Univariate and Multivariate Conditionally Autoregressive Spatial Modeling in the Analysis of Areal Population Data

Kuo-Ping Li, University of North Carolina at Chapel Hill
Chirayath Suchindran, University of North Carolina at Chapel Hill

Areal data such as census data of counties are widely used in population researches. However, the spatial dependence inherent in these data is often ignored by researchers, causing biases in all statistical inferences. Thus, models that consider spatial correlation are desirable. In this study, we applied two hierarchical Bayesian models that account for spatial correlation in the analysis of county population data. The conditionally autoregressive (CAR) model was used to deduct the dependence of population of age 0-17 and age 65+ on the household income of 100 North Carolina counties. This model successfully accounted for spatial clustering effects. The multivariate CAR (MCAR) model was used to access the spatial correlation between two outcomes (the two population proportions). In some situations MCAR models tend to overweight the spatial correlation. Although caution in application should be exercised, MCAR models can be very useful in the analysis of multivariate areal data.