Empirical Zoning Distributions for Small Area Data
It is well established that using data summaries for a set of geographic areas or zones to estimate the parameters of a statistical model, commonly called ecological inference, frequently leads to the modifiable area unit problem (MAUP). In this article, the zoning effect of the MAUP is investigated for a range of scales. A zoning distribution is defined, and then used to characterize the zoning effect for parameter estimates from ecological analyses. Zone-independent parameter estimates are obtained using the mean of the zoning distribution, and assessed using the variance of the zoning distribution. Zoning distributions are illustrated for parameter estimates from two ecological regression models at multiple scales using Australian National Health Survey data. For both a continuous response variable and a binary response variable, the empirical zoning distributions are unimodal, relatively symmetrical with appreciable variation, even when based on a large number of zones. The "ecological mean," or expected value of the empirical zoning distribution at each scale, displays systematic variation with scale and the zoning distribution variance also depends on scale. The results demonstrate that the zoning effect should not be ignored, and the sensitivity of ecological analysis results to the analysis zones should be assessed.