Statistical Modelling 23 (1) (2023), 930
Alleviating confounding in spatio-temporal areal models with an application on crimes against women in India
Aritz Adin,
Department of Statistics,
Computer Science and Mathematics, InaMat2,
Public University of Navarre,
Pamplona,
Spain.
Tom´s Goicoa,
Department of Statistics,
Computer Science and Mathematics, InaMat2,
Public University of Navarre,
Pamplona,
Spain.
James S Hodges,
Division of Biostatistics,
School of Public Health,
University of Minnesota,
Minneapolis,
USA.
Patrick M Schnell,
Division of Biostatistics,
College of Public Health,
The Ohio State University,
Columbus,
USA.
María D Ugarte,
Department of Statistics,
Computer Science and Mathematics, InaMat2,
Public University of Navarre,
Pamplona,
Spain.
e-mail: lola@unavarra.es
Abstract:
Assessing associations between a response of interest and a set of covariates in spatial areal models
is the leitmotiv of ecological regression. However, the presence of spatially correlated random effects
can mask or even bias estimates of such associations due to confounding effects if they are not carefully
handled. Though potentially harmful, confounding issues have often been ignored in practice leading to wrong
conclusions about the underlying associations between the response and the covariates. In spatio-temporal
areal models, the temporal dimension may emerge as a new source of confounding, and the problem may be even
worse. In this work, we propose two approaches to deal with confounding of fixed effects by spatial and
temporal random effects, while obtaining good model predictions. In particular, restricted regression and
an apparently -- though in fact not -- equivalent procedure using constraints are proposed within both fully
Bayes and empirical Bayes approaches. The methods are compared in terms of fixed-effect estimates and model
selection criteria. The techniques are used to assess the association between dowry deaths and certain
socio-demographic covariates in the districts of Uttar Pradesh, India.
Keywords:
INLA; PQL; Orthogonal constraints, Restricted regression
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