.

Value

The submitted "domir" object, invisibly.

Summary method for domin

Description

Reports dominance designation results from the domin class object.

Usage

## S3 method for class 'domin'
summary(object, ...)

Arguments

object

an object of class "domin".

...

further arguments passed to or from other methods. Not used currently.

Details

The summary method for class domin is used for obtaining the strongest dominance designations (i.e., general, conditional, or complete) among the independent variables.

Value

The originally submitted "domin" object with an additional Strongest_Dominance element added.

Strongest_Dominance

Matrix comparing the independent variable in the first row to the independent variable in the third row. The second row denotes the strongest designation between the two independent variables.

Summary method for domir

Description

Reports dominance designation results from the domir class object.

Usage

## S3 method for class 'domir'
summary(object, ...)

Arguments

object

an object of class "domir".

...

further arguments passed to or from other methods. Not used currently.

Details

The summary method for class domir objects is used for obtaining the strongest dominance designations (i.e., general, conditional, or complete) among all pairs of dominance analyzed elements.

Value

The submitted "domir" object with an additional Strongest_Dominance element added.

Strongest_Dominance

Matrix comparing the element in the first row to the element in the third row. The second row denotes the strongest designation between the two elements.