What Is a Discrete Choice Experiment? A Worked Example With Real Numbers
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A discrete choice experiment asks people to choose between a few complete options whose features have been varied on purpose, then estimates how much each feature moved the choice. Choice-based conjoint is a form of discrete choice experiment. The output is not a rating or a ranking given by respondents. It is a set of estimated effects for each non-reference feature level, measured against a stated baseline level and each with a confidence interval, estimated from the observed choices. Subconscious runs discrete choice experiments on simulated buyers and grades the results against published human studies. On the Hainmueller and Hopkins immigrant conjoint, the registry's saved run of 2026-11-06 shows 26 of 29 significant effects with the right sign and a rank correlation of 0.83, but three significant effects reversed and the registry grades the size comparison inconclusive (simulated effects 1.13 times the human ones) (registry record, read 2026-11-12). The sections below use that replication to show what the numbers mean.
The design in four parts
- Attributes and levels. The things that vary, and the values each can take. In the immigrant conjoint of Hainmueller and Hopkins, respondents saw hypothetical applicants described by nine attributes: gender, education, language skills, country of origin, profession, job experience, employment plans, reason for applying and prior trips to the United States, each with several levels (registry record, read 2026-11-12).
- An experimental design. Levels are assigned to options by a plan (full factorial, orthogonal or randomized) that varies the attributes so the specified effects can be estimated; the design's restrictions decide which comparisons it supports.
- Choice tasks. Each respondent sees several sets of options and picks one in each set; some designs add a "none" option. The outcome is the choice, not a stated opinion.
- A choice model. A logit model such as conditional logit or mixed logit estimates a utility coefficient (part-worth) for each level, on the model's own scale; changes in choice probability can be calculated from those coefficients. In conjoint analysis an average marginal component effect (AMCE) is the average change in choice probability from one level relative to a reference level, averaged over the design's distribution of the other attributes. The worked example below reports AMCEs estimated with ordinary least squares (a linear probability model), per the registry page.
How to read an effect and its interval
In the human study, the effect of "college degree" against a reference of "no formal education" was +0.196: an applicant with a college degree had an estimated choice probability about 20 percentage points higher, averaged over the design's distribution of the other attributes (registry record). A confidence interval gives the range of effect sizes the data are consistent with, at the stated confidence level. An interval that crosses zero means the data cannot rule out an effect in either direction. An interval that excludes zero supports a direction; if it is wide, the size is still imprecisely estimated. For the Hainmueller study the registry publishes a 95 percent half-width for each human effect: the college-degree effect is +0.196 plus or minus 0.045, an interval that excludes zero.
Two effects are compared by their estimates and their intervals together. To decide whether one level beats another, use a confidence interval for their difference rather than eyeballing two separate intervals.
A worked example: a simulated replication of a published study
The Hainmueller and Hopkins study surveyed 1,407 Americans. Subconscious replicated the study on a simulated population and compared the estimated effects with the published human results. The registry's saved run of 2026-11-06 reports that the simulated sample got 26 of 29 significant effects in the right direction, ranked the effects at a Spearman correlation of 0.83, and produced effects 1.13 times as large as the human ones, a size result the registry calls inconclusive (registry record). Three significant effects reversed, including Iraq origin relative to the reference country India (human -0.106, calibrated synthetic +0.006). An earlier run reported in the July 2026 working paper (not peer reviewed) reached a Spearman correlation of 0.64 with signs agreeing on 73 percent, and its flips concentrated in origin and legal-history effects (fidelity.subconscious.ai).
Read as a discrete choice result, that says three things. The simulated and human estimates had the same sign for 26 of the 29 significant effects. The simulated sample ordered the effects closely but not exactly (rank correlation 0.83, registry record). The simulated sizes were 1.13 times the human ones after the registry's calibration step, and the registry says agreement after scaling does not establish agreement in raw sizes, so human confirmation is still needed before relying on a size. The single-study walkthrough lists each flipped effect, and the validation page carries the same comparison for 308 studies.
Conjoint, MaxDiff and a rating scale
| Instrument | What the respondent does | What you get | What it cannot give you |
|---|---|---|---|
| Discrete choice experiment (choice-based conjoint) | Chooses one option from a set of complete options | Effect of each feature level on choice, with intervals; preference share for whole options | Realized sales |
| Standard item-based MaxDiff (best-worst scaling) | Picks the best and worst item from a short list | A ranking of items on one scale, with intervals | Trade-offs between features and price inside one option |
| Rating scale | Scores each feature on importance | A stated importance score | Choice behavior; importance ratings can differentiate weakly when respondents rate many features highly |
Choose the discrete choice experiment when the decision is a trade-off between features and price inside an offer. Choose MaxDiff when the question is which of many items matters most and nothing is bundled. An importance rating records stated importance; a choice task estimates trade-offs.
Sample size and the simulated case
In a human study, the number of respondents and tasks helps determine how narrow the intervals are; the design and the variability of choices matter too. In a simulated study the interval describes the noise inside the model and design; it does not include how far the simulated population sits from the human one. That gap is what the replication comparison above measures, and the public registry shows that it varies by study: in its 308 detailed comparisons (read 2026-11-12), direction held in 127, was mixed in 92 and failed in 89 (study registry). Treat a simulated effect as a candidate to test with people, and size the human study from the smallest difference that would change your decision.
To scope a choice experiment for a pricing or product decision, see how to test pricing before launch or book a decision review.
How this page was made
By: Avi Yashchin, CEO and Co-Founder. Drafted with AI assistance on 2026-11-07 and updated on 2026-11-12 from the public registry record for Hainmueller 2014 (saved run of 2026-11-06), the study registry index and the fidelity.subconscious.ai summary of the July 2026 working paper, all read on 2026-11-12.