Spatial Autocorrelation Statistics of Areal Prevalence Rates under High Uncertainty in Denominator Data

Abstract

We propose a new estimator of spatial autocorrelation of areal incidence or prevalence rates in small areas, such as crime and health indicators, for correcting spatially heterogeneous sampling errors in denominator data. The approach is dubbed the heteroscedasticity‐consistent empirical Bayes (HC‐EB) method. As American Community Survey (ACS) data have been released to the public for small census geographies, small‐area estimates now form the demographic landscape of neighborhoods. Meanwhile, there is growing awareness of the diminished statistical validity of global and local Moran’s I when such small‐area estimates are used in denominator data. Using teen birth rates by census tracts in Mecklenburg County, North Carolina, we present comparisons of conventional and new HC‐EB estimates of Global and Local Moran’s I statistics created on ACS data, along with estimates on ground truth values from the 2010 decennial census. Results show that the new adjustment method dramatically enhances the statistical validity of global and local spatial autocorrelation statistics.

Multivariate Neighborhood Trajectory Analysis: An Exploration of the Functional Data Analysis Approach

“…One possible approach would be to use demographic data based on higher survey frequency, such as 5-year estimates at the census-tract level of American Community Survey data without overlapping of sampling-year windows. However, that survey's high degree of data uncertainty should be treated appropriately (Spielman, Folch, and Nagle 2014;Folch et al 2016;Jung, Thill, and Issel 2019a), using advanced statistical tools-such as empirical or hierarchical Bayesian estimationswith uncertain information (Jung, Thill, and Issel 2019b). Combining the FDA approach with empirical or hierarchical Bayesian estimations in future research would enable the production of multivariate neighborhood curves that represent neighborhood change with greater accuracy.…”

Spatial Analytics Based on Confidential Data for Strategic Planning in Urban Health Departments

“…Also, it is well known that denominator data that rely on annual data sampling to apprehend the at-risk population (denominator)-such as annual American Community Survey data-is affected by large and spatially variable margins of error across the urban region. While some methods have been developed to provide unbiased estimates of statistics [64,65], many analyses continue to ignore this important and impactful data uncertainty [66].…”

Exploratory Statistical Analysis of Spatial Structures in Urban Datasets

“…Rates are standardised with a constant global mean estimated from raw counts (instead of averaging the rates) and a variance estimate taking into account local numbers of cases. A similar but improved method has been proposed recently by Jung et al (2019b). Jackson et al (2010) propose to include the spatial weights matrix in the variance estimator used in the denominator of Moran's I.…”