Updating and transferring Random Effect models: The case of operating speed percentile estimation

Random Effect (RE) models are used for analyzing data that are non-independent or when data are characterized by a hierarchical structure. In traffic and highway engineering, RE models have been successfully employed to estimate free-flow speed distributions from data containing observations that are naturally nested according to different levels (i.e. direction, sections, roads). Empirical studies conducted on both urban arterials and rural two-lane highways have shown that RE models, by properly accounting for the survey design, are superior to traditional Fixed Effect (FE) models. However, RE models are non-transferable because of the unknown RE value for roads or road sections belonging to a different network or roadd of the same network that were not originally used to develop the model. In this paper, the transferability of RE models to road sections that were not in the original sample used for model estimation was studied, under the assumption that for these additional sections very few observations are available or can be collected. This problem poses two challenges. First, random effects for the new road sections should be estimated in order to make out-of-sample predictions. Second, the original model formulation makes use of speed quantiles as predictors of the linear model which are not readily available for the new sections. The method proposed estimates an auxiliary model, in which the RE of the original model are correlated to the RE to be defined for the new section, with the former being used to predict the latter. The RE pairs are modeled jointly, taking advantage of their potential mutual correlation. The model coefficients obtained are also validated using a jackknife technique. Results show that the method converges quite fast and that a handful of observations for the new road section are sufficient for good RE estimates.