2019/12/23 by Virgilio Gómez‐Rubio, Gómez-Rubio, Virgilio, Michela Cameletti +3
Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #Computation (stat.CO) #Economic and Environmental Valuation #FOS: Computer and information sciences #Methodology (stat.ME) #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1912.10981
openalex publication_date 2019/12/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper we recast the problem of missing values in the covariates of a\nregression model as a latent Gaussian Markov random field (GMRF) model in a\nfully Bayesian framework. Our proposed approach is based on the definition of\nthe covariate imputation sub-model as a latent effect with a GMRF structure. We\nshow how this formulation works for continuous covariates and provide some\ninsight on how this could be extended to categorical covariates.\n The resulting Bayesian hierarchical model naturally fits within the\nintegrated nested Laplace approximation (INLA) framework, which we use for\nmodel fitting. Hence, our work fills an important gap in the INLA methodology\nas it allows to treat models with missing values in the covariates.\n As in any other fully Bayesian framework, by relying on INLA for model\nfitting it is possible to formulate a joint model for the data, the imputed\ncovariates and their missingness mechanism. In this way, we are able to tackle\nthe more general problem of assessing the missingness mechanism by conducting a\nsensitivity analysis on the different alternatives to model the non-observed\ncovariates.\n Finally, we illustrate the proposed approach with two examples on modeling\nhealth risk factors and disease mapping. Here, we rely on two different\nimputation mechanisms based on a typical multiple linear regression and a\nspatial model, respectively. Given the speed of model fitting with INLA we are\nable to fit joint models in a short time, and to easily conduct sensitivity\nanalyses.\n