Package {rwa}

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

Plot the rescaled importance values from the output of rwa()

Description

Pass the output of rwa() and plot a bar chart of the rescaled importance values. Signs are always calculated and taken into account, which is equivalent to setting the applysigns argument to TRUE in rwa().

Usage

plot_rwa(rwa)

Arguments

Examples

library(ggplot2)
# Use a smaller sample for faster execution
diamonds_small <- diamonds[sample(nrow(diamonds), 1000), ]
diamonds_small %>%
  rwa(outcome = "price",
      predictors = c("depth","carat", "x", "y", "z"),
      applysigns = TRUE) %>%
  plot_rwa()

Remove any columns where all the values are missing

Description

Pass a data frame and returns a version where all columns made up of entirely missing values are removed.

Usage

remove_all_na_cols(df)

Arguments

Details

This is used within rwa().

Create a Relative Weights Analysis (RWA)

Description

This function creates a Relative Weights Analysis (RWA) and returns a list of outputs. RWA provides a heuristic method for estimating the relative weight of predictor variables in multiple regression, which involves creating a multiple regression with on a set of transformed predictors which are orthogonal to each other but maximally related to the original set of predictors. rwa() is optimised for dplyr pipes and shows positive / negative signs for weights.

Usage

rwa(
  df,
  outcome,
  predictors,
  applysigns = FALSE,
  method = "auto",
  sort = TRUE,
  bootstrap = FALSE,
  n_bootstrap = 1000,
  conf_level = 0.95,
  focal = NULL,
  comprehensive = FALSE,
  include_rescaled_ci = FALSE,
  use = "pairwise.complete.obs",
  weight = NULL
)

Arguments

Details

rwa() produces raw relative weight values (epsilons) as well as rescaled weights (scaled as a percentage of predictable variance) for every predictor in the model. Signs are added to the weights when the applysigns argument is set to TRUE. See https://www.scotttonidandel.com/rwa-web for the original implementation that inspired this package.

This function is a wrapper around rwa_multiregress() and rwa_logit(), automatically selecting the appropriate method based on the outcome variable or the method argument.

In brief, for the two missing-data and weighting arguments:

• Without weight, missing values are handled by use, which defaults to pairwise deletion when correlating predictors.

• With weight, the analysis always uses complete cases across the outcome, the predictors, and the weight. Weighted pairwise deletion is not implemented, so use does not change a weighted result.

• In both cases, rows with a missing outcome are dropped first.

Use weights when the analysis should represent a target population rather than the achieved sample. Comparing weighted with unweighted results is informative: a large difference indicates that sample composition matters.

Multiple-regression estimates require a finite joint correlation matrix. Its smallest eigenvalue must be at least minus sqrt(.Machine$double.eps) * max(1, max(abs(eigenvalues))). The predictor block must have strictly positive computed eigenvalues and the transformation must be solvable. No additional conditioning cutoff is imposed on previously estimable models; highly correlated predictors can still yield sensitive estimates. Calculated R-squared must not exceed one by more than sqrt(.Machine$double.eps); the fit is checked separately because small matrix errors can be amplified by nearly collinear predictors. An exactly fitted outcome (a singular joint matrix) is allowed when the predictor block is positive definite. Invalid matrices, constant variables, and insufficient observations cause informative errors; variables are not dropped and matrices are not silently repaired.

Weighted analysis is observation-weighted RWA. Bootstrap intervals use independent, identically distributed (iid) individual-row resampling, with each row's original weight carried along, not sampling proportional to weights. Rows with missing outcomes are removed before resampling; other missing-data filters are applied within each sample, preserving the outcome-complete sampling frame. A degenerate sample stops the bootstrap with an error: samples are not skipped, retried, or allowed to lose predictors. Clusters, strata, and replicate-weight survey designs are not supported; a weight column alone does not provide general complex-survey variance. See vignette("weighted-missing-data") for examples and limitations.

Value

rwa() returns a list of outputs, as follows:

• predictors: character vector of names of the predictor variables used.

• rsquare: the rsquare value of the regression model (multiple regression only).

• result: the final output of the importance metrics (sorted by Rescaled.RelWeight in descending order by default).

  • The Rescaled.RelWeight column sums up to 100.

  • The Sign column indicates whether a predictor is positively or negatively correlated with the outcome.

  • When bootstrap = TRUE, includes confidence interval columns for raw weights.

  • When bootstrap = TRUE, Random.Diff.CI.Lower/Random.Diff.CI.Upper give the interval for the difference between each predictor's weight and the weight of a randomly generated variable, and Raw.Significant is TRUE when Random.Diff.CI.Lower is above zero. Significance is assessed this way, and not from the interval around the weight itself, because raw relative weights are non-negative: an unrelated predictor still receives a small positive weight, so an interval around it would almost always exclude zero. Comparing each weight to that of a randomly generated variable is the approach suggested by Tonidandel, LeBreton and Johnson (2009; doi:10.1037/a0017735) as a way to judge whether a weight exceeds what chance alone would produce. The Raw.Significant cutoff applied here is directional: a predictor is significant only when it exceeds the random variable (Random.Diff.CI.Lower > 0), because an interval lying entirely below zero indicates the predictor performed worse than noise, which is not evidence of importance in either direction.

  • Rescaled weight CIs are available via include_rescaled_ci = TRUE but not recommended for inference.

• n: complete-case observation count for the selected analysis variables (and weight, if supplied). Unweighted pairwise correlations may use more observations than this conservative count.

• n_weighted: weighted results only; sum of original weights after all analysis filters. This is a population-size estimate only for appropriately calibrated weights and the retained population scope.

• n_effective: weighted results only; Kish's unequal-weighting effective sample size, (sum(w)^2) / sum(w^2), calculated using scaled weights for numerical stability. This diagnostic ignores clustering, stratification, and weight/outcome relationships; it is not model degrees of freedom or the exact precision of RWA.

• bootstrap: bootstrap results (only present when bootstrap = TRUE), containing:

  • ci_results: confidence intervals for weights

  • boot_object: raw bootstrap object for advanced analysis

  • n_bootstrap: number of bootstrap samples used

• lambda: lambda matrix from the RWA calculation.

• RXX: Correlation matrix of all the predictor variables against each other. Not available for logistic regression.

• RXY: Correlation values of the predictor variables against the outcome variable. Not available for logistic regression.

See Also

plot_rwa() for plotting results, rwa_multiregress() and rwa_logit() for the underlying implementations.

Examples

library(ggplot2)
# Basic RWA (results sorted by default)
rwa(diamonds, "price", c("depth", "carat"))

# RWA without sorting (preserves original predictor order)
rwa(diamonds, "price", c("depth", "carat"), sort = FALSE)

# Plot results using plot_rwa()
diamonds |>
  rwa("price", c("depth", "carat", "x", "y")) |>
  plot_rwa()


# For faster examples, use a subset of data for bootstrap
diamonds_small <- diamonds[sample(nrow(diamonds), 1000), ]

# RWA with different missing data handling
# Use complete.obs for listwise deletion
rwa(diamonds_small, "price", c("depth", "carat"), use = "complete.obs")

# RWA with weights
diamonds_small$sample_weight <- runif(nrow(diamonds_small), 0.5, 2)
rwa(diamonds_small, "price", c("depth", "carat"), weight = "sample_weight")

# RWA with bootstrap confidence intervals (raw weights only)
rwa(diamonds_small, "price", c("depth", "carat"),
    bootstrap = TRUE, n_bootstrap = 100)

# Include rescaled weight CIs (use with caution for inference)
rwa(diamonds_small, "price", c("depth", "carat"),
    bootstrap = TRUE, include_rescaled_ci = TRUE, n_bootstrap = 100)

# Comprehensive bootstrap analysis with focal variable
result <- rwa(diamonds_small, "price", c("depth", "carat", "table"),
              bootstrap = TRUE, comprehensive = TRUE, focal = "carat",
              n_bootstrap = 100)
# View confidence intervals
result$bootstrap$ci_results


# Based on logistic regression (auto-detected from binary outcome)
diamonds$IsIdeal <- as.numeric(diamonds$cut == "Ideal")
rwa(diamonds, "IsIdeal", c("depth", "carat"))

Create a Relative Weights Analysis with logistic regression

Description

This function performs Relative Weights Analysis (RWA) for binary outcome variables using logistic regression. RWA provides a method for estimating the relative importance of predictor variables by transforming them into orthogonal variables while preserving their relationship to the outcome. This implementation follows Johnson (2000) for logistic regression.

Usage

rwa_logit(df, outcome, predictors, applysigns = FALSE)

Arguments

Value

rwa_logit() returns a list of outputs, as follows:

• predictors: character vector of names of the predictor variables used.

• rsquare: the pseudo R-squared value (sum of epsilon weights) for the logistic regression model.

• result: the final output of the importance metrics.

  • The Rescaled.RelWeight column sums up to 100.

  • The Sign column indicates whether a predictor is positively or negatively associated with the outcome.

• n: indicates the number of observations used in the analysis.

• lambda: the Lambda transformation matrix from the analysis.

Examples

# Create a binary outcome variable
mtcars_binary <- mtcars
mtcars_binary$high_mpg <- ifelse(mtcars$mpg > median(mtcars$mpg), 1, 0)

# Basic logistic RWA
result <- rwa_logit(
  df = mtcars_binary,
  outcome = "high_mpg",
  predictors = c("cyl", "disp", "hp", "wt")
)

# View the relative importance results
result$result

# With sign information
result_signed <- rwa_logit(
  df = mtcars_binary,
  outcome = "high_mpg",
  predictors = c("cyl", "disp", "hp", "wt"),
  applysigns = TRUE
)
result_signed$result

Create a Relative Weights Analysis (RWA)

Description

This function creates a Relative Weights Analysis (RWA) and returns a list of outputs. RWA provides a heuristic method for estimating the relative weight of predictor variables in multiple regression, which involves creating a multiple regression with on a set of transformed predictors which are orthogonal to each other but maximally related to the original set of predictors. rwa_multiregress() is optimised for dplyr pipes and shows positive / negative signs for weights.

Usage

rwa_multiregress(
  df,
  outcome,
  predictors,
  applysigns = FALSE,
  use = "pairwise.complete.obs",
  weight = NULL
)

Arguments

Details

rwa_multiregress() produces raw relative weight values (epsilons) as well as rescaled weights (scaled as a percentage of predictable variance) for every predictor in the model. Signs are added to the weights when the applysigns argument is set to TRUE. See https://www.scotttonidandel.com/rwa-web for the original implementation that inspired this package.

This is observation-weighted RWA when weight is provided, not a complex-survey variance estimator. See rwa() for joint-matrix and predictor positive-definiteness tolerances, bootstrap sampling assumptions, and diagnostics. See vignette("weighted-missing-data") for worked examples.

Value

rwa_multiregress() returns a list of outputs, as follows:

• predictors: character vector of names of the predictor variables used.

• rsquare: the rsquare value of the regression model.

• result: the final output of the importance metrics.

  • The Rescaled.RelWeight column sums up to 100.

  • The Sign column indicates whether a predictor is positively or negatively correlated with the outcome.

• n: complete-case observation count for the selected variables and weight, if supplied. Unweighted pairwise correlations may use more observations.

• n_weighted: weighted results only; sum of original weights after outcome, missing-weight, and predictor-completeness filters. Population-size meaning requires appropriately calibrated weights and retained population scope.

• n_effective: weighted results only; Kish's unequal-weighting effective sample size, (sum(w)^2) / sum(w^2), evaluated using scaled weights. This is not model degrees of freedom or exact RWA precision and ignores clustering, stratification, and weight/outcome relationships.

• lambda: the transformation matrix that maps the original correlated predictors to orthogonal variables while preserving their relationship to the outcome. Used internally to compute relative weights.

• RXX: Correlation matrix of all the predictor variables against each other.

• RXY: Correlation values of the predictor variables against the outcome variable.

Examples

# Basic multiple regression RWA
result <- rwa_multiregress(
  df = mtcars,
  outcome = "mpg",
  predictors = c("cyl", "disp", "hp", "wt")
)

# View the relative importance results
result$result

# With sign information
result_signed <- rwa_multiregress(
  df = mtcars,
  outcome = "mpg",
  predictors = c("cyl", "disp", "hp", "wt"),
  applysigns = TRUE
)
result_signed$result

# Using listwise deletion for missing data
rwa_multiregress(
  df = mtcars,
  outcome = "mpg",
  predictors = c("cyl", "disp"),
  use = "complete.obs"
)

# With observation weights
mtcars_weighted <- mtcars
mtcars_weighted$w <- runif(nrow(mtcars), 0.5, 2)
rwa_multiregress(
  df = mtcars_weighted,
  outcome = "mpg",
  predictors = c("cyl", "disp"),
  weight = "w"
)