Multilevel linear models analysis using generalized maximum entropy
Abstract
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This paper introduces the general multilevel models and discusses the generalized maximum entropy (GME) estimation method (Golan et al 1996) that may be used to fit such models. The proposed procedure is applied to two-level data generated in a simulation study. The GME estimates are compared with Goldstein’s generalized least squares estimates. The comparisons are made by two criteria, bias and efficiency. We find that the estimates of the fixed effects and variance components are substantially and significantly biased using Goldstein’s generalized Least Squares approach. However, the GME estimates are unbiased and consistent; we conclude that the GME approach is a recommended procedure to fit multilevel models.
This paper introduces the general multilevel models and discusses the generalized maximum entropy (GME) estimation method (Golan et al 1996) that may be used to fit such models. The proposed procedure is applied to two-level data generated in a simulation study. The GME estimates are compared with Goldstein’s generalized least squares estimates. The comparisons are made by two criteria, bias and efficiency. We find that the estimates of the fixed effects and variance components are substantially and significantly biased using Goldstein’s generalized Least Squares approach. However, the GME estimates are unbiased and consistent; we conclude that the GME approach is a recommended procedure to fit multilevel models.
DOI Code:
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Keywords:
Multilevel Models; Generalized Maximum Entropy; Simulation; Goldstein’s Generalized Least Squares
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