Spatial modeling using mixed models: an ecologic study of visceral leishmaniasis in Teresina, Piauí State, Brazil.

Guilherme L Werneck,James H Maguire

doi:10.1590/s0102-311x2002000300007

Abstract

Most ecologic studies use geographical areas as units of observation. Because data from areas close to one another tend to be more alike than those from distant areas, estimation of effect size and confidence intervals should consider spatial autocorrelation of measurements. In this report we demonstrate a method for modeling spatial autocorrelation within a mixed model framework, using data on environmental and socioeconomic determinants of the incidence of visceral leishmaniasis (VL) in the city of Teresina, Piauí, Brazil. A model with a spherical covariance structure indicated significant spatial autocorrelation in the data and yielded a better fit than one assuming independent observations. While both models showed a positive association between VL incidence and residence in a favela (slum) or in areas with green vegetation, values for the fixed effects and standard errors differed substantially between the models. Exploration of the data's spatial correlation structure through the semivariogram should precede the use of these models. Our findings support the hypothesis of spatial dependence of VL rates and indicate that it might be useful to model spatial correlation in order to obtain more accurate point and standard error estimates.

Highlights

In ecologic studies, geographical areas are the usual units of observation, data on outcome are expressed as incidence rates, and data on explanatory variables may include aggregate, environmental or global measures (Morgenstern, 1998)
In this report we demonstrate a method for modeling spatial autocorrelation within a mixed model framework, using data on environmental and socioeconomic determinants of the incidence of visceral leishmaniasis ( VL) in the city of Teresina, Piauí, Brazil
In this paper we describe a strategy for modeling spatial covariance structure in ecologic studies within a mixed model framework

Summary

Introduction

Geographical areas are the usual units of observation, data on outcome are expressed as incidence rates, and data on explanatory variables may include aggregate, environmental or global measures (Morgenstern, 1998). Areal data can be considered a two-dimensional counterpart of time series data, in which observations are correlated in the single dimension of time. As in the analysis of time series, it is important to model the spatial correlation structure among observations in order to obtain valid estimates of effect size, confidence intervals, and significance levels (Cressie, 1991). In this paper we describe a strategy for modeling spatial covariance structure in ecologic studies within a mixed model framework. Since errors in mixed models for spatial data are correlated, spatial covariance is modeled through the error term. As an illustration of these methods, we present data of an ecologic study of environmental and socioeconomic determinants of the incidence of visceral leishmaniasis (VL) in Teresina, Piauí, Brazil

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Conclusion