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Testing for space–time interaction in conditional autoregressive models
Author(s) -
Ugarte M.D.,
Goicoa T.,
Etxeberria J.,
Militino A.F.
Publication year - 2012
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.1126
Subject(s) - econometrics , computer science , autoregressive model , null hypothesis , context (archaeology) , parametric model , statistics , bayes' theorem , parametric statistics , bayesian probability , mathematics , artificial intelligence , geography , archaeology
Data on disease incidence or mortality over a set of contiguous regions have been commonly used to describe geographic patterns of disease, helping epidemiologists and public health researchers to identify possible etiologic factors. Nowadays, the availability of historical mortality registers offers the possibility of going further, describing the spatio‐temporal distribution of risks. The literature on spatio‐temporal modeling of risks is very rich, and it is mainly focused on the use of conditional autoregressive models from a fully Bayesian perspective. The complexity of the estimation procedure makes the Empirical Bayes approach a plausible alternative. In this context, it is of interest to test for interaction between space and time, as an absence of space–time interactions simplifies modeling and interpretation. In this work, a score test is derived as well as a bootstrap approximation of its null distribution. A parametric bootstrap test is also provided for comparison purposes. Results are illustrated using brain cancer mortality data from Spain in the period 1996–2005. Copyright © 2011 John Wiley & Sons, Ltd.