Extended Generalized Linear Latent and Mixed Model

The generalized linear latent and mixed modeling (GLLAMM framework) includes many models such as hierarchical and structural equation models. However, GLLAMM cannot currently accommodate some models because it does not allow some parameters to be random. GLLAMM is extended to overcome the limitation by adding a submodel that specifies a distribution of the additional random effects (Extended-GLLAMM). The extension is extremely simple to implement through the Bayesian framework with the WinBUGS software. Our approach is illustrated through the analysis of data from a youth tobacco cessation study.

[1]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[2]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[3]  S. Rabe-Hesketh,et al.  Generalized multilevel structural equation modeling , 2004 .

[4]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[5]  D B Rubin,et al.  Markov chain Monte Carlo methods in biostatistics , 1996, Statistical methods in medical research.

[6]  Yuk Fai Cheong,et al.  HLM 6: Hierarchical Linear and Nonlinear Modeling , 2000 .

[7]  K. Jöreskog.  A General Method for Estimating a Linear Structural Equation System. , 1970 .

[8]  Sophia Rabe-Hesketh,et al.  Generalized latent variable models: multilevel, longitudinal, and structural equation models , 2004 .

[9]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[10]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[11]  Risto Lethonen.  Multilevel Statistical Models (3rd ed.) , 2005 .

[12]  H. Goldstein.  Multilevel Statistical Models , 2006 .

[13]  F. Scholz.  Maximum Likelihood Estimation , 2006 .

[14]  James P. Hobert,et al.  Hierarchical Models: A Current Computational Perspective , 2000 .

[15]  R. Mermelstein,et al.  A national survey of tobacco cessation programs for youths. , 2007, American journal of public health.

[16]  S. Rabe-Hesketh,et al.  Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects , 2005 .

[17]  A. Brix.  Bayesian Data Analysis, 2nd edn , 2005 .

[18]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[19]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .