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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

- 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

- When people can estimate frequency of usage in a context—as examples:
- Soft drink choice
- Breakfast cereals
- Prescriptions given diagnosis
- Multiple supplier contracts

- 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?

- 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

- 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

- 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)

- 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.

- 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

- 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

- 78% hit rate
- Mean average error predicting choice share
2.5 share points

- Respondents differed strongly on their use of none

- 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

- All coefficients significant and highly variable
- Correlation between predicted and holdout volumes = .73

- 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

- 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