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Laplace approximation in measurement error models
Author(s) -
Battauz Michela
Publication year - 2011
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201000095
Subject(s) - laplace's method , mathematics , laplace transform , estimator , covariate , gaussian quadrature , quadrature (astronomy) , dimension (graph theory) , generalized linear model , hierarchical generalized linear model , gaussian , integral equation , statistics , mathematical analysis , nyström method , physics , engineering , quantum mechanics , pure mathematics , electrical engineering
Likelihood analysis for regression models with measurement errors in explanatory variables typically involves integrals that do not have a closed‐form solution. In this case, numerical methods such as Gaussian quadrature are generally employed. However, when the dimension of the integral is large, these methods become computationally demanding or even unfeasible. This paper proposes the use of the Laplace approximation to deal with measurement error problems when the likelihood function involves high‐dimensional integrals. The cases considered are generalized linear models with multiple covariates measured with error and generalized linear mixed models with measurement error in the covariates. The asymptotic order of the approximation and the asymptotic properties of the Laplace‐based estimator for these models are derived. The method is illustrated using simulations and real‐data analysis.