Statistical Modelling 11 (2011), 351370
Random covariances and mixed-effects models for imputing multivariate
multilevel continuous data
Recai M Yucel
Department of Epidemiology and Biostatistics,
School of Public Health,
University at Albany, SUNY
One University Place, Room 139
Rensselaer, NY 12144-3456
USA
eMail: ryucel@albany.edu
Abstract:
Principled techniques for incomplete data problems are increasingly part
of mainstream statistical practice. Among many proposed techniques so far,
inference by multiple imputation (MI) has emerged as one of the most popular.
While many strategies leading to inference by MI are available in
cross-sectional settings, the same richness does not exist in multilevel
applications. The limited methods available for multilevel applications
rely on the multivariate adaptations of mixed-effects models. This approach
preserves the mean structure across clusters and incorporates distinct
variance components into the imputation process. In this paper, I add to
these methods by considering a random covariance structure and develop
computational algorithms. The attraction of this new imputation modelling
strategy is to correctly reflect the mean and variance structure of the
joint distribution of the data and allow the covariances differ across the
clusters. Using Markov chain Monte Carlo techniques, a predictive distribution
of missing data given observed data is simulated leading to creation of MIs.
To circumvent the large sample size requirement to support independent
covariance estimates for the level-1 error term, I consider distributional
impositions mimicking random-effects distributions assigned a priori. These
techniques are illustrated in an example exploring relationships between
victimization and individual and contextual level factors that raise the
risk of violent crime.
Keywords:
complex sample surveys; linear mixed-effects models; missing data;
mixed effects; multiple imputation; random covariances
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