A spatial random-effects model for interzone flows: commuting in Northern Ireland

Government policy on employment, transport, and housing often depends on reliable information about spatial variation in commuting flows across a region. Simple commuting rates summarising inter-area flows may not provide a full perspective on the underlying levels of commuting attractivity of different areas (as destinations), or the varying dependence of different areas (as origins) on outside employment. Areas also vary in the degree of commuting self-containment, as expressed in intra-area flows. This paper uses a spatial random-effects model to develop indices of attractivity, extra-dependence, and self-containment using a latent factor method. The methodology allows consideration of the degree to which different explanatory influences (e.g. socioeconomic structure, characteristics of road networks, employment density) affect these aspects of commuting. The particular application is to commuting flows in Northern Ireland, using 139 zones that aggregate smaller areas (wards), so avoiding undue sparsity in the flow matrix. The analysis involves Bayesian estimation, with the outputs comprising full densities for extra-dependence, and attractivity scores and scores for intra-area containment of zones. Spatial patterning in these aspects of commuting is allowed for in the model used. One key pattern is the difference in latent effect estimates for urban (in particular, Belfast) and rural areas reflecting variable job opportunities in these areas.