Characteristics of empirical zoning distributions for small area health data

Many studies of health utilise a multilevel modelling framework and if individual level data are not available use ecological inference to obtain individual level parameter estimates using area-level data summaries, resulting in biased parameter estimates and increased variance. For these studies, the modifiable area unit problem means that the scale of the analysis and the zones used to aggregate the data affect the amount and direction of the bias and the increase in variance. To investigate the effects of scale and zoning, in this paper the distribution of the parameter estimates for over many sets of zones at the same scale (the zoning distribution) is obtained for parameter estimates from an ecological model at multiple scales of analysis. The distributions are typically symmetrical and unimodal and can be considered to follow a normal distribution. The estimated average parameter estimate (ecological average) displays systematic variation with scale and is related to √M - 1. The variance of the distribution is related to the average number of observations in the areas. The implications of creating and using a zoning distributions are wide ranging as they allow the estimates for a given set of zones at the same or a different scales to be compared and assessed.