Accounting for Preference Heterogeneity in Discrete Choice Experiments Using Hierarchical Bayes
Bibliographic record
Abstract
The econometric modelling of discrete choice experiments (DCEs) in health economics has recently incorporated preference heterogeneity using the mixed logit (MXL) specification. Modelling heterogeneity combines estimates of the population distribution with information from individuals' choices. There are, however, some known difficulties with the estimation of the MXL model if a frequentist approach is taken. Namely, convergence to the maximum of the simulated likelihood (MSL) function can be difficult if the starting values are not close to their maximum, or if certain distributions are specified. This is because the likelihood function may have multiple local maxima, or not be well approximated by a quadratic. An alternative strategy for estimating the MXL model is to employ a hierarchical Bayes (HB) approach. HB shares the same behavioural assumptions of the frequentist MXL approach, but differs in its estimation procedure and interpretive philosophy. HB uses Gibbs sampling and Metropolis-Hastings to determine the joint posterior. HB does not require the maximization of a likelihood function, thus avoiding issues of local versus global maxima. Despite their differences, HB and MSL may produce the same numerical results. The Bernstein-von Mises theorem states that if the mean of the posterior is taken as an estimate, it will converge asymptotically to the maximum likelihood estimator. This result may not hold in small samples because the approaches differ in their treatment of uncertainty. The objective of this study was to investigate the specification, estimation and performance of the HB approach using data collected from a DCE researching preferences for a novel technology identifying genetic causes of developmental delay. 756 respondents recruited using a market research company completed 16 choice questions, each with three alternatives. The first two alternatives differed on the bases of three attributes: likelihood of genetic diagnosis, time waiting for results, and cost. The third alternative is an opt-out option to model non-demanders. The advantages and comparability of the HB and MSL approaches are also investigated by applying the same random parameter structure using normal and log normal distributions; both models also accounted for the panel structure of the data. Given that the scale parameter may confound a direct comparison of the parameters, the estimates from the frequentist MXL will be rescaled such that the cost coefficient is normalized to be the same for the two procedures. We also test the forecasting ability of either approach using the expected coefficients in the logit formula to calculate the probability of a respondent choosing an alternative. If a model specification is accurate, the alternative with the highest probability in a given choice set should be chosen in the majority of circumstances. The HB and MSL models yielded similar parameter estimates and were equally successful in predicting within-sample responses. In this particular analysis, the HB approach resulted in a quicker estimation time; however, this result may not hold if other distributions are specified. This is because drawing from the conditional posterior becomes complicated if non-normal distributions are specified.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.094 | 0.179 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".