1. Appropriate Use of Constant Sum Data Joel Huber-Duke University Eric Bradlow-Wharton School Sawtooth Software Conference September 2001

2. 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

3. Single Choice Task Choose a potato chip snack given these options LaysEagleStore brand Sour CreamBarbecueRegular Chips ½ oz bag¾ oz bag1 oz bag $.50$.65$.75

4. Constant Sum Task In ten purchases indicate how many of each you would buy LaysEagleStore brand Sour CreamBarbecueRegular Chips ½ oz bag¾ oz bag1 oz bag $.50$.65$.75

5. Volumetric Task If available how many of each would you buy? LaysEagleStore brand Sour CreamBarbecueRegular Chips ½ oz bag¾ oz bag1 oz bag $.50$.65$.75

6. 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

7. 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?

8. 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

9. 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

10. 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)

11. 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.

12. 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

13. 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

14. Holdout choice accuracy 78% hit rate Mean average error predicting choice share 2.5 share points Respondents differed strongly on their use of none

15. Heterogeneous response to None

16. Error predicting holdout share Alternative Actual Volume Predicted Share Error 112%11%1% 230%27%3% 321%24%3% 414%12%2% None23%26%3%

17. 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

18. Effectiveness of Dual Model All coefficients significant and highly variable Correlation between predicted and holdout volumes =.73

19. Error predicting holdout volumes Alternative Actual Volume Predicted Volume Error 13.93.8.1 26.27.21.0 35.86.3.5 45.14.4.6

20. 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

21. 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