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On this page: what a discrete choice experiment (DCE) actually asks respondents to do; how to select attributes and levels without collapsing them into meaningless categories; how a full factorial explodes and why a fractional factorial or D-efficient design fixes that; how profiles get paired into choice sets; how conditional logit turns choice data into attribute-level utility; and a fully worked design-and-analysis example with every number computed directly, not asserted.
What a discrete choice experiment measures
A discrete choice experiment presents respondents with a series of choice tasks, each showing two or more hypothetical options (“profiles”) built by varying a small set of attributes across defined levels, and asks the respondent to pick the option they prefer — or, in most modern designs, to also allow “neither” as a valid answer. Unlike a Likert-scale item that asks how much someone agrees with a single statement, a DCE never asks about one attribute in isolation. Every choice forces a trade-off: a respondent who prefers a lower price but also prefers a shorter wait time has to reveal, through repeated choices, how much of one they’ll give up for the other. That trade-off structure is the entire point of the method — it is a form of survey instrument built specifically to recover the relative weight respondents place on each attribute, not just whether they like or dislike it.
The method sits inside random utility theory: each respondent is assumed to attach an unobserved (to the researcher) utility to every profile, and to choose the profile with the highest utility on a given task, subject to random noise the analyst can’t observe. That assumption is what lets choice data — a simple record of which option a respondent picked — be decomposed back into how much each individual attribute contributed to the decision. DCEs are used across health economics and health-preference research (this is where the bulk of the applied methodology literature lives, including ISPOR’s published good-practice task force reports on conjoint analysis in health), transportation and environmental valuation (the method’s origin, developed from Daniel McFadden’s work on conditional logit models of travel-mode choice, which contributed to his 2000 Nobel Memorial Prize in Economic Sciences), and increasingly in research-administration contexts — eliciting researcher preferences among funding-mechanism designs, repository policies, or publishing-venue terms.
Selecting attributes: the step most designs get wrong first
An attribute is a characteristic of the thing being evaluated that you expect to actually drive the choice; a level is a specific value that attribute can take in a given profile. Two design failures dominate weak DCEs, and both happen at this stage, before any statistical machinery is involved:
- Too many attributes. Each additional attribute multiplies the size of the full factorial (see below) and increases the cognitive burden on the respondent per choice task. Applied DCE guidance generally converges on 4–6 attributes as a practical ceiling for a single-profile comparison task; past roughly 6–7, respondents measurably start using simplifying heuristics (ignoring some attributes, anchoring on one) rather than genuinely weighing all of them, which corrupts exactly the trade-off signal the method exists to capture.
- Levels that aren’t independently crossable. An attribute level has to make sense in combination with every other attribute’s levels, because a fractional factorial design will generate combinations you didn’t hand-pick. If “same-day delivery” and “no shipping fee” are actually the same underlying policy dressed as two attributes, the design will generate internally contradictory profiles (same-day delivery, but paid shipping disabled) that respondents can’t evaluate coherently.
Attributes and levels are normally identified through a qualitative phase before any quantitative design work — literature review, expert interviews, or focus groups — specifically to avoid the researcher’s own priors substituting for what actually drives the target population’s decisions. Skipping that step and hand-picking attributes from intuition is one of the most common quality gaps in applied DCEs; it produces a statistically valid design measuring the wrong thing.
Why a full factorial doesn’t scale, and what a fractional factorial does instead
A full factorial design generates every possible combination of every level of every attribute. With k attributes each having L levels, that’s Lk profiles — four attributes at three levels each is already 34 = 81 profiles; five attributes at four levels is 45 = 1,024. No respondent can evaluate anywhere near that many choice tasks, so no real DCE uses the full factorial directly.
A fractional factorial design selects a deliberately structured subset of the full factorial — not a random subset, but one chosen so that the attribute columns remain orthogonal (statistically uncorrelated with one another across the selected profiles). Orthogonality is what lets the eventual analysis attribute a change in choice probability to one specific attribute rather than to a confound between two attributes that happened to always move together in the profiles shown. The classic construction method assigns a subset of attributes directly from a base full factorial and derives the remaining attribute levels from a generator — an algebraic rule (e.g., the level of attribute D is set equal to the product of the levels of A, B, and C) that determines the rest of the design while preserving orthogonality on main effects. This sacrifices the ability to independently estimate every interaction effect (two-factor interactions become “aliased with,” i.e. statistically indistinguishable from, other effects), which is an accepted trade-off in most applied DCEs, where the attributes are chosen expecting mainly additive, main-effect utility.
A D-efficient design goes further: instead of relying on a fixed classical construction, an algorithm (available in Ngene, SAS %MktEx, R’s idefix/support.CEs, and similar tools) searches for the specific set of profiles and choice-set pairings that minimizes the D-error of the resulting parameter-estimate covariance matrix, given either flat “no prior” assumptions or Bayesian priors from a pilot study. In practice, most published DCEs today use software-generated D-efficient designs rather than hand-built fractional factorials, precisely because the algorithm can directly optimize for statistical efficiency (tighter confidence intervals for a given sample size) instead of only guaranteeing orthogonality. The fractional-factorial logic below is still the right way to understand what the software is doing and why orthogonality matters, even when a D-efficient algorithm produces the final design.
From profiles to choice sets
Once a set of profiles exists, they still have to be grouped into choice sets — the actual tasks a respondent sees, each showing 2–4 profiles side by side (2 or 3 is most common; more than 4 reintroduces the cognitive-overload problem attribute selection was trying to avoid). A common construction pairs each profile with its foldover — the profile created by flipping every attribute to its opposite level — which guarantees that within a pair, no single attribute is held constant (every attribute genuinely varies within every choice task, maximizing the information each task provides). Most current designs also add a “none” / opt-out option to every choice set, because forcing a choice between two options a respondent would reject in the real world (forced choice) inflates the apparent preference strength for whichever option is merely “less bad,” and the opt-out lets the researcher separately estimate how many people wouldn’t choose either option at all.
Worked example: attributes, design, and analysis together
The scenario, attributes, and part-worth utility weights below are constructed for this page to demonstrate the mechanics end to end. They are not drawn from a real study, and every number that follows — the design matrix, the orthogonality check, and the choice probabilities — was computed directly with a short script, not asserted; the arithmetic is reproducible from the formulas shown.
Illustrative research question: which combination of terms makes researchers most willing to publish in a given open-access venue? Four attributes, each at two levels:
| Attribute | Level −1 | Level +1 |
|---|---|---|
| A — Article Processing Charge | $500 | $3,000 |
| B — Embargo period | 0 months (immediate OA) | 12 months |
| C — License | CC BY | CC BY-NC |
| D — Repository type | Institutional repository | Subject-specific repository |
A full factorial here is 24 = 16 profiles. Using the standard half-fraction generator D = A×B×C, the eight profiles below are generated by enumerating all combinations of A, B, and C and deriving D from the generator:
| Profile | A | B | C | D |
|---|---|---|---|---|
| P1 | −1 | −1 | −1 | −1 |
| P2 | −1 | −1 | +1 | +1 |
| P3 | −1 | +1 | −1 | +1 |
| P4 | −1 | +1 | +1 | −1 |
| P5 | +1 | −1 | −1 | +1 |
| P6 | +1 | −1 | +1 | −1 |
| P7 | +1 | +1 | −1 | −1 |
| P8 | +1 | +1 | +1 | +1 |
Checking orthogonality directly: summing the product of every pair of attribute columns across all eight profiles (A·B, A·C, A·D, B·C, B·D, C·D) gives zero for all six pairs — confirmed by script, not assumed — so no two main effects are confounded with each other in this design.
Pairing each profile with its foldover (P1↔P8, P2↔P7, P3↔P6, P4↔P5) produces four two-profile choice tasks; adding an opt-out option to each gives the final choice-set structure a respondent would see. Task 4 pairs P4 (APC $500, 12-month embargo, CC BY-NC, institutional repository) against P5 (APC $3,000, immediate OA, CC BY, subject-specific repository) plus “neither.”
To show how that task would be analyzed, assign illustrative part-worth utility weights (invented for this demonstration only, not fitted to any real data) and apply the standard conditional logit (multinomial logit) choice formula, Pi = exp(Vi) / ∑j exp(Vj), where V is each option’s total utility:
- βAPC = −0.0006 per dollar
- βembargo = −0.05 per month
- βCC BY-NC = −0.30 (penalty relative to CC BY)
- βsubject-repo = +0.15 (bonus relative to institutional)
- βopt-out = −1.20 (fixed alternative-specific constant)
For Task 4: Option X (P4) has utility V = (−0.0006×500) + (−0.05×12) + (−0.30) + 0 = −1.2000. Option Y (P5) has utility V = (−0.0006×3000) + 0 + 0 + 0.15 = −1.6500. The opt-out has V = −1.2000 by construction. Exponentiating and normalizing:
| Option | Utility (V) | exp(V) | Choice probability |
|---|---|---|---|
| X — P4 (cheap, delayed, restrictive license, institutional) | −1.2000 | 0.3012 | 37.9% |
| Y — P5 (expensive, immediate, open license, subject repository) | −1.6500 | 0.1920 | 24.2% |
| Z — Neither (opt-out) | −1.2000 | 0.3012 | 37.9% |
The three probabilities sum to 1.000000, confirming the arithmetic. In a real DCE, these β weights are not assumed — they are the coefficients a conditional logit model estimates from many respondents’ actual choices across many such tasks; this worked task only demonstrates how already-estimated (or, here, illustrative) weights convert into a predicted choice share for one specific task. Estimating the weights themselves from real choice data requires maximum-likelihood estimation across the full panel of responses, standard in dedicated choice-modeling software or in R packages such as mlogit, gmnl, or apollo; a simple multinomial logistic regression framework is the right starting point for understanding the underlying model even where a dedicated choice-modeling package is used for the final estimation, and the logit model that conditional logit generalizes is worth reviewing first if the log-odds mechanics aren’t already familiar.
Sample size, and what analysis actually recovers
Because each respondent answers multiple choice tasks, a DCE generates far more observations than respondents — but the tasks from one respondent aren’t independent of each other, which is why analysis uses multinomial/conditional logit rather than treating each task as an unrelated observation, and why sample-size guidance for DCEs is expressed in rules of thumb tied to the number of choice tasks, alternatives, and attribute levels (a widely cited heuristic from the applied conjoint-analysis literature is roughly 500 × (largest number of levels on any attribute) ÷ (number of alternatives per task) ÷ (number of tasks per respondent) as a starting estimate) rather than the single-proportion or single-mean formulas covered in general power-analysis guidance. The output of a fitted model is a set of part-worth utilities per attribute level, which can be rescaled into relative importance weights, willingness-to-pay estimates (when one attribute is a price/cost), or predicted uptake shares for specific hypothetical profiles — the same mechanical step demonstrated above, just with estimated rather than illustrative coefficients.
Frequently asked questions
What’s the difference between a discrete choice experiment and conjoint analysis?
“Conjoint analysis” is the broader family of stated-preference methods that trace back to mathematical psychology and market research; a discrete choice experiment is specifically the choice-based variant, where respondents pick one full profile from a set rather than rating or ranking single profiles individually. In current practice the terms are often used loosely and interchangeably, but “DCE” specifically signals the choice-based task format described on this page.
How many attributes and levels should a DCE use?
Most applied guidance converges on 4–6 attributes with 2–4 levels each as a practical range; more attributes or levels increase both the cognitive burden per task and the number of choice tasks needed for a statistically efficient design.
Do I need statistical software to build the design, or can I do it by hand?
A small hand-built fractional factorial (as in the worked example above) is workable for teaching the mechanics or for a genuinely small design. For anything beyond a handful of attributes, purpose-built design software (Ngene, SAS, or R’s idefix/support.CEs packages) is standard practice, because D-efficient search over the space of possible designs isn’t practical by hand once the attribute count grows.
Why add a “none”/opt-out option to a choice set?
Without it, every respondent is forced to pick between two options even when they’d genuinely reject both in the real world, which distorts the apparent preference strength for whichever option is merely less unattractive. An opt-out lets the model separately estimate genuine non-uptake.
Related reading: Research Methods & Statistics · Questionnaire design · Likert scale survey design · Levels of measurement · Multinomial logistic regression · Logistic regression (the logit model) · Statistical power analysis.
