Non-Hierarchical Multilevel Models

In the models discussed in this book so far we have assumed that the structures of the populations from which the data have been drawn are hierarchical. This assumption is sometimes not justified. In this chapter two main types of non-hierarchical model are considered. Firstly, cross-classified models. The notion of cross-classification is probably reasonably familiar to most readers. Secondly, we consider multiple membership models, where lower level units are influenced by more than one higher-level unit from the same classification. For example, some pupils may attend more than one school. We also consider situations that contain a mixture of hierarchical, crossed and multiple membership relationships.

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

[2]  Harvey Goldstein,et al.  Multilevel Models in the Study of Dynamic Household Structures , 2000 .

[3]  H. Goldstein.  Multilevel mixed linear model analysis using iterative generalized least squares , 1986 .

[4]  Noreen Goldman,et al.  An assessment of estimation procedures for multilevel models with binary responses , 1995 .

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

[6]  H. Goldstein,et al.  Efficient Analysis of Mixed Hierarchical and Cross-Classified Random Structures Using a Multilevel Model , 1994 .

[7]  Contents , 1997, Current Opinion in Neurobiology.

[8]  William J. Browne,et al.  Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models , 2006 .

[9]  William J. Browne,et al.  Modelling non-hierarchical structures , 2001 .

[10]  Harvey Goldstein,et al.  Multiple membership multiple classification (MMMC) models , 2001 .

[11]  Jianxin Pan,et al.  Generalized linear mixed models: An improved estimating procedure , 2000 .

[12]  Harvey Goldstein,et al.  Multilevel modelling of health statistics , 2001 .

[13]  Harvey Goldstein,et al.  Improved Approximations for Multilevel Models with Binary Responses , 1996 .

[14]  David Clayton,et al.  Estimation in large cross random‐effect models by data augmentation , 1999 .

[15]  Eric R. Ziegel,et al.  COMPSTAT: Proceedings in Computational Statistics, 2000 , 2002, Technometrics.

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

[17]  R Ecochard,et al.  Multi-level modelling of conception in artificial insemination by donor. , 1998, Statistics in medicine.

[18]  Joseph L Schafer,et al.  Analysis of Incomplete Multivariate Data , 1997 .

[19]  Graham D. Riley,et al.  Parallel implementation of a multilevel modelling package , 1999 .

[20]  J. Nelder,et al.  Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions , 2001 .

[21]  Stephen W. Raudenbush,et al.  A Crossed Random Effects Model for Unbalanced Data With Applications in Cross-Sectional and Longitudinal Research , 1993 .

[22]  Andrew B. Lawson,et al.  Disease Mapping with WinBUGS and MLwiN , 2003 .