Empirical Zoning Distributions for Small Area Data

Abstract

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.

Overcoming inefficiencies arising due to the impact of the modifiable areal unit problem on single-aggregation disease maps

“…OAM's zonations must completely segment the geographical study area. Following previous authors [32,33], we show how suitable zonations can be created using the freely-available software AZTool [35,36]. Briefly, AZTool operates by zoning a set of minimal units according to a target denominator size and potentially other constraints (e.g.…”

“…While some association studies have examined the impact of the MAUP's zonation aspect (e.g. see [24,32,33]), to our knowledge, no similar study exists in disease mapping. Further, as far as we are aware, no previous study has investigated the impact of the MAUP in the context of efficiency.…”

Constraint Choice for Spatial Microsimulation

“…This section demonstrates the use of the d ‐statistic for selecting constraint variables for a study considering the microsimulation of realistic health outcome and covariate data for the population of New South Wales (NSW), Australia. The data were simulated to study the modifiable areal unit problem for regression parameter estimates of aggregate health data (Burden & Steel, ). Individual level health data were simulated using the SA approach and the co software (Williamson et al ., ; Williamson, , available at http://pcwww.liv.ac.uk/~william/microdata/).…”

“…The socioeconomic index was calculated for the simulated data using methods comparable with the Australian Bureau of Statistics socioeconomic indices (Australian Bureau of Statistics, ). Further details can be found in Burden and Steel ().…”

“…SMM are used to model local and/or regional geographic effects for a diverse range of application areas, including labour force participation (Ballas et al, 2006;Morrissey & O'Donoghue, 2011), economic policy analysis (Chin et al, 2005;Campbell & Ballas, 2013), social policy analysis (Miranti et al, 2011;Tanton, 2011;Gong et al, 2012;Rahman et al, 2013), environmental applications (Hynes et al, 2009), education (Kavroudakis et al, 2013), retail market analysis (Hanaoka & Clarke, 2007), and transport modelling (Lovelace et al, 2014;Ma et al, 2014). They have also been used as the basis for dynamic microsimulation models (Ballas et al, 2005), geographical analysis of zoning distributions (Burden & Steel, 2013), behavioural models (van Leeuwen & Dekkers, 2013), health surveillance (Cataife, 2014), econometric analysis (Cullinan, 2011;Cullinan et al, 2011), and planning support (Ballas et al, 2007b).…”