Understanding the Potential Role of the Latent Mix Model Comprising a Combination of Latent Class and Mixed Logit
P Davidson, C Teye-Ali, R Culley, Peter Davidson Consultancy, UK
This paper investigates the model formed when mixed logit is combined with latent class logit such as may be needed to explain data which forms clusters within which data forms a distribution about its centre
Mixed logit explains choice on the basis of fitting the shape of a given distribution to the many different values of (for example) the value of time, found between people. On the other hand latent class puts people into different "bins" or classes with all those in one class having the same (or similar) value of time, so as to account for the variation between people's value of time. How good each is at explaining choice, depends upon whether the variation found in the choice data falls into clusters (which mitigates for latent class) or forms a continuum (which mitigates for mixed logit).
One may suppose that data could comprise clusters of (say) the value of time with each cluster having its own continuum where this continuum falls entirely within the range of the cluster. Such data might be better explained by using the latent class model to define the clusters and mixed logit to explain the variation within the cluster. Such a model would comprise a latent class model with mixed logit (which we have abbreviated to a latent mix model).
This is complicated by the potential to need 2, 3, 4, or many more classes for the latent class model, by requiring the mixed logit distribution to be pre-specified and by the number sequence of draws needed for the mixed logit model.
This paper explores the ability of the latent mix model to explain a series of datasets which have been specifically constructed to see how well the model estimation process can recover the coefficients used to construct the data. The latent mix model is compared to usual armory of multinomial, nested, cross nested, mixed and latent class logit models at explaining these data.
This paper is unique in that there is not much published on using a combined mixed and latent class model and this paper opens up this topic for investigation.
Association for European Transport