One of the celebrated capabilities of CBC (Choice-Based Conjoint) is the ability to model different price curves for different brands/SKUs. People often think this necessarily involves adding interaction effects to the utility models, or by creating nested alternative-price attributes within each brand/SKU. But, that’s not always the case…
Back in the day when aggregate logit was the main game in town (think early 1990s), including the interaction effect (or using alternative-specific price attributes) was the only way to model the different price slopes or idiosyncratic kinks for each brand/SKU. Then, HB came along in the late 90s, giving us utility estimates for each respondent. HB is often now the default standard. Indeed, HB can estimate models with interactions, but sometimes it just isn’t necessary and big HB models with interaction effects can become too large for HB to manage well (leading to potential overfitting problems).
When you have individual-level utilities, each respondent’s personal choice can be predicted using a what-if (market) simulator. We’ve found that different price slopes per brand/SKU often are represented quite well in choice simulator output when using HB with just main effects models. If studying 30 SKUs, 5 price points, and the None, an HB model that estimates 30+5+1 main effect utilities often is enough…without having to estimate the 30x5 additional interaction terms. How is that possible?
Let’s imagine we’re studying choice of wine, where our CBC experiment involves premium and discount wines. Also imagine that half of the respondents are price sensitive and often choose the discount wines at lower prices, whereas the other half of respondents are less price sensitive and often choose the premium wines at the higher prices. If we estimate a main effects model using HB, for each respondent we’ll obtain utilities for the wine SKUs and the independent effect (utility) of price. It won’t surprise us to find that the same people who are discount brand choosers also tend to be more price sensitive than those who are premium brand choosers.
Now, we place the respondent utilities (again, just main effects) in a choice simulator. Imagine we create a base case where the discount brands are set at lower prices and the premium brands at higher prices. Take a discount brand and raise or lower its price, and the people voting for that discount brand are likely to change their vote to another discount brand or to the None alternative. The simulated price curves for discount brands have relatively steep slopes. The opposite occurs for premium brands, leading to flatter price curves. Without formally including an interaction term for brand and price, the large differences in price sensitivity between discount and premium brands may indeed be reflected in the individual-level choice simulator. And, it owes principally to HB's ability to capture the patterns of price sensitivity across people with different tastes.
Modeling heterogeneity of tastes via HB also allows other interaction effects involving other attributes to naturally occur (via default main effects models) in choice simulator analysis. For example, the same people who tend to favor sports cars also tend to like having those cars in red, etc.
But, don’t get lazy! We’ve seen some CBC data sets where this heterogeneity of tastes explanation for interaction effects cannot fully account for differing price sensitivities across brands/SKUs, so sometimes the basic HB main effects model won’t entirely do the job. Then, we rely on limited interaction effects or we try grouping SKUs into similar “tiers” for which we can estimate alternative-specific price effects common to the SKUs in each tier.
If these kinds of topics interest you, we hope to see you at the upcoming SKIM/Sawtooth Software conference in Paris (April 9-12, 2019, https://www.sawtoothsoftware.com/paris2019) or at the Sawtooth Software Conference in San Diego (September 25-27).