Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Rebecca Killick, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
Authors: Ali Reza Fotouhi
Title: Comparisons of Estimation Procedures for Nonlinear Multilevel Models
Abstract: We introduce General Multilevel Models and discuss the estimation procedures that may be used to fit multilevel models. We apply the proposed procedures to three-level binary data generated in a simulation study. We compare the procedures by two criteria, Bias and efficiency. We find that the estimates of the fixed effects and variance components are substantially and significantly biased using Longford's Approximation and Goldstein's Generalized Least Squares approaches by two software packages VARCL and ML3. These estimates are not significantly biased and are very close to real values when we use Markov Chain Monte Carlo (MCMC) using Gibbs sampling or Nonparametric Maximum Likelihood (NPML) approach. The Gaussian Quadrature (GQ) approach, even with small number of mass points results in consistent estimates but computationally problematic. We conclude that the MCMC and the NPML approaches are the recommended procedures to fit multilevel models.

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DOI: 10.18637/jss.v008.i09

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