Missing data analysis and imputation via latent Gaussian Markov random fields
Gómez-Rubio, Virgilio (Universidad de Castilla-La Mancha)
Cameletti, Michela (University of Bergamo)
Blangiardo, Marta (Imperial College London)

Data:	2022
Resum:	This paper recasts the problem of missing values in the covariates of a regression model as a latent Gaussian Markov random field (GMRF) model in a fully Bayesian framework. The proposed approach is based on the definition of the covariate imputation sub-model as a latent effect with a GMRF structure. This formulation works for continuous covariates but for categorical covariates a typical multiple imputation approach is employed. Both techniques can be easily combined for the case in which continuous and categorical variables have missing values. The resulting Bayesian hierarchical model naturally fts within the integrated nested Laplace approximation (INLA) framework, which is used for model fitting. Hence, this work fills an important gap in the INLA methodology as it allows to treat models with missing values in the covariates. As in any other fully Bayesian framework, by relying on INLA for model fitting it is possible to formulate a joint model for the data, the imputed covariates and their missingness mechanism. In this way, it is possible to tackle the more general problem of assessing the missingness mechanism by conducting a sensitivity analysis on the different alternatives to model the non-observed covariates. Finally, the proposed approach is illustrated in two examples on modeling health risk factors and disease mapping.
Ajuts:	Ministerio de Economía y Competitividad MTM2016-77501-P Ministerio de Economía y Competitividad PID2019-106341GB-I00
Nota:	Acknowledgements. V. Gomez-Rubio has been supported by grants MTM2016-77501-P and PID2019-106341GB-I00 from the Spanish Ministry of Economy and Competitiveness co-fnanced with FEDER funds, grant SBPLY/17/180501/000491 and SBPLY/21/180501/000241 funded by Consejería de Educacion, Cultura y Deportes (JCCM, Spain) and FEDER. Marta Blangiardo acknowledges partial support through the grant R01HD092580 funded by the National Institute of Health and from the MRC Centre for Environment and Health, which is currently funded by the Medical Research Council (MR/S019669/1).
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Imputation ; Missing values ; GMRF ; INLA ; Sensitivity analysis
Publicat a:	SORT : statistics and operations research transactions, Vol. 46 Núm. 2 (2022) , p. 217-244 (Articles) , ISSN 2013-8830

Adreça original: https://raco.cat/index.php/SORT/article/view/409433
DOI: 10.2436/20.8080.02.124

28 p, 783.0 KB

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