Using a sequential latent class approach for model averaging: Benefits in forecasting and behavioural insights

Despite the frequent use of model averaging in many disciplines from weather forecasting to health outcomes, it is not yet an idea often considered in travel behaviour or choice modelling. The idea behind model averaging is that a single model can be created by calculating contribution weights for a set of candidate models, depending on their relative performance, thus creating an ‘average’. There are different ways of doing this, with a clear distinction between looking at the overall performance of each model or by doing this at the level of individual agents or observations. In this paper, we demonstrate that a relatively straightforward adaptation of latent class models can be used for the latter approach and show how this can be an effective method for travel behaviour modelling. We identify two key opportunities for model averaging. The first is the situation where an analyst faces the difficult choice between a number of advanced models, all with some desirable properties. The second is the situation where advanced models cannot be used due to the size of the data and/or choice sets. Our tests demonstrate that in both cases, model averaging using a sequential latent class framework results in a consistent improvement in model fit for both estimation and in forecasting with subsets of validation samples. Additionally, we demonstrate that model averaging can be used to obtain more reliable elasticities and welfare measures by averaging across outputs obtained from the set of candidate models. In terms of actual implementation of model averaging, we present a simple expectation–maximisation (EM) algorithm which can deal with very large numbers of candidate models within the same model averaging structure, unlike the typical case with classical estimation approaches for latent class.