A Geostatistical Linear Regression Model for Small Area Data

Abstract

We present a new linear regression model for use with aggregated, small area data thatare spatially autocorrelated. Because these data are aggregates of individual-level data,we choose to model the spatial autocorrelation using a geostatistical model specifiedat the scale of the individual. The autocovariance of observed small area data is de-termined via the natural aggregation over the population. Unlike lattice-based auto-regressive approaches, the geostatistical approach is invariant to the scale of dataaggregation. We establish that this geostatistical approach also is a valid autoregressivemodel; thus, we call this approach the geostatistical autoregressive (GAR) model. Anasymptotically consistent and efficient maximum likelihood estimator is derived forthe GAR model. Finite sample evidence from simulation experiments demonstrates therelative efficiency properties of the GAR model. Furthermore, while aggregation resultsin less efficient estimates than disaggregated data, the GAR model provides the mostefficient estimates from the data that are available. These results suggest that the GARmodel should be considered as part of a spatial analyst’s toolbox when aggregated,small area data are analyzed. More important, we believe that the GAR model’s at-tention to the individual-level scale allows for a more flexible and theory-informedspecification than the existing autoregressive approaches based on an area-level spa-tial weights matrix. Because many spatial process models, both in geography and inother disciplines, are specified at the individual level, we hope that the GAR covari-ance specification will provide a vehicle for a better informed and more interdisci-plinary use of spatial regression models with area-aggregated data.