Discrete Choice Experiment

What a discrete choice experiment measures

Choices are analysed using random utility models to estimate how attribute levels influence preferences and the trade-offs respondents are willing to make. This page explains DCE development, experimental design, choice modelling, willingness to pay, heterogeneity and use in health economics.

A DCE measures stated choices under constructed conditions. Its results are not automatically equivalent to real-world behaviour, welfare or policy value outside the population and choice context studied.

Alternatives are built from attributes and levels

An attribute is a feature of the service, treatment or outcome being evaluated, while a level is a specific value that the attribute can take. A choice task combines levels into two or more alternatives and may include an opt-out, current-care or status-quo option.

For example, a treatment DCE might use:

Attributes should be understandable, decision-relevant and capable of plausible trade-offs. Too many attributes, unrealistic combinations or unclear levels can increase cognitive burden and weaken the interpretation of choices.

Random utility theory connects choices to preferences

For respondent (n), alternative (j) and choice task (t), utility is represented as:

$$U_{njt}=V_{njt}+\varepsilon_{njt}$$

where (V_{njt}) is the systematic utility explained by observed attributes and parameters, and (\varepsilon_{njt}) contains unobserved influences. A common linear specification is:

$$V_{njt} = \beta_1x_{1,njt} +\beta_2x_{2,njt} +\cdots+ \beta_Kx_{K,njt}$$

The respondent chooses alternative (j) when its utility exceeds that of every other available alternative. Because the error term is unobserved, the model estimates choice probabilities rather than deterministic choices.

Conditional logit gives a basic choice probability

If the random errors are independent and identically distributed type-I extreme value, the conditional logit probability is:

$$P_{njt} = \frac{\exp(V_{njt})} {\sum_{k\in C_{nt}}\exp(V_{nkt})}$$

where (C_{nt}) is respondent (n)'s choice set in task (t). Increasing an alternative's systematic utility increases its probability of being chosen relative to the other available alternatives.

The model implies independence of irrelevant alternatives for the unobserved utility components. That property can be unrealistic when alternatives share unobserved features, repeated choices from the same respondent are correlated or preference heterogeneity is substantial.

A worked probability example

Suppose a two-alternative task has systematic utilities:

$$V_A=0.80 \qquad\text{and}\qquad V_B=0.20$$

The conditional-logit probability of choosing A is:

$$P(A) = \frac{e^{0.80}} {e^{0.80}+e^{0.20}} \approx0.6457$$

The probability of choosing B is:

$$P(B)=1-P(A)\approx0.3543$$

Only the utility difference matters in this binary task. Adding the same constant to both utilities leaves the probabilities unchanged, illustrating why utility location must be normalised for identification.

Coefficients quantify preference direction and strength

A positive coefficient means higher values of the coded attribute increase systematic utility, while a negative coefficient means they reduce it, conditional on the specification. Magnitude cannot be interpreted independently of the attribute's units, coding and the model's unidentified utility scale.

Continuous linear coding assumes a constant marginal effect across the full range. Categorical levels require an explicit coding scheme:

• Dummy coding compares each included level with an omitted reference level.
• Effects coding compares levels with an overall pattern and represents the omitted level through the negative sum of included coefficients.
• Ordinal linear coding imposes equally spaced effects and should be used only when substantively credible.
• Non-linear continuous functions or splines can represent changing marginal preferences.

Coding changes coefficient interpretation but should not change fitted utilities when equivalent parameterisations span the same design space.

Utility scale limits comparisons across models and groups

In random utility models, estimated coefficients are confounded with the scale of the unobserved error. If error variance differs between datasets or groups, raw coefficient magnitudes can differ even when underlying preference trade-offs are similar. The conventional logit scale normalisation is necessary because utility has no absolute observable unit.

Consequences include:

• Raw coefficients should not be compared across separately estimated models without addressing scale.
• Apparent preference differences between groups may partly reflect different choice consistency.
• Ratios of coefficients within a model can cancel a common scale factor, although their uncertainty and model dependence remain.
• Joint models can estimate relative scale under suitable identification restrictions.

Scale heterogeneity and preference heterogeneity are conceptually different but can be difficult to separate empirically.

Marginal rates of substitution express trade-offs

When utility is linear and two coefficients are defined on compatible marginal scales, the trade-off between attribute (x_a) and attribute (x_b) is:

$$\operatorname{MRS}_{a,b} =- \frac{\beta_a}{\beta_b}$$

If (x_b) is cost and (\beta_{\text{cost}}<0), marginal willingness to pay for an increase in attribute (a) is:

$$\operatorname{WTP}_a =- \frac{\beta_a}{\beta_{\text{cost}}}$$

The result inherits the cost variable's currency and unit. It is valid only when the cost coefficient represents the relevant marginal utility of money and when the utility specification supports the ratio over the stated range.

A worked willingness-to-pay calculation

Suppose a model estimates a coefficient of (0.40) for reducing waiting time by one month and a cost coefficient of (-0.008) per pound. The estimated willingness to pay for a one-month reduction is:

$$\operatorname{WTP} =- \frac{0.40}{-0.008} =£50$$

This is a model-based marginal trade-off for the sampled respondents under the stated coding. It is not automatically a reimbursement threshold, market price or population welfare estimate.

Uncertainty for a coefficient ratio should be calculated using an appropriate method, such as the delta method, Fieller-type methods, bootstrap or draws from the joint parameter distribution. Dividing the endpoints of separate coefficient intervals is not generally valid.

Attribute development begins before statistical design

Attributes and levels should be derived through a transparent process combining the decision problem, evidence and input from people who understand the choice context. Qualitative research is often essential because analysts may overlook features that respondents consider central or may describe levels in ways respondents interpret differently.

Development can include:

• Literature and policy review.
• Interviews or focus groups with patients, carers, professionals or decision-makers.
• Analysis of real service or treatment options.
• Expert review of clinical and operational plausibility.
• Cognitive interviews to test interpretation and decision strategies.
• Piloting to examine burden, dominance, non-attendance and completion.

Removing an attribute merely because it is difficult to design can undermine content validity if it is central to the real decision.

Experimental design selects informative choice tasks

A full factorial design contains every possible combination of attribute levels and is usually too large. Experimental design selects a subset of profiles and pairs or groups them into tasks that identify the required effects efficiently while avoiding prohibited or implausible combinations.

Design criteria may seek to:

• Ensure parameters are identifiable.
• Balance level appearances and reduce correlation among attributes.
• Maximise D-efficiency or another information-based criterion.
• Use prior parameter values to avoid statistically uninformative tasks.
• Control overlap, dominance and task difficulty.
• Allocate tasks across questionnaire blocks.

A statistically efficient design can still be poor if respondents cannot understand it or if alternatives are unrealistic. Statistical and response efficiency must be considered together.

Priors can improve design but may also mislead it

Efficient designs often use prior beliefs about coefficient direction and magnitude. Priors can come from earlier studies, pilot estimates, expert judgement or broad distributions. A locally optimal design assumes fixed prior values, while a Bayesian efficient design averages a criterion over a prior distribution.

Misspecified strong priors can produce tasks that are poorly informative for the true preferences. Designs should be tested across plausible prior scenarios and updated after a pilot when appropriate. The pilot should resemble the intended study population and administration mode.

Choice-task construction affects validity

Each task should offer a credible choice with sufficient variation to reveal trade-offs. Dominant alternatives may be useful as comprehension checks in limited circumstances, but too many obvious tasks contribute little information about trade-offs. Conversely, near-identical alternatives can create noise and frustration.

Important decisions include:

• Labelled versus unlabelled alternatives.
• Number of alternatives per task.
• Inclusion of a status quo, current care or opt-out option.
• Attribute order and visual presentation.
• Number of tasks completed by each respondent.
• Blocking and randomisation of tasks.
• Prohibited level combinations.
• Accessibility and comprehension for the target population.

An opt-out can improve realism when declining all offered options is feasible, but it may also be selected for reasons unrelated to attributes, such as fatigue or protest.

Sample size depends on the design and estimand

There is no universal observations-per-attribute rule. Precision depends on the number of respondents, tasks per respondent, alternatives, level balance, true parameter sizes, choice consistency, model complexity, subgroup analyses and preference heterogeneity.

Planning approaches include:

• Simulation using plausible parameter values and the proposed design.
• Precision targets for priority coefficients or willingness-to-pay measures.
• Power for prespecified differences or interactions.
• Requirements for latent-class or mixed-logit models.
• Allowances for incomplete surveys, straight-lining or quality exclusions.

Repeated tasks increase the number of choices but do not create independent respondents. Sample-size calculations must account for within-person dependence and the intended model.

Panel structure must reflect repeated choices

Each respondent usually completes multiple choice tasks, so observations from the same person are correlated. A simple conditional logit model can estimate mean preferences but may underrepresent repeated-choice dependence and heterogeneity if its assumptions are used uncritically.

Panel-aware approaches include:

• Cluster-robust standard errors at the respondent level.
• Mixed logit with respondent-specific random coefficients.
• Generalised multinomial logit models incorporating additional heterogeneity.
• Latent-class models representing discrete preference groups.
• Hybrid choice models incorporating latent attitudes under stronger assumptions.

The selected model should be driven by the estimand and data, not by a desire to report the most complex available specification.

Mixed logit represents continuous preference heterogeneity

In a mixed-logit model, coefficients vary across respondents according to a specified distribution:

$$\beta_n\sim g(\beta\mid\Omega)$$

The unconditional choice probability integrates the conditional logit probability over that distribution:

$$P_{njt} = \int P_{njt}(\beta) g(\beta\mid\Omega) \,d\beta$$

The integral is generally approximated by simulation. Distribution choice matters: a normal cost coefficient allows positive marginal utility of cost for some respondents, while constrained or transformed distributions may better reflect theory but can create long tails in willingness-to-pay estimates.

Estimated standard deviations describe modelled heterogeneity, not automatically identifiable individual-level preference estimates.

Latent-class models represent discrete preference groups

A latent-class model assumes the population contains unobserved groups with different coefficient vectors. The probability of a choice is averaged across class-specific probabilities using estimated class-membership probabilities.

For classes (c=1,\ldots,C):

$$P_{njt} = \sum_{c=1}^{C} \pi_{nc} P_{njt\mid c}$$

where (\pi_{nc}) is respondent (n)'s probability of membership in class (c). Classes are statistical segments and should not be labelled as real clinical or social types without supporting evidence. The number of classes requires fit, stability, interpretability and external validation.

Preference heterogeneity can be observed or unobserved

Observed heterogeneity can be investigated through interactions between attributes and respondent characteristics. For characteristic (z_n), an interaction can be written as:

$$V_{njt} = \beta x_{njt} +\gamma(x_{njt}z_n)$$

The marginal preference for (x) then depends on (z_n). Subgroup analyses should be prespecified where possible and supported by adequate variation and sample size. Multiple exploratory interactions can generate unstable or chance findings.

Unobserved heterogeneity is represented through random coefficients or latent classes. Neither approach proves why preferences differ.

Predicted uptake is conditional on the offered choice set

Estimated utilities can predict the probability of choosing alternatives with specified attribute levels. For policy scenario (s), predicted share for alternative (j) is obtained by applying the model to every alternative in the scenario and averaging over respondents or the parameter distribution.

Predicted uptake depends on:

• Which alternatives are included.
• The attribute levels assigned to each alternative.
• The model's substitution assumptions.
• Whether an opt-out or status quo is available.
• The population distribution of preferences.
• External constraints such as eligibility, access and provider capacity.

DCE choice shares should not be presented as real market uptake without calibration or validation against observed behaviour.

Validity involves understanding, consistency and external relevance

No single test proves that a DCE measures valid preferences. Quality assessment should combine qualitative evidence, response behaviour, model diagnostics and comparison with independent information.

Possible checks include:

• Cognitive interviews showing that respondents understand attributes and tasks.
• Pilot evidence on burden, completion time and attribute interpretation.
• Expected coefficient signs where theory is unambiguous.
• Stability across task order, blocks and plausible model specifications.
• Sensitivity to excluding respondents who fail prespecified quality criteria.
• Internal prediction or holdout-choice performance.
• Comparison with revealed behaviour or external stated-choice evidence.
• Examination of dominant choices, lexicographic strategies and attribute non-attendance.

A respondent who fails one dominance task is not automatically irrational; misunderstanding, preference for an omitted feature or random error may explain the choice.

Attribute non-attendance needs careful interpretation

Respondents may ignore an attribute, use a simplifying heuristic or appear insensitive over the displayed range. Stated non-attendance from follow-up questions and inferred non-attendance from model patterns do not necessarily measure the same behaviour.

Automatically fixing a coefficient to zero for respondents who say they ignored an attribute can introduce bias if the self-report is imperfect or if attendance varies across tasks. Sensitivity analyses should compare plausible attendance specifications and distinguish low preference weight from true non-use of information.

DCEs contribute to health-economic and policy decisions

Health DCEs can quantify trade-offs among treatment outcomes, risks, service features and access conditions. They can support benefit–risk assessment, programme design and preference-sensitive economic evaluation when the sampled population and attributes match the decision.

Applications include:

• Estimating patient or public preferences for treatment features.
• Valuing reductions in waiting time, risk or burden.
• Designing healthcare services and appointment pathways.
• Measuring benefit–risk trade-offs for medicines or devices.
• Predicting relative uptake under alternative programme designs.
• Investigating preference heterogeneity and equity-relevant differences.
• Estimating willingness to pay when a credible cost attribute is included.
• Informing multi-criteria or distributional discussions alongside other evidence.

DCE preference weights are not QALY weights unless the design and valuation framework specifically establish that interpretation.

Welfare interpretation requires stronger assumptions

Willingness to pay can provide a monetary measure of a utility trade-off, but welfare interpretation depends on the validity of the cost coefficient, budget realism, consequentiality and the relation between stated choices and real constraints. Income differences can affect willingness to pay even when underlying health preferences are similar.

For public decisions, analysts should consider:

• Whether respondents believed choices could influence real policy.
• Whether the payment vehicle was credible and unavoidable.
• Whether cost levels were meaningful across income groups.
• Whether opt-out and status-quo conditions reflected real alternatives.
• Whether aggregate willingness to pay would double-count benefits already represented elsewhere.
• Whether equity concerns make unweighted monetary preferences inappropriate for the decision rule.

A statistically precise WTP estimate can still be unsuitable for resource-allocation decisions.

Common errors weaken DCE conclusions

DCEs require linked qualitative, design and statistical decisions. Weakness at an early stage cannot always be repaired by a sophisticated choice model.

• Selecting attributes without qualitative work can omit what matters to respondents.
• Using implausible combinations can elicit choices about artefacts rather than real trade-offs.
• Treating repeated tasks as independent observations understates uncertainty.
• Comparing raw coefficients across separately estimated models ignores scale differences.
• Assuming linear attribute effects can hide thresholds or diminishing sensitivity.
• Reporting WTP without joint uncertainty can overstate precision.
• Using a positive or near-zero cost coefficient can create unstable or uninterpretable WTP ratios.
• Interpreting latent classes as real population types can overstate statistical segmentation.
• Removing respondents solely for unexpected choices can bias the sample.
• Presenting predicted choice shares as actual uptake ignores behaviour and access constraints.
• Treating DCE estimates as QALYs or revealed preferences changes their meaning.

A defensible discrete-choice-experiment workflow

A high-quality DCE connects the decision question, qualitative evidence, experimental design, respondent experience and statistical model. Each stage should be documented because later estimates depend on assumptions made before any choices are observed.

1. Define the decision: State the population, alternatives, perspective and preference quantities required.
2. Develop attributes: Use evidence and qualitative research to identify relevant, understandable and actionable features.
3. Set levels: Choose plausible ranges and combinations with meaningful units and reference conditions.
4. Design the experiment: Ensure identification and efficiency while controlling burden, dominance and prohibited profiles.
5. Build the instrument: Present accessible tasks, explanations, practice questions and a realistic opt-out or status quo where appropriate.
6. Pilot thoroughly: Test comprehension, burden, priors, response patterns and the full data pipeline.
7. Plan the sample: Base size and blocking on priority estimands, repeated tasks, heterogeneity and expected exclusions.
8. Estimate appropriate models: Account for coding, panel structure, scale, heterogeneity and simulation uncertainty.
9. Validate results: Examine signs, non-linearity, robustness, response quality, predictive performance and external relevance.
10. Report interpretation: Present trade-offs, joint uncertainty, population limits, design details and consequences for the health-economic decision.

A discrete choice experiment is most credible when respondents face understandable and realistic trade-offs and the statistical model preserves the meaning of those choices. Efficient design and advanced estimation cannot substitute for valid attributes or a clearly defined decision context.