Predicting best with mixed logit models: Understanding some confounding effects

A Mixed Logit (ML) model utility function is characterised by an error term with two components; the first, is designed to capture white noise effects and allows obtaining a basic logit probability. The second allows achieving a fairly general covariance matrix and has a distribution that can be freely chosen by the modeller. This flexible structure is at the roots of the great popularity of the ML but is also the cause of a potentially major problem, as several effects, such as correlation, response and preference unobserved heterogeneity and heteroskedasticity, might be confounded. We analyse the problem raised by the confounding effects in the ML and their relation with the trade-offs implicit in the typical linear in the parameters with additive disturbances utility structure. In particular, we refer to three assumptions common to almost any discrete choice model: (a) that individuals evaluate alternatives making a trade-off among attributes; (b) that unobserved attributes might be accounted for by an additive random structure, and (c) that only the difference between alternatives matters. Using simulated and real data we demonstrate that confounding effects are intrinsic to the "true" role of any random term, either distinguishing or adding commonality to pairs of alternatives. This is not as obvious as it may appear, and thinking of error terms as "proxy" for unobserved omitted structures helps to understand their "true" role and aids in the search for better model specifications.