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. Many parametric specifications for these models are available. We test a range of alternative assumptions and model averaging to test if or how model outputs are affected. Design: Scoping review of current modeling practices. Seven alternative distributions and model averaging over all distributional assumptions were compared on 4 datasets: 2 were stated preference, 1 was revealed preference, and 1 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 allowing for greater flexibility and 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 affected predictions from models. Limitations: Our focus was on mixed logit models since these models are the most common in health, although 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. Highlights: Health modelers use normal mixing distributions for preference heterogeneity. Alternative distributions offer more flexibility and improved model fit. Model averaging offers yet more flexibility and improved model fit. Distributions and willingness to pay differ substantially across alternatives.