A break from the norm? Parametric representations of preference heterogeneity for discrete choice models in health

Background: Any sample of individuals has its own, unique distribution of preferences for choices that they make. Discrete choice models try to capture these distributions. Mixed logits are by far the most commonly used choice model in health. A raft of parametric model specifications for these models are available. We test a range of alternatives assumptions, and model averaging, to test if or how model outputs are impacted. Design: Scoping review of current modelling practices. Seven alternative distributions, and model averaging over all distributional assumptions, were compared on four datasets: two were stated preference, one was revealed preference, and one was simulated. Analyses examined model fit, preference distributions, willingness-to-pay, and forecasting. Results: Almost universally, using normal distributions is the standard practice in health. Alternative distributional assumptions outperformed standard practice. Preference distributions and the mean willingness-to-pay varied significantly across specifications, and were seldom comparable to those derived from normal distributions. Model averaging offered distributions allowed for greater flexibility, further gains in fit, reproduced underlying distributions in simulations, and mitigated against analyst bias arising from distribution selection. There was no evidence that distributional assumptions impacted predictions from models. Limitations: Our focus was on mixed logit models since these models are the most common in health, though latent class models are also used. Conclusions: The standard practice of using all normal distributions appears to be an inferior approach for capturing random preference heterogeneity. Implications: Researchers should test alternative assumptions to normal distributions in their models.