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?

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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

Volumetric TaskIf available how many of each would you 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

Heterogeneous response to None

Error predicting holdout share

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

Error predicting holdout volumes


  • 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

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