Empirical Bayes Estimation for Unbalanced Multilevel Structural Equation Models via the EM algorithm
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The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are removing estimation bias due to measurement error and incorporating variability associated with the social milieu in which individuals are situated. This paper presents empirical Bayes estimation by means of the EM algorithm in the context of unbalanced sampling designs. The EM algorithm is particularly useful when the analytic expressions exist for the conditional expectations of the missing data given complete data and for the maximum likelihood estimators (MLE) of the model parameters. The accuracy of the algorithm was tested using a set of artificial data. The numerical results suggest that this new methodology is a useful mean for studying hypothesized relations among latent variables varying at two levels of hierarchy.
Abstract
The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are removing estimation bias due to measurement error and incorporating variability associated with the social milieu in which individuals are situated. This paper presents empirical Bayes estimation by means of the EM algorithm in the context of unbalanced sampling designs. The EM algorithm is particularly useful when the analytic expressions exist for the conditional expectations of the missing data given complete data and for the maximum likelihood estimators (MLE) of the model parameters. The accuracy of the algorithm was tested using a set of artificial data. The numerical results suggest that this new methodology is a useful mean for studying hypothesized relations among latent variables varying at two levels of hierarchy.