Annals of Applied Statistics

Measuring the vulnerability of the Uruguayan population to vector-borne diseases via spatially hierarchical factor models

Hedibert F. Lopes, Alexandra M. Schmidt, Esther Salazar, Mariana Gómez, and Marcel Achkar

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We propose a model-based vulnerability index of the population from Uruguay to vector-borne diseases. We have available measurements of a set of variables in the census tract level of the 19 Departmental capitals of Uruguay. In particular, we propose an index that combines different sources of information via a set of micro-environmental indicators and geographical location in the country. Our index is based on a new class of spatially hierarchical factor models that explicitly account for the different levels of hierarchy in the country, such as census tracts within the city level, and cities in the country level. We compare our approach with that obtained when data are aggregated in the city level. We show that our proposal outperforms current and standard approaches, which fail to properly account for discrepancies in the region sizes, for example, number of census tracts. We also show that data aggregation can seriously affect the estimation of the cities vulnerability rankings under benchmark models.

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Ann. Appl. Stat., Volume 6, Number 1 (2012), 284-303.

First available in Project Euclid: 6 March 2012

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Areal data Bayesian inference model comparison spatial interpolation spatial smoothing


Lopes, Hedibert F.; Schmidt, Alexandra M.; Salazar, Esther; Gómez, Mariana; Achkar, Marcel. Measuring the vulnerability of the Uruguayan population to vector-borne diseases via spatially hierarchical factor models. Ann. Appl. Stat. 6 (2012), no. 1, 284--303. doi:10.1214/11-AOAS497.

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Supplemental materials

  • Supplementary material A: MCMC scheme and Model Selection. The full conditional distributions for both the spatially hierarchical factor model (SHFM) and the unstructured hierarchical factor model (UHFM) are presented in this supplement. We also provide a brief overview of the model comparison criteria used in the paper, namely, (i) expected posterior deviation (EPD), (ii) deviance information criterion (DIC), (iii) continuous ranked probability score (CRPS), (iv) mean absolute error (MAE), and (v) mean square error (MSE).
  • Supplementary material B: Ox Code for SHFM. The folder data contains files with the 11 socio-economic indicators (the columns of the files) observed at the census tract level (the rows of the file) for each one of the 19 Uruguayan capitals (montevideo.txt, for instance, has 1,031 rows and 11 columns). The folder neigmat contains 19 files with the neighborhood matrices for each one of the 19 capitals after rearranging the numbering of the census tract using the GMRFLib-library of Rue et al. (2007). The files shfm.ox and functions.ox contain the Ox code to perform MCMC-based posterior inference for our spatially hierarchical factor model (SHFM).