Accounting for attribute non-attendance and common-metric aggregation in a probabilistic decision process mixed multinomial logit model: a warning on potential confounding

Latent class models offer an alternative perspective to the popular mixed logit form, replacing the continuous distribution with a discrete distribution in which preference heterogeneity is captured by membership of distinct classes of utility description. Within each class, preference homogeneity is usually assumed, although interactions with observed contextual effects are permissible. A natural extension of the fixed parameter latent class model is a random parameter latent class model which allows for another layer of preference heterogeneity within each class. A further extension is to overlay attribute processing rules such as attribute non-attendance (ANA) and aggregation of common-metric attributes (ACMA). This paper sets out the random parameter latent class model with ANA and ACMA, and illustrates its application using a stated choice data set in the context of car commuters and non-commuters choosing amongst alternative packages of travel times and costs pivoted around a recent trip in Australia. What we find is that for the particular data set analysed, in the presence of attribute processing together with the discrete distributions defined by latent classes, that adding an additional layer of heterogeneity through random parameters within a latent class only very marginally improves on the statistical contribution of the model. Nearly all of the additional fit over the fixed parameter latent class model is added by the account for attribute processing. This is an important finding that might suggest the role that attribute processing rules play in accommodating attribute heterogeneity, and that random parameters within class are essentially a potentially confounding effect. An interesting finding, however, is that the introduction of random parameters increases the probability of membership to full attribute attendance classes, which may suggest that some individuals assign a very low marginal disutility (but not zero) to specific attributes or that there are very small differences in the marginal disutility of common-metric attributes, and this is being accommodated by random parameters, but not observed under a fixed parameter latent class model.