Key Driver Analysis (Relative Weights and Shapley Values)

Why ordinary regression is not enough

Key driver analysis asks a simple question: which of these attributes, such as price, quality, service or delivery, has the biggest influence on an overall outcome such as satisfaction, likelihood to recommend or repurchase intent? The obvious answer is to run a multiple regression and compare the standardized coefficients (betas). Unfortunately, survey ratings are almost always correlated with each other, because customers who are happy with one aspect tend to be happy with the others (the “halo effect”). When predictors are correlated, regression coefficients become unstable: a driver can get a small or even negative beta although it is strongly related to the outcome, simply because another correlated driver has taken the credit. Zero-order correlations have the opposite problem: they double-count shared variance.

Relative importance methods solve this by asking a different question: how much of the explained variance (R²) does each driver account for, including its share of the variance it shares with other drivers? The answer is a set of importance weights that are all positive, add up to R² and do not depend on the order of the predictors.

Relative weights (Johnson’s method)

Johnson’s (2000) relative weights analysis transforms the correlated drivers into a set of uncorrelated variables that are as close as possible to the originals (via the symmetric square root of the correlation matrix), regresses the outcome on these orthogonal variables, and then maps the explained variance back onto the original drivers. Each driver’s raw relative weight is its contribution to R²; dividing by R² gives its share of the explained variance in percent. The method is fast even with 20 or more drivers, and the tool adds percentile bootstrap confidence intervals (500 resamples by default) so you can see which differences in importance are reliable.

Shapley value regression (dominance analysis)

The Shapley value approach, also called general dominance weights or LMG after Lindeman, Merenda and Gold, comes from game theory. It fits a regression for every possible subset of drivers, measures how much R² increases when a driver is added to each subset, and averages these increments over all possible orders of entry. The Shapley values also add up exactly to R². They are the gold standard but require 2^p regressions, so the tool computes them for up to 14 drivers (16,384 subsets). In practice, relative weights and Shapley values almost always agree closely, as they do in the example; seeing both gives reassurance.

Worked example with the built-in data

The example contains 320 customers who rated seven aspects of an online retailer on a 1–10 scale, plus overall satisfaction. The seven drivers together explain 61% of the variance in satisfaction. Price value accounts for about 23% of the explained variance, product quality 21% and customer service 19%; returns process matters least (about 6%). Shapley shares are within half a point of these figures. Notice that the correlations of the drivers with satisfaction all lie between .38 and .56: correlations alone would suggest that every driver is about equally important, which is exactly the halo problem relative weights resolve.

The priority matrix

Importance alone does not tell you where to act; you also need to know how well you perform on each driver. The priority matrix (also called a derived importance–performance map) plots each driver’s share of explained variance against its mean rating rescaled to 0–100, with lines at the averages. The four quadrants are:

• Improve first: above-average importance, below-average performance. These are the most valuable improvement opportunities, highlighted in red.
• Maintain strengths: important and performing well; protect them.
• Low priority: less important and performing below average.
• Possible overkill: performing well on something that matters little; resources could be moved elsewhere.

In the example, price value is the most important driver but has one of the lowest mean ratings, so it lands in the improve-first quadrant together with customer service: these two are the clearest levers for raising satisfaction.

Preparing your data

Use one row per respondent, one numeric column for the outcome and one for each driver. Ratings on 5-, 7-, 10- or 11-point scales are all fine; the method is based on correlations, so drivers can be on different scales. Missing values are handled by listwise deletion: respondents with a missing answer on any selected variable are left out, and the tool reports how many. If many respondents skip items such as “returns process” because they never returned anything, consider analysing that driver separately or imputing values first with the data cleaning tool.

How many drivers and respondents?

Relative weights work with up to 20 drivers in this tool. Aim for at least 10–15 respondents per driver, and preferably 200 or more in total, for stable estimates and tight bootstrap intervals. Very high correlations between drivers (VIF above about 5) mean the data cannot really separate those drivers; consider combining them into one index or using factor analysis first to group items into broader dimensions.

Interpreting with care

• Derived, not causal. Importance here means association with the outcome in this sample. A driver can look important because it is a symptom rather than a cause; experiments or longitudinal data are needed to prove causation.
• Linear and additive. The method assumes drivers relate linearly to the outcome. Must-be attributes in the Kano sense (only matter when performance is bad) can be underestimated; the Kano tool and IPMA/cIPMA on this site complement this view.
• Do not rank by betas. When a beta has the opposite sign to the driver’s correlation with the outcome (shown in red in the table), it is a suppression effect, not evidence that the driver hurts satisfaction.
• Look at the intervals. Drivers whose bootstrap intervals overlap heavily should be treated as similarly important.

Reporting

Report the outcome, the drivers, the sample size, R², each driver’s relative weight (and Shapley value) with its share of R² and bootstrap confidence interval. Example: “A relative weights analysis (Johnson, 2000) of seven drivers of overall satisfaction (N = 320, R² = .614) showed that price value accounted for the largest share of explained variance (22.8%, 95% CI for the raw weight [.094, .189]), followed by product quality (21.0%) and customer service (19.0%).”

Glossary of driver analysis terms

• Stated importance: importance that respondents report directly, which tends to rate everything as important.
• Derived importance: importance inferred statistically from the relationship between drivers and the outcome.
• Multicollinearity: strong correlation among drivers, which makes regression coefficients unstable.
• Halo effect: the tendency of respondents who like a brand overall to rate it highly on every attribute.
• Suppression: when a driver’s coefficient takes the opposite sign to its correlation because of overlap with other drivers.
• General dominance: a driver’s average contribution to R² across all subset models, equal to its Shapley value.
• VIF: variance inflation factor; values above about 5 signal problematic collinearity.
• Bootstrap: resampling respondents with replacement to estimate the uncertainty of the weights.

Key references: Johnson (2000), Multivariate Behavioral Research; Tonidandel and LeBreton (2011), Journal of Business and Psychology; Budescu (1993), Psychological Bulletin; Grömping (2006), Journal of Statistical Software (relaimpo).