Author: Martin Chan
Date: 2026-01-20

# Evaluating the Tonidandel & LeBreton Relative Weights Analysis Method

#### Martin Chan

#### 2026-01-20

# Evaluation of the Tonidandel & LeBreton Relative Weights Analysis Method

Relative Weights Analysis (RWA), as articulated by Scott Tonidandel and James LeBreton, is a statistical technique designed to determine the relative importance of predictor variables in a regression model, especially when those predictors are intercorrelated (multicollinearity). In essence, RWA partitions the model’s total explained variance (_R_²) among the predictors to show how much each contributes to predicting the outcome. This method was inspired by earlier work on variance partitioning (e.g. Lindeman et al., 1980) and addresses shortcomings of traditional regression metrics under multicollinearity. Below we evaluate the current validity of RWA for handling multicollinearity, compare it to other methods (highlighting where it excels or falls short), and discuss practical considerations and scenarios for its use.

## What is Relative Weights Analysis and How Does it Address Multicollinearity?

Relative Weights Analysis (RWA) (also known as relative importance analysis) is a technique that transforms the original predictors into a new set of orthogonal (uncorrelated) variables and uses them to apportion variance in the outcome back to each predictor. The result is a set of weights for each predictor that sum up to the model’s total R² (explained variance). In other words, each weight represents the portion of outcome variance uniquely attributable to that predictor, taking into account its overlap with other predictors. This definition of “relative importance” considers a predictor’s contribution by itself and in combination with others, giving a more holistic measure than a simple regression coefficient.

### Why is this useful for multicollinearity?

In standard multiple regression, when predictors are highly correlated, the usual indicators of importance (like standardized beta coefficients or p-values) can be misleading. Regression coefficients may become unstable, change signs, or appear nonsignificant due to shared variance among predictors. For example, a predictor that is strongly correlated with the outcome might get a near-zero or even negative beta if another collinear predictor “soaks up” the variance when both are in the model. Tonidandel & LeBreton (2011) note that commonly used indices “fail to appropriately partition variance to the predictors when they are correlated”. RWA directly tackles this by partitioning the overlapping variance in a principled way: it attributes the shared (collinear) variance between predictors to those predictors in proportion to their structure with the outcome. In effect, RWA untangles multicollinearity to show each variable’s true impact. This means that even if two predictors are strongly correlated with each other, each can still receive a substantial relative weight if each contributes to predicting Y. Crucially, the weights are all non-negative and sum to R², making them interpretable as a percentage of explained variance (e.g. a weight of 0.30 in a model with R²=0.60 means that predictor accounts for 0.30/0.60 = 50% of the explained variance).

In technical terms, the Johnson (2000) algorithm for RWA works as follows: it performs an eigenvalue decomposition of the predictor correlation matrix to create uncorrelated principal components, then regresses the outcome on these components. The resulting regression coefficients and component loadings are combined to compute each predictor’s share of variance in the outcome. This procedure yields weights virtually identical to what would be obtained by averaging a predictor’s incremental R² contribution over all possible subsets of predictors (the logic used in dominance analysis). However, RWA does this without brute-force search over subsets, which is why it’s computationally efficient. By using an orthogonal basis, RWA preserves the interpretability of the original predictors (each weight maps back to an original variable) while circumventing the multicollinearity problem in the model fitting step. Essentially, it achieves what a principal components regression might — decorrelating predictors — but then translates the result back into variance attributed to each original variable.

### Is RWA still a valid approach for evaluating predictor power under multicollinearity?

Yes – RWA remains a widely accepted and useful method for this purpose. It is specifically designed for situations with correlated predictors and is “particularly useful when predictors are correlated since it deals with issues of multicollinearity.”. Since its introduction, numerous studies have validated that RWA indeed gives a fair assessment of each variable’s importance even in high-correlation settings. In practice, RWA better partitions variance than standard regression: researchers applying it have found that it reveals important predictors that regression beta weights had obscured due to multicollinearity. For example, in one organizational study, a “serial tactics” variable appeared unimportant in a standard regression (its beta was non-significant because another variable was collinear), but the RWA showed it actually explained meaningful variance in the outcome, supporting its theoretical importance. This illustrates RWA’s value in preserving each predictor’s contribution.

That said, RWA is not a magic bullet that completely nullifies all multicollinearity concerns (more on its limitations later). If two predictors are essentially measuring the same underlying construct, RWA will correctly indicate that together they contribute to prediction, but it will split the credit between them, potentially making each look less important individually. In extreme cases (e.g. r ≈ 0.98 between two variables), their individual weights might be small and nearly equal, because each one’s predictive power is redundant with the other. This is statistically appropriate – it reflects that one alone can do the job of both – but a user must recognize that the pair as a whole may be very important even if each alone has a modest weight. In short, RWA handles multicollinearity well in that it partitions variance consistently and more informatively than naive methods. It remains a valid and recommended approach for evaluating predictor contributions under multicollinearity, provided we interpret the results with the proper theoretical context (e.g. recognizing when two variables are essentially interchangeable measures of one factor).

## Strengths of RWA Relative to Other Methods

Because RWA was developed to address deficiencies in standard approaches, it has several strengths and advantages over other methods of gauging predictor importance:

### 1. Superior to Standard Regression Coefficients (under multicollinearity)

In a typical regression analysis, researchers often look at the magnitude and significance of standardized beta coefficients to judge importance. However, this can be very misleading when predictors are correlated. A variable’s beta reflects unique contribution holding others constant, which in presence of multicollinearity might severely underestimate a variable that shares variance with others. Tonidandel & LeBreton observed that many authors mistakenly labeled variables as “not meaningful” based on nonsignificant betas, when in fact those variables did explain variance in the criterion. RWA, by contrast, gives credit to a predictor for the variance it shares with the outcome jointly with other variables. This often reveals that a predictor has substantial importance even if its regression coefficient is suppressed by multicollinearity. Indeed, Courville & Thompson (2001) found cases where a predictor had near-zero beta but was actually one of the top contributors to R² – something RWA would clearly show (since the variable’s relative weight would be relatively large, reflecting its combined effect). In short, RWA is a more equitable and interpretable metric of importance than raw beta weights when predictors overlap. It considers both direct and indirect (shared) effects, whereas beta only reflects the direct unique portion. This makes RWA far superior to relying on p-values of coefficients or semi-partial correlations for assessing “which predictors matter” in correlated systems.

### 2. Better than Stepwise or Bivariate Ranking

Sometimes analysts try to circumvent multicollinearity by using stepwise regression or looking at bivariate correlations with the outcome. These approaches have drawbacks that RWA avoids. Stepwise methods will arbitrarily pick one of a set of collinear variables and drop the others, which might lead you to conclude the dropped variables are unimportant. In reality, they might be just as important, but their contribution was redundant with the chosen variable. RWA would show those collinear variables each have high relative weights (indicating they each could account for variance if considered). Unlike stepwise selection, RWA does not throw away information; it tells you how much each predictor contributes given the whole set. As Tonidandel & LeBreton caution, relative weights should not be used to select or eliminate variables – the correct model should be decided first, then RWA helps interpret it. Compared to simple bivariate correlations with Y, RWA is also superior. A high correlation may exaggerate a variable’s standalone importance, while a low one may hide a variable that acts in combination with others. RWA puts all predictors on a level playing field by evaluating them together. As one primer notes, if predictors are uncorrelated, RWA and simple squared correlations give the same ranking, but when predictors are correlated (the usual case), more “elaborate methods” like RWA are needed to properly assess importance. In essence, RWA automatically accounts for suppressor effects and synergy among predictors that simple correlations or stepwise methods can miss.

### 3. Advantages over Principal Component or Factor Approaches

A common strategy to handle multicollinearity is to perform a principal component analysis (PCA) or factor analysis on the predictors, then use those uncorrelated components in regression. While this addresses the numerical multicollinearity problem, it buries the identity of individual predictors – you end up with composite factors that are not as interpretable as the original variables. In contrast, RWA uses an orthogonalization behind the scenes but ultimately returns to the original predictor scale. Each predictor gets a weight in the same units of variance explained (e.g. an R² share). Thus, RWA retains interpretability: you can say “Variable X accounts for 20% of the explainable variance in Y,” which is straightforward. With PCA, you might find that a principal component is important, but that component might be a mix of several original variables – not as actionable or intuitive. Additionally, PCA-based regression typically still won’t tell you how much variance each original variable is responsible for; you would have to do additional calculations to map component importance back to variables. RWA essentially does that mapping for you (via the Johnson’s formula). So, RWA can be seen as a more direct way to get “interpretable principal components” importance. It’s worth noting that if predictors are extremely multicollinear due to measuring the same construct, one could combine them a priori (e.g. average them) to create a single predictor – but that is a decision outside the scope of statistical measures. RWA’s job is to measure contributions of the predictors as given, and it does so in a way that leverages techniques like PCA while keeping results in terms of the original features.

### 4. Comparable Outcome to Dominance Analysis, with Greater Speed and Extras

Dominance analysis (or Shapley value regression) is often considered a gold-standard for determining relative importance because it exhaustively considers every subset of predictors. RWA’s greatest achievement is that it produces almost the same result as dominance analysis, but far more efficiently. Monte Carlo research by LeBreton, Ployhart & Ladd (2004) found the rankings of predictors by Johnson’s relative weights were essentially the same as those by general dominance weights across a variety of conditions. The correlation between the two methods’ importance scores is typically >0.99 in simulations and real datasets. In fact, with only two predictors, it has been proven that Johnson’s RWA and the Shapley value exactly coincide. Thus, one doesn’t lose meaningful accuracy by using RWA. Meanwhile, the time saved is enormous: dominance analysis requires examining 2^p models (for p predictors). With p=10, that’s 1,024 subset regressions; with p=20, over 1 million; with p=30, over 1 billion subset models. This quickly becomes computationally infeasible.

Johnson’s RWA bypasses that combinatorial explosion by solving a set of equations instead. The difference is dramatic. For example, one practitioner noted that a model with 30 predictors would take “days to run” with Shapley regression, whereas RWA computes it “almost instantly” on a modern computer. RWA’s negligible computation time means you can include as many predictors as your theory and data allow (within reason) without worrying about algorithmic blow-up. Another strength is that RWA more easily provides analytical tools like confidence intervals and significance tests for weights. Because RWA has a closed-form solution, researchers like Johnson (2004) and Tonidandel et al. (2009) derived methods to estimate the standard errors of the weights (often using bootstrapping). This lets you test if a weight is significantly greater than zero (i.e. the predictor contributes significantly to R²) , something not straightforward in dominance analysis except via intensive bootstrapping. Tonidandel et al. (2009) even provided a technique to test if one predictor’s weight is significantly different from another’s by examining their bootstrap distributions. These statistical comparison capabilities are now built into tools like RWA Web. By contrast, dominance analysis typically requires custom resampling methods to assess variability. RWA is also easier to extend to other modeling contexts: for instance, Tonidandel & LeBreton (2010) showed how to apply a variant of RWA to logistic regression (where a traditional R² doesn’t exist, but one can use analogues) , and LeBreton & Tonidandel (2008) extended it to multivariate criterion (multiple outcomes) cases. Dominance analysis can be extended too, but it becomes even more computationally arduous in those settings. In summary, RWA gives you the benefits of a rigorous relative importance measure without the downsides of computational complexity, and it adds convenient features (like significance testing and adaptability to non-OLS models) that make it very practical for users.

### 5. Proven in Practice and Accessible

Another soft “strength” of RWA is that it has been embraced in various fields as a reliable tool. It’s not just a theoretical construct; many researchers have found it helpful for real data problems. For example, organizational psychologists use it to determine which employee or job factors are most important in predicting performance or satisfaction, without being misled by intercorrelations among those factors. Marketing scientists use it in “key driver analysis” to figure out which product attributes drive overall customer satisfaction, when those attributes ratings tend to move together. In fact, a 2017 tutorial calls relative weights analysis “a way of exploring the relative importance of predictors” and demonstrates its utility in psychological research scenarios with multicollinear predictors. Because of such uptake, there are now user-friendly software packages: an R package relaimpo (Grömping, 2006) and a newer one rwa implement Johnson’s method, and the aforementioned RWA Web tool provides a point-and-click interface. In other words, the method’s strengths have been recognized to the point that it’s readily available to analysts and doesn’t require hand-coding. This broad usage confirms that the method remains highly relevant and advantageous for analyzing predictor importance under multicollinearity.

## Limitations and Comparisons: Where RWA Falls Short or Other Methods Prevail

While RWA has many strengths, it is important to understand its limitations and how it compares to alternative methods in scenarios where it might not be the top choice. No single technique is best in all respects, and RWA is no exception. Key points to consider include:

### 1. Not a Replacement for Theory or Causal Insight

RWA is ultimately a descriptive, variance-partitioning tool. It tells us “how much of the prediction was attributable to X” but does not imply causation or policy. Tonidandel & LeBreton (2011) stress that relative weights “are not causal indicators and thus do not necessarily dictate a course of action”. For example, if one predictor has the highest weight, it means it was most important in the regression sense; it doesn’t automatically mean that changing that predictor will have the largest effect on the outcome (because causality and manipulability are separate issues). So RWA should be used to enhance interpretation of regression models, but decisions should still be guided by substantive theory. It aids theory building by correctly identifying which predictors matter more, which can refine theoretical models , but it cannot tell you why a predictor is important or if an unmeasured confounder is at play. In short, it supplements but does not replace the need for careful theoretical reasoning.

### 2. Dominance Analysis vs. RWA – a matter of precision vs. practicality:

Dominance analysis (DA) is an alternative that, in principle, provides even more information than RWA. Where RWA gives each predictor one number (its weight), DA breaks down the predictor’s contributions in every subset of predictors. From DA, you can derive additional nuanced concepts like complete dominance, conditional dominance, and general dominance (which examine importance at different subset sizes). This can surface insights such as suppressor variables – predictors that have low importance by themselves but increase another variable’s importance in combination. Tonidandel & LeBreton acknowledge that if such detailed information is of interest, dominance analysis would be preferred over RWA. In other words, RWA compresses the information into a single summary per predictor, whereas DA can tell you, for example, that predictor A dominates B in all subset sizes, or that A is only important when combined with C, etc. However, these situations (like identifying complex suppression patterns) are relatively specialized. In most research scenarios, a single importance score per variable is sufficient and more interpretable. The authors note that in cases with many predictors or when significance testing of weights is needed, RWA is more practical and thus often preferred over dominance analysis.

Moreover, as computing power grows, one might attempt DA more often, but even today, dominance analysis can become unwieldy with a large predictor set or more complex models. A recent methods article (Braun et al., 2019) pointed out that although modern computing allows DA for typical regression sizes, the sampling variability in DA estimates (due to finite sample) can make ranks unstable, requiring confidence intervals and caution just like RWA. In summary: If absolute mathematical rigor is needed and p is small, dominance analysis could be considered “superior” (as it directly implements the definition of relative importance via subset contributions). But in practice, RWA’s near equivalence and added convenience usually outweigh the negligible theoretical loss of information. Indeed, some recent authors suggest performing DA when feasible and using RWA in cases where DA is computationally difficult (e.g. multivariate outcomes). It’s telling that even critics of RWA concede that for most applications the results are very similar, and differences become theoretical in nature. One specific critique by Thomas et al. (2014) argued that RWA’s mathematical derivation has flaws and could in some contrived cases lead to “distorted inferences” compared to DA. However, they also “warned” against using RWA only while acknowledging the approaches give very similar results for most practical data and are geometrically identical with two predictors. In effect, the critique underscores that dominance analysis is the conceptually pure method, but it did not provide evidence that RWA mis-ranks important predictors in realistic scenarios. Thus, most methodologists continue to view RWA as a legitimate technique, using dominance analysis as a cross-check when convenient.

### 3. Multicollinearity still matters if it means redundancy

As mentioned earlier, RWA isn’t a panacea for extreme multicollinearity stemming from redundant predictors. It will partition variance among highly collinear predictors, but that might yield misleadingly low weights for each – misleading in the sense that one might incorrectly infer each variable is unimportant, whereas in truth the set of them is important but they share the same contribution. Tonidandel & LeBreton explicitly caution: “One mistakenly held belief is that importance weights solve the problem of multicollinearity…. If two or more predictors are very highly correlated because they tap the same underlying construct, the resulting importance weights can be misleading…. One would need to consider dropping one of the highly multicollinear variables or forming a composite.”. They go on to say there’s no absolute statistical cutoff for “too much” multicollinearity – it’s more a theoretical question of whether two variables are essentially measuring the same thing. If they are merely related but distinct (e.g. income and education are correlated but not identical), RWA will partition variance appropriately and actually performs much better than regression coefficients in those conditions; if they are duplicitous (e.g. income and income in euros), RWA will simply split the income variance between them, making each look half as important. So, the onus is on the researcher to diagnose cases of redundant predictors. In scenarios of theoretical redundancy, RWA is not “inferior” per se – it correctly reflects that individually those variables add less because they overlap – but the interpretation can trip up unwary users. The remedy is straightforward: either combine such variables into one composite predictor or acknowledge that their weights should be considered in sum. This limitation is essentially shared by any importance method: even dominance analysis would show two redundant predictors each with roughly half the total combined importance, and one would similarly have to decide to drop or merge them.

### 4. Sample Size and Sampling Error

RWA, like multiple regression, relies on sample estimates of correlations and can be unstable with small samples or a high predictor-to-sample ratio. It doesn’t inherently “fix” the issue of having too little data. Tonidandel & LeBreton (2011) note that importance weights derived from a given sample can differ from true population values due to sampling error and measurement error, just as regression coefficients can. Bootstrapping helps to quantify this uncertainty by producing confidence intervals for the weights , but “bootstrapping will not overcome the inherent limitations associated with a small sample size”. In practice, one should ensure their sample is large enough to support stable estimation of a multiple regression model in the first place. A rule of thumb often used: have at least 10–15 observations per predictor (and generally N > 100) for regression-type analyses. If you violate this, RWA might yield weights, but their confidence intervals will be huge and conclusions uncertain. In comparison to other methods, this is not a unique weakness of RWA – any method of assessing importance will suffer with insufficient data. However, one could argue that simpler methods (like looking at bivariate correlations) might “work” with smaller N because they require estimating fewer parameters. For instance, an internal analytics note pointed out that a correlation analysis can sometimes be done with N ~ 30, whereas a full regression with many predictors might demand N > 100 to get reliable estimates. In such cases, if sample size cannot be increased, the analyst might opt for simpler exploratory measures (acknowledging their limitations) or focus on a smaller set of predictors. RWA is not inferior so much as more data-hungry than a simple correlation approach. The bottom line is: with adequate sample, RWA excels; with very small sample, no method will perform well, and one must be cautious. Using the bootstrap confidence intervals and even comparing the weights to those of a “random noise” variable (a technique suggested by Tonidandel et al., 2009) can help judge whether a weight is significantly above what random chance would produce.

### 5. Interpretation of Weights – Communication Challenges

While easier to interpret than many alternatives, relative weights might still confuse audiences not familiar with them. For example, some might mistakenly think a higher weight means a variable has a higher beta or a larger causal effect. It falls on the analyst to properly explain that “Variable X had a relative importance of 0.30, meaning it accounted for 30% of the explained variance in Y in our model.” That interpretation – essentially as a type of “importance percentage” – tends to be intuitive once explained. In fact, rescaled relative weights (expressed as percentages of R²) are often reported for easy communication. However, one must avoid over-interpreting the exact percentages as precise in the population; they are subject to confidence intervals. Also, because the weights always sum to R², they have a compositional nature (an increase in one weight means a decrease in others, if R² is fixed). This means we typically shouldn’t treat differences in weights as very meaningful unless they are statistically significant or large. For instance, if one predictor has 25% and another 20% of R², they might not be significantly different given sampling error. Thus, RWA users should embrace statistical tests or at least bootstrap intervals to compare weights, rather than blindly ranking tiny differences – the same caution that applies to any importance metric. Recent research (Braun et al., 2019) found that the rank ordering of predictors by importance can itself have sampling error, and recommended techniques like reporting confidence intervals for ranks or performing paired comparisons of weights. So, one limitation is that people may be tempted to over-interpret a rank ordering without regard to overlap in intervals. The remedy is good practice in reporting: give the weights, perhaps give their standard errors or CIs, and highlight only clear distinctions.

### 6. When other methods might be considered “superior”

Aside from dominance analysis (discussed above), there are a few other methods and contexts to mention. If one’s goal is purely predictive accuracy rather than interpretability, methods like ridge regression or lasso regression would handle multicollinearity by shrinking or selecting predictors, possibly yielding a better prediction model. But those methods do not provide a straightforward variance decomposition of the original variables; they answer a different question (improving prediction by regularization) and can drop correlated variables entirely. Therefore, in terms of “evaluating predictive power of variables,” RWA is more directly informative than lasso feature selection – RWA will tell you that two collinear variables together explain, say, 40% of variance (split 20%/20%), whereas lasso might simply keep one and discard the other, telling you nothing about the discarded variable’s potential importance.

Another approach is random forest or other machine-learning variable importance measures. These can capture complex non-linear importance and also handle correlated predictors to some extent (a random forest’s permutation importance, for example, can be interpreted as how much prediction error increases when a variable is permuted). Random forests tend to indicate one variable of a correlated group as very important and the others as low importance (since once one is used in splits, the others add little new). This might be seen as an advantage (it picks a representative) or disadvantage (it doesn’t inform on overlap) depending on the goal. A 2023 article recommends using both dominance analysis and random forest importance to robustly identify key predictors. However, those ML methods are “black box” in the sense that the importance is measured on the model’s terms (like Gini impurity reduction or out-of-bag error), not as a percentage of variance as in RWA. So, if the question is specifically about variance explained and relative contribution in a linear model, RWA is more interpretable and aligned with that goal than ML feature importance. On the other hand, if one suspects non-linear effects or interactions drive importance, RWA (being based on a linear model) might miss those, in which case methods like random forests or boosted trees could be considered complementary.

In summary, RWA is a very robust method for assessing variable importance in the presence of multicollinearity, but it is not infallible nor universally best for every purpose. Its “inferiors” are mainly the naive methods it was designed to improve upon (raw betas, stepwise routines, etc.), and it clearly outperforms those in delivering insight. Its “superior or equal peers” are dominance analysis (which is essentially equivalent in result, albeit with more effort) and, in specific aims, other approaches like regularization or machine learning (which serve different objectives). RWA’s limitations are generally well-understood and can be managed by the user: ensure you have a solid theoretical model, be cautious with essentially duplicate predictors, use RWA results as part of a bigger interpretive picture (alongside coefficient estimates, etc.), and communicate the findings with the appropriate nuance (e.g. include CIs, emphasize proportions of variance, not causal effect sizes). As Stadler et al. (2017) concluded in their primer, relative weights and dominance analysis provide valuable additional information beyond classical regression, but do not fix all problems and should be used as supplements to regression rather than replacements. That perspective nicely captures RWA’s role: an important tool in the toolkit, best used with awareness of its assumptions and in concert with other analyses.

## Considerations and Best Practices for Using RWA

If a researcher or analyst decides to use the Tonidandel & LeBreton RWA method to evaluate predictor importance, there are several practical considerations and scenarios to bear in mind in order to get the most from the method:

### 1. Ensure the Model is Well-Specified:

RWA assumes you have chosen a set of predictors to analyze (i.e. the “correct” model). It does not tell you which predictors to include – you should determine that based on theory, prior research, or other model selection techniques. As noted, RWA isn’t for variable selection and can actually mislead if used that way (e.g., a variable with a small weight in a big model might still be worth keeping if it’s theoretically critical or its weight would grow in a smaller model). So, first specify your regression model (perhaps after checking multicollinearity diagnostics, transforming variables if needed, etc.), then apply RWA to interpret that model. If you’re unsure about including a variable because of high correlation with another, consider the purpose: if both measure something similar and you only need one, combine or pick one before running RWA. But if both are conceptually important distinct constructs, include both and let RWA partition their influence – just be ready to interpret the result (maybe their weights will be split). For example, if education and income are both in a job performance model and correlate 0.8, decide if they’re distinct predictors or one proxy for socioeconomic status; if the latter, combine them into one index. This decision is outside RWA’s scope. RWA presupposes the set of predictors is given and meaningful.

### 2. Check Data and Assumptions:

RWA shares the basic assumptions of multiple regression: linear relationships between predictors and outcome (unless you explicitly include polynomial terms or interactions), and reliable measurement of variables. Extreme multicollinearity (e.g. variables that are linear combinations of each other) will cause computational issues (singular matrices). If you get warnings about the correlation matrix being singular or near-singular, you must address that (by removing or combining collinear variables) before trusting the weights. One good practice is to inspect the correlation matrix of predictors for any very high correlations (say > 0.9). If found, make a conscious decision how to handle those variables. Also, handle missing data (RWA typically uses listwise deletion by default, like regression does) – ensure missingness isn’t introducing bias. Outliers can affect regression and thus RWA; if your data has extreme outliers that distort correlations, consider remedying that (via robust methods or transformations) prior to RWA. Essentially, treat RWA as you would a regression analysis in terms of preparing clean, appropriate input data.

### 3. Adequate Sample Size:

It’s worth emphasizing again – use RWA on datasets where N is large enough to support your model. If you have a small sample with many predictors, your weights will have large uncertainty. In such cases, a bootstrap procedure is highly recommended to get confidence intervals for the weights. Many RWA software implementations can bootstrap easily (for example, Tonidandel & LeBreton’s RWA web tool and the R packages allow specifying a number of bootstrap resamples). A common practice is using 500 or 1,000 bootstrap samples to derive 95% confidence intervals for each weight. If a predictor’s interval includes very low values (relative to others or relative to zero), be cautious in declaring it important. Tonidandel et al. (2009) also suggest a clever bootstrap test: include a completely random “noise” variable in your model and compute RWA. If your real predictors have weights significantly larger than the noise variable’s weight, that’s evidence they truly contribute beyond chance. This addresses the issue that relative weights, being proportions of R², are never exactly zero in sample (even noise will get some tiny share). The bottom line – the more predictors you have, the larger your sample should be to get stable estimates. If you have say 10 predictors, a sample of 50 is quite low; if you cannot get more data, at least be very tentative about the results. Conversely, in big data scenarios (N in the thousands), RWA can shine – it will give very precise estimates of importance.

### 4. Interpreting the Output (Weights):

When you run RWA, you will get “Raw Relative Weights” for each predictor, which sum to the model’s R². Often there is also a column of those weights rescaled to percentages of R² (summing to 100%) for convenience. You should interpret these as measures of effect size or importance. A weight of 0.10 (out of R² = 0.50, i.e. 20%) might be considered moderately important; something like 0.30 out of 0.50 (60%) is very important. There’s no rigid cut-off for what constitutes “high” importance – it’s relative. One good practice is to rank the predictors by their weights and see if there is a natural drop-off point or clustering. For example, you might find two top predictors with weights around 0.25 each, and then a third with 0.15, fourth 0.05, etc. That tells you two predictors clearly dominate in importance. However, always refer to uncertainty: if two weights are close (say 0.25 vs 0.22), check if that difference is likely real or just sampling noise. If you’ve bootstrapped, see if the 95% CIs overlap. If they do, you might say those predictors are tied in importance statistically. If one’s interval is wholly above the other’s, then you can more confidently say predictor A is more important than B. Additionally, look at the signs of relationships if provided. By default, relative weights are concerned only with magnitude of explained variance (they are inherently non-negative). Some implementations, like the rwa R package, offer a signed version where the sign of a predictor’s correlation with the outcome is attached to the weight for context – e.g. “X accounts for 15% of variance and its effect is positive (higher X -> higher Y)”. This can be useful to report, because stakeholders often ask not just “how important is it?” but “in which direction does it influence the outcome?”. So, best practice: report relative weights alongside the sign of the predictor’s correlation or regression coefficient. For example: “Education had a relative importance of 0.18 (36% of R²) in predicting income, and it was positively related to income (higher education associated with higher income).” This gives a full picture: importance and direction.

### 5. Comparing Weights and Groups

If your analysis calls for comparing predictors’ importances within different groups or models, RWA has procedures for that too. For instance, you might run RWA separately for males and females to see if the pattern of importance differs. Tonidandel & LeBreton (2015) discuss methods to statistically compare weights across groups (essentially by pooling bootstraps or using tests for differences). If using their web tool or other software that supports it, you can test, say, whether “education is a significantly stronger predictor of job performance for males than for females.” This is an advanced use-case but shows the flexibility of RWA – something that would be cumbersome to do with dominance analysis or other methods. If doing such comparisons, ensure the models are comparable and the groups have sufficient sample each.

### 6. Use Case Scenarios – when to use RWA

You should consider using RWA whenever you face a regression analysis where understanding the relative contribution of correlated predictors is important to your goals. Classic scenarios:

    - **Key Driver Analysis:** In marketing or HR analytics, you have many survey items or factors that all correlate (e.g. many aspects of customer satisfaction, or many employee engagement factors) and you want to know which ones matter most for an outcome (like loyalty or performance). RWA is ideal here because it will handle the inter-correlations among those drivers and yield a list of the top drivers by importance. It's been used widely in these domains to present results as a bar chart of percentage contributions, which is easy for managers to digest.
    - **Multicollinear Predictors in Scientific Research:** In fields like ecology, psychology, or economics, you may have variables that naturally occur together (e.g. various climate variables, or socioeconomic indicators). If you include them in a regression, you'll want to partition their effects. RWA has been recommended in psychology precisely for such situations – e.g., intelligence research often measures different cognitive abilities that inter-correlate; RWA can tell which ability accounts for more variance in academic performance, for instance.
    - **Suppressor Situations:** If you suspect suppressor effects (where a variable increases another's predictive validity by being included), RWA can help illuminate that. A suppressor variable might not correlate strongly with Y itself but helps remove irrelevant variance from another predictor, thereby boosting that predictor's beta. In RWA, the suppressor could still get a moderate weight because in combination it contributes to R², and the combination effects are inherently counted. Dominance analysis could pinpoint which subsets show suppression, but RWA will at least not ignore the joint contribution.
    - **Logistic Regression "Pseudo-R²" analysis:** If your outcome is binary (yes/no) or categorical, and you use logistic regression, you don't have an exact R², but you can still use analogues (like Nagelkerke R² or just treat it as variance in log-odds explained). Tonidandel & LeBreton (2010) extended RWA to logistic regression by deriving weights using an analogous approach. If you have software that supports it (some implementations do), you can interpret importance in logistic models similarly. For example, in predicting employee turnover (left vs stayed), where predictors might be job satisfaction, pay, tenure, etc., RWA can tell which contributes most to the prediction of turnover, even though it's a non-linear model.
    - **Multiple Outcomes:** If you're interested in which predictors are important across multiple outcomes (say you have a set of related outcome variables), the multivariate RWA extension (LeBreton & Tonidandel, 2008) can be used to determine overall importance in explaining the multivariate criterion space. This is more complex, but it basically combines the idea of canonical correlation with relative importance. This could be useful, for instance, in educational research where you care about predicting a bundle of outcomes (grades in math _and_ science, for example) from some predictors; you'd get a sense of which predictors are globally most important to the set of outcomes.
    - **Interactions or Nonlinear Terms:** If your model includes interaction terms or polynomial terms (which themselves are often highly correlated with the main effects), you have to be careful because importance analysis methods assume predictors are not an arbitrary set but include all necessary components. Tonidandel & LeBreton (2009) provided guidance on handling models with interactions – essentially suggesting a procedure where higher-order terms are residualized with respect to lower-order terms to maintain interpretability. If you are examining relative importance in such models, consult their work; it's a more advanced scenario. In many cases, one might enter interaction terms and simply use RWA, but due to the hierarchy, the interpretation of weights for main effect vs interaction needs care (since the interaction's importance is conditional on being allowed to explain something above and beyond the main effects). This is a niche consideration but worth noting if your analysis goes in that direction.

### 7. Presenting and Reporting Results:

When reporting RWA results, it’s best to be transparent and thorough. Report the model’s R² (so readers know total variance explained) and how the R² is partitioned among predictors. You can present a table with predictors, their raw relative weight, and the rescaled weight (% of R²). It’s also useful to report standard errors or confidence intervals for the weights , especially if you want to make claims about significance (“predictor A’s weight is significantly greater than zero” or “A is significantly more important than B”). If space permits, you might include both RWA results and the traditional regression coefficients for reference, to give a full picture. Often they will tell complementary stories: for instance, a variable might have a low beta (due to suppression) but a high relative weight – that juxtaposition itself is a finding to discuss. Make sure to explain in prose what the weights mean (“this variable accounted for X% of the explainable variance in Y”). Using visuals can help: a bar chart of rescaled weights is intuitive, or a pie chart of R² division (though pie charts can be less precise – bar or column chart is preferred). Always cite the source of the method (e.g., “using the relative weight analysis approach of Johnson (2000), as recommended by Tonidandel and LeBreton (2011)”). This signals to readers that a known method was used, and they can refer to those papers for methodology.

### 8. Be Mindful of Audience:

Finally, consider who will consume the results. If it’s an academic audience, they may be more familiar with beta coefficients than with relative weights. In such cases, you might have to spend a few sentences educating the reader on RWA. Tonidandel & LeBreton (2011) is a great reference to cite for the rationale, and you can briefly say “we computed relative importance weights to mitigate multicollinearity issues; these represent each predictor’s proportional contribution to R².” If it’s a business audience or general audience, they may actually find relative weights more intuitive (“X contributes 25% of the prediction”) than regression coefficients (“a one-unit change in X changes Y by …”). So, tailoring the explanation is key. Just avoid jargon like “Johnson’s epsilon” (sometimes the weights are denoted epsilon\_i in literature) when communicating – translate it to plain language.

# Summary

In conclusion, Tonidandel and LeBreton’s relative weights analysis method remains a valuable and valid approach for assessing predictor importance in the presence of multicollinearity. It offers a balanced way to look at the predictive power of variables by accounting for intercorrelations that confound other metrics. RWA is generally superior to naive methods (standardized betas, stepwise selection, etc.) in those situations because it more faithfully represents each variable’s contribution. It performs similarly to rigorous methods like dominance analysis, while being more feasible to use and extending readily to additional analyses (significance testing, other model types). Its chief limitations are that it does not automatically resolve issues of redundant predictors or small sample sizes – those require researcher input and cautious interpretation. By following best practices – verifying model assumptions, using bootstrap confidence intervals, and interpreting the results in context – a user can effectively harness RWA to gain insights into which variables truly drive outcomes and to what extent. In many research and business analytics scenarios today, RWA provides a clear, quantifiable answer to the question, “which of these factors matter most, and how much do they each contribute?” – an answer that is often obscured when using standard regression in a collinear world but is illuminated by the relative weights method. With the considerations outlined above, one can confidently apply relative weights analysis and communicate its findings to guide decisions, theory development, or further model refinement, making it a valuable component of the analytical toolkit in 2025 and beyond.

# References

1. Relative Importance Analysis: A Useful Supplement to Regression Analysis on JSTOR

2. Stadler, M., Cooper-Thomas, H. D., & Greiff, S. (2017). A primer on relative importance analysis: Illustrations of its utility for psychological research. Psychological Test and Assessment Modeling, 59(4), 381–403.

3. Introduction to Relative Weights Analysis with the rwa package

4. Stadler, M., Cooper-Thomas, H. D., & Greiff, S. (2017). A primer on relative importance analysis: Illustrations of its utility for psychological research. Psychological Test and Assessment Modeling, 59(4), 381–403.

5. 4 reasons to compute importance using Relative Weights rather than Shapley Regression | R-bloggers

6. Relative Importance and RWA Web — Scott Tonidandel, Ph.D.