Utility Constraints, Including Customized Constraints

The HB and Monotone Regression estimation routines included in ACBC software allow you to impose monotonicity constraints (utility constraints).  For example, if you know that the relationship between price and preference should be negative for all respondents, you can constrain all respondents' partworths to reflect a negative slope for price.

 

Specify utility constraints by clicking the Use Constraints box from the Attribute Information tab (within the HB or Monotone estimation dialogs).  Then, click the Edit... button that is enabled.  A drop-down control appears that lets you specify constraints for attributes in your study.

 

If you use the Summed Price option in ACBC, we generally recommend constraining its slope to be negative.

 

Constraints have the benefit of eliminating "reversals" in partworths (out-of-order relationships among levels with known rational preference order).  Constrained utilities generally will show improved individual-level hit rates of holdout tasks.  But, constraints introduce some bias in the parameters and sometimes result in models that have slightly lower aggregate predictive accuracy (such as for shares of preference).  As another potential problem, if constraints are applied to some attributes, but not to others, this can change the sensitivity of the simulation models in favor of the constrained attributes.

 

If the main goal of the research is individual-level predictive accuracy, we recommend applying constraints for all attributes: global constraints for attributes with known a priori order, and customized constraints for other attributes based on responses to additional questions in the survey.  If the main goal of the research is share prediction accuracy for segments or for the population, we generally recommend avoiding utility constraints (except for Summed Price, which generally should be constrained).  However, if using ACBC with very small sample sizes (especially n<30), constraints across all attributes may be a good idea both for individual-level prediction and aggregate share prediction accuracy.

 

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Global (Universal) Constraints

 

Global constraints may be applied when one can safely assume that all respondents agree regarding the relative preference order of levels within an attribute.  When imposing constraints in ACBC, a grid appears for each attribute, such as:

 

Speed (Pages Per Minute):

 

To impose global utility constraints, you can specify relative preference values in the right-hand column of the grid.  Larger values indicate higher preference.  For example:

 

Speed:

 

We could easily have used values of [10, 20, 30, 40] or [1, 3, 10, 1000] instead of [1, 2, 3, 4], and the results would be the same.  The values found in the grid for Relative Preference are only referenced to constrain the relative preference order of the final utilities.  The utility for 12 PPM will be constrained to be higher than the utility for 10 PPM (because a "4" is greater than a "3"), etc.

 

When fields within the Relative Preference column are all either missing (blank) or equal, the attribute's utilities are not constrained.

 

Partially-Constrained Attributes

 

If only some levels of an attribute should be constrained, then the value for the non-constrained levels should be left "blank".  For example:

 

Style:

 

In the example above, level 1 is constrained to be preferred to level 2.  But, levels 3 and 4 are unconstrained.

 

Multiple Independent Chains of Constraints within Attributes

 

Consider a situation where Style A--Version 1 is preferred to StyleA--version 2 AND Style C is preferred to Style B.  But, we don't know how the two pairs of levels interrelate.  In that case, you can add another column to the grid:

 

Style:

 

In the example above, level 1 is constrained to be preferred to level 2.  Levels 4 is preferred to level 3.  But, the relationship of levels 1 & 2 relative to 3 & 4 is not constrained.

 

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Customized Constraints

 

ACBC can apply customized (idiosyncratic) constraints in addition to global constraints.  Attributes like speed and price may have rational preference order across all respondents (global).  But, attributes such as brand, color, and style do not have the same preference order for every respondent.  ACBC allows you to specify customized constraints for such attributes, using information collected in another part of the survey.  Customized constraints only involve within-attribute utility constraints, not between-attribute (importance) constraints, such as have been implemented in Sawtooth Software's ACA system.

 

For example, you might ask respondents to rate different brands (in a question named RateBrand) on a scale from 1 to 5.  The answers to this question can be used as customized ordinal constraints (you must ensure that higher values correspond with higher preference for any questions you reference as constraints).  For example:

 

Brand:

 

The values stored within the RateBrand question are used to determine the applicable constraints for each respondent.  For example, if a respondent rates the brands as follows:

 

 

Then, utilities for this respondent are constrained according to the following ordinal relationships:

 

Brand A > Brand B

Brand A > Brand C

Brand A > Brand D

Brand B > Brand D

Brand C > Brand D

 

Notice that brands B and C are not constrained with respect to one another (neither are they tied); their utility values with respect to one another are left to be determined by the data.

 

Partially-constrained attributes (as with global constraints) can be specified by using a missing/blank value for a non-constrained level.  A blank relative preference indicates that this level should not be constrained.

 

Note: If using summed pricing and associating price premiums with levels, any ratings applied as constraints should refer to the relative utility of the level independent of any level-based pricing.  Respondents should be asked to rate the levels assuming all else equal, including price.