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## Appropriate Use of Constant Sum Data

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**Appropriate Use of Constant Sum Data**Joel Huber-Duke University Eric Bradlow-Wharton School Sawtooth Software Conference September 2001**Appropriate Use of Constant Sum Data**• What is Constant Sum Scale data? • When will CSS data work? • When will it fail? • An analysis of Volumetric Data using both HBsum and HBreg**Single Choice TaskChoose a potato chip snack given these**options**Constant Sum TaskIn ten purchases indicate how many of each**you would buy**Appropriate CSS usage**• When people can estimate frequency of usage in a context—as examples: • Soft drink choice • Breakfast cereals • Prescriptions given diagnosis • Multiple supplier contracts**Inappropriate CSS usage**• As a measure of preference strength • Allocate 10 points proportional to your preferences • As a measure of choice uncertainty • Indicate the probability of choosing each alternative • As a summary across different usage contexts • What proportion of beverage purchases will be Coke?**An example of conditional beverage choices**• Drink Coke when tired • Drink Sprite when thirsty • Drink Heinekens with in-laws • Drink Iron City with friends • Drink Turning Leaf when romantic • Drink Ripple when depressed**Alternative to constant sum**• Condition choices on usage situation • Derive situation frequency from a separate direct question • Ask a single choice questions • Derive variability by conditioning on context, or error in choice model**Analysis of Volumetric Choice Data**• Volume estimates among four frequently purchased non-durables • Each alternative defined by brand, type, size, incentive and price • 10 different randomized sets of alternatives • One fixed holdout set • Task: How many of each would you choose? (max=10)**People reacted differently to this task**• 22% of sets produced exactly one purchase • 33% of the sets produced none • 45% chose more than one purchase • People differed in their likelihood to use these strategies.**Two-stage analysis process**• Need to model both choice share and volume • First stage: Constant sum model with ‘none’ option • Second stage: Hierarchical Bayes regression with item utilities from the first stage**Constant Sum Stage**• Sawtooth’s HBSUM estimates 13 parameters for each person. • Model: Sums are normalized as if generated from five independent probabilistic choices • Choice weight =5 • Ten tasks equivalent to 50 independent probabilistic choices • None is included as a fifth alternative**Holdout choice accuracy**• 78% hit rate • Mean average error predicting choice share 2.5 share points • Respondents differed strongly on their use of none**HBreg predicts volume as a function of:**• A constant for each individual • The utility of each item (from HBsum) • Adjusting for the utility of the set • Coefficient will be negative to the extent that volumes are proportional to the relative value within a set**Effectiveness of Dual Model**• All coefficients significant and highly variable • Correlation between predicted and holdout volumes = .73**Conclusions**• Constant sum scale measures are mainly appropriate when frequencies are easy to estimate given a set of alternatives • Volumetric estimates require even more of respondents, and thus are even more rare • Hierarchical Bayes methods are critical for correct modeling, because of the heterogeneity in the ways people respond to the task**Conclusions**• We found heterogeneity with respect to • The use of None • The average volume • The partworths attached to the attributes • The degree to which alternatives are contrasted with others in the set • A two-stage HB allows people with idiosyncratic processes to be represented