Shapley Value Regression

Driver Analysis Motivation: Don’t Ask Why Why not just ask respondents directly why they purchase a particular product? Consumers are generally unconscious of why we do what we do when it comes to product purchase decisions. Respondents will tell you answers that they think you want to hear. You get their justifications for their purchase, not their motivation. We recommend using a derived importance method through driver analysis.

Driver Analysis Motivation: Stated Importance Why not ask respondents to state the importance of product/service attributes? The traditional approach of asking respondents to indicate the importance of attributes on a scale requires no tradeoff: “Everything is really important” No Differentiation between what’s truly important to the business and what are the marginal items. Tradeoff methods such as Conjoint and/or MaxDiff are more suitable, but are often more costly and time consuming.

SV Regression Background Shapley Value Regression is part of the family of the techniques used in Driver Analysis models. In Driver analysis, we seek to understand the motivation behind consumer behaviours by observing the pattern of associations and correlations between their decisions and their perception/experience with the product/service being offered If we are interested in what drives consumer purchase decisions, we look for correlations between purchase decision and consumer perception and experience with the product. If we are interested in what drives customer satisfaction, we look for correlations between overall customer satisfaction rating and their satisfaction with key service points.

SV Regression Background Shapley Value Regression is able to deal effectively with the multicollinearity issue that’s often present in Market Research data. Multicollinearity is when there are strong correlations between the various aspects of consumer perceptions to the point that it affects the stability of the results in the driver analysis via traditional approaches. Similar to other methods used in driver analysis, variables with little variations will not show up as key drivers. Table stake attributes are unlikely to show up as key drivers. All airlines are safe, so safety is not a key driver of airline choice among travelers.

SV Regression Advantage & Disadvantages Key Advantages Effectively deals with the correlated nature of market research data (i.e. multicollinearity). It is inherently stable and can be used as a tracking tool. Clients who are used to running regression will be open to this approach. Key Disadvantages Requires complete data for every variable. Missing data must be replaced with the mean, or other value. Alternatively, a reduced base size must be used in the analysis. Does not distinguish between drivers of satisfaction and drivers of dissatisfaction. Not predictive. The analysis is based on observation of current behavior of consumers only, not predictive of their future behavior.

SV Regression: Correlation & Causation

SV Regression Methodology Model Specification Dependent variable is the response variable you want to study. Has to be at least ordinal, i.e. 3 ordered response category or more. Interval or ratio scales are preferred. Independent variables are the potential drivers that could influence the response variable. can be metric or non-metric. Examples: brand association questions: which of the following brands do you associate with these attributes? What sample size do you need? We require at least 10 cases of data for each potential drivers. If there are 20 potential drivers, we need at least n=200 cases of data. As the ratio falls below 10:1, we encounter the risk of overfitting the model to the sample, making the results too specific to the sample and lacking generalizability.

SV Regression Example Output R2 – How much do the potential drivers together influence the response variable Relative Importance – the relative importance of the potential drivers (sums to 100%).

SV Regression Application: Example: Quadrant Map The relative importance of attributes can be combined with other information to create Quadrant maps.

SV Regression Application: Example: Quadrant Map Top Priority for Enhancement High Importance Low Performance Strength High Importance High Performance Importance Second Priority for Enhancement Low Importance Low Performance Maintenance Low Importance High Performance Performance

Appendix

Contribution measured by R-square SV Regression Details The Shapley Value Principle was developed to evaluate an ordering of the worth of players in a multi-player cooperative game. The key to understanding its utility is that it represents the worth of each player over all possible combinations of players. In Shapely Value Regression, we extend this to the problem of comparative usefulness of potential drivers. SV regression assigns a value for each potential drivers calculated over all possible combinations of all the other drivers in regressions. We use Ordinary Least Square (OLS) regression for all possible combinations of explanatory variables Contribution measured by R-square

SV Regression Output - Details R2 - Coefficient of Determination Measures the proportion of the variance of the response variable that is explained by all the potential drivers. It varies between 0 and 1. The higher the R2, the stronger the association between potential drivers and the response variable. SV – Shapley Value the contribution of each potential driver to the overall R2 of the regression sdSV – Standard deviations of the Shapley Values Relative Importance Rebasing the Shapley Values so that they sum to 100%. The relative importance of an item = SV/ Overall R2.