Fitting conditional and simultaneous autoregressive spatial models in hglm

We present a new version (> 2.0) of the hglm package for fitting hierarchical generalized linear models (HGLMs) with spatially correlated random effects. CAR() and SAR() families for conditional and simultaneous autoregressive random effects were implemented. Eigen decomposition of the matrix describing the spatial structure (e.g., the neighborhood matrix) was used to transform the CAR/SAR random effects into an independent, but eteroscedastic, Gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR and SAR models. This gives a computationally efficient algorithm for moderately sized problems.

Methodological issues in applying Location Models to Rural areas

Location Models are usedfor planning the location of multiple service centers in order to serve a geographicallydistributed population. A cornerstone of such models is the measure of distancebetween the service center and a set of demand points, viz, the location of thepopulation (customers, pupils, patients and so on). Theoretical as well asempirical evidence support the current practice of using the Euclidian distancein metropolitan areas. In this paper, we argue and provide empirical evidencethat such a measure is misleading once the Location Models are applied to ruralareas with heterogeneous transport networks. This paper stems from the problemof finding an optimal allocation of a pre-specified number of hospitals in alarge Swedish region with a low population density. We conclude that the Euclidianand the network distances based on a homogenous network (equal travel costs inthe whole network) give approximately the same optimums. However networkdistances calculated from a heterogeneous network (different travel costs indifferent parts of the network) give widely different optimums when the numberof hospitals increases.  In terms ofaccessibility we find that the recent closure of hospitals and the in-optimallocation of the remaining ones has increased the average travel distance by 75%for the population. Finally, aggregation the population misplaces the hospitalsby on average 10 km.