Correlation and scale in mixed logit models

This paper examines sources of correlation among utility coefficients in models allowing for random heterogeneity, including correlation that is induced by random scale heterogeneity. We distinguish the capabilities and limitations of various models, including mixed logit, generalized multinomial logit (G-MNL), latent class, and scale-adjusted latent class. We demonstrate that (i) mixed logit allows for all forms of correlation, including scale heterogeneity, (ii) G-MNL is a restricted form of mixed logit that, with an appropriate implementation, can allow for scale heterogeneity but (in its typical form) not other sources of correlation, (iii) none of the models disentangles scale heterogeneity from other sources of correlation, and (iv) models that assume that the only source of correlation is scale heterogeneity necessarily capture, in the estimated scale parameter, whatever other sources of correlation exist.