In spatio-temporal disease mapping models, identifiability constraints affect PQL and INLA results

  • T. Goicoa
  • A. Adin
  • M. D. Ugarte
  • J. S. Hodges
Original Paper


Disease mapping studies the distribution of relative risks or rates in space and time, and typically relies on generalized linear mixed models (GLMMs) including fixed effects and spatial, temporal, and spatio-temporal random effects. These GLMMs are typically not identifiable and constraints are required to achieve sensible results. However, automatic specification of constraints can sometimes lead to misleading results. In particular, the penalized quasi-likelihood fitting technique automatically centers the random effects even when this is not necessary. In the Bayesian approach, the recently-introduced integrated nested Laplace approximations computing technique can also produce wrong results if constraints are not well-specified. In this paper the spatial, temporal, and spatio-temporal interaction random effects are reparameterized using the spectral decompositions of their precision matrices to establish the appropriate identifiability constraints. Breast cancer mortality data from Spain is used to illustrate the ideas.


Breast cancer INLA Leroux CAR prior PQL Space-time interactions 



This work has been supported by the Spanish Ministry of Economy and Competitiveness (project MTM2014-51992-R), and by the Health Department of the Navarre Government (Project 113, Res.2186/2014). We would like to thank the National Epidemiology Center (area of Environmental Epidemiology and Cancer) for providing the data, originally created by the Spanish Statistical Office. Thanks are also given to two anonymous reviewers for their comments that have contributed to improve the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Statistics and O.R.Public University of NavarrePamplonaSpain
  2. 2.Institute for Advanced Materials (InaMat)Public University of NavarrePamplonaSpain
  3. 3.Division of Biostatistics, School of Public HealthUniversity of MinnesotaMinneapolisUSA
  4. 4.Research Network on Health Services in Chronic Diseases (REDISSEC)MadridSpain

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