Small area adjustment of spatial autocorrelation estimator for heteroscedastic sampling errors

Authors: Paul Jung*, University of North Carolina at Charlotte, Jean-Claude Thill, University of North Carolina at Charlotte, Michele Issel, University of North Carolina at Charlotte
Topics: Spatial Analysis & Modeling, Quantitative Methods, Geographic Information Science and Systems
Keywords: Spatial Autocorrelation, Sampling Error, Data Uncertainty, American Community Survey, Small Area Estimates, Empirical Bayes Smoothing
Session Type: Paper
Day: 4/13/2018
Start / End Time: 10:00 AM / 11:40 AM
Room: Borgne Room, Sheraton, 3rd Floor
Presentation File: No File Uploaded


We propose a new estimator of spatial autocorrelation of areal incidence rates in small areas, such as crime and disease, for correcting sampling errors of denominator data. As American Community Survey (ACS) data have been released to the public for census block groups or census tracts, small area estimates now constitute a prominent representation of the demographic landscape of neighborhoods. Meanwhile, there is growing awareness and understanding of data uncertainty in ACS and of different patterns of data reliability across census tracts. Such small area estimates with large sampling errors may diminish the statistical validity of Global Moran’s I and local indicators of spatial association (LISA) when they are used as denominator data. We propose an adjusted Moran’s I estimator that features the current empirical Bayes smoothing originally advocated by Marshall to account for heteroscedasticity not only from different population sizes but also different sampling errors of denominator data, as measured by the coefficient of variation. Using teen birth rates and crime rates by census tracts in Mecklenburg county, North Carolina, we present comparisons of conventional and empirical Bayes estimates of Global Moran’s I statistics and LISA of raw rates created on ACS data, and estimates on ground truth value from the decennial census statistics. The result shows that sampling errors cause distortions of spatial autocorrelation detection and the new adjustment method improves the statistical validity of global and local spatial autocorrelation statistics.

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