A Structural Equation Approach to Spatial Dependence Models

A strong increase in the availability of space-time data has occurred during the past decades. This has led to the development of a substantial literature dealing with the two particular problems inherent to this kind of data, i.e. serial dependence between the observations on each spatial unit over time, and spatial dependence between the observations on the spatial units at each point in time (e.g. Elhorst, 2001, 2003). Typical for spatial panel data models is that the causal direction cannot be based on instantaneous relationships between simultaneously measured variables. Rather the so-called cross-lagged panel design studies compare the effects of variables on each other across time. Although they circumvent the difficult problem of assessing causal direction in cross-sectional research, the cross-lagged panel design studies are usually performed in discrete time (Oud, 2002). Because of different discrete time observation intervals within and between studies, outcomes are often incomparable or appear to be contradictory (Gollob & Reichardt, 1987). This paper will describe the problems of cross-lagged space-time models in discrete time and propose how these problems can be solved through a continuous time approach. In this regard special attention will be paid to structural equation modelling (SEM). In addition, we shall describe how space-time dependence can he handled in a SEM framework