ABSTRACT
Significant discrepancies are often found between the spatial-temporal data that we observe and the predictions from a space-time separable model. Such departures from space-time separability, indicative of the presence of space-time interaction, can arise for many different reasons. In order to move from a space-time separable model to a space-time inseparable model, it is necessary to add a space-time interaction component, a new “block”, that is, to accommodate space-time interaction. The specification of such a block will draw on the two fundamental properties of spatial-temporal data: dependency (the basis for information borrowing) and heterogeneity (the form of which informs the specification of the parameters in the space-time interaction component). Four types of modelling strategy are discussed. Each modelling strategy is an assumption that imposes a dependence structure on the parameters in the space-time interaction component. The implications of each strategy (or assumed dependence structure) is considered for the purposes of information sharing and parameter estimation. These strategies are illustrated using small area annual burglary count data. The computational challenge that arises when fitting some of these space-time inseparable models is considered.
