Cross-classified and multiple membership structures in multilevel models : an introduction and review
Digital Education Resource Archive (University College London)Published 1 January 2006Open access
Antony Fielding, Harvey Goldstein
Citations161
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
This review provides an introduction to the role of statistical modelling of complex social situations, in particular considering the application of advanced methodologies to an educational context by building an overview of techniques such as cross classified multi-level modelling and multiple membership structures.
Abstract
This review provides an introduction to the role of statistical modelling of complex social situations, in particular considering the application of advanced methodologies to an educational context. By building an overview of techniques such as cross classified multi-level modelling and multiple membership structures and through a comprehensive review of the application of these techniques the review should inform advances in educational research. The application of these advanced statistical techniques which allow for hierarchically structured data will assist the Department in accurately identifying the individual and independent effects of various factors on attainment and in particular the simultaneous effects of area of residence effects and school effects in educational production functions.
Keywords
Social SciencesAgricultural and Biological Sciences
Applied Longitudinal Data Analysis
10,585 Citations2003J. David Singer, John B. Willett
BiometricsRandom-Effects Models for Longitudinal Data
8,915 Citations1982Nan M. Laird, James H. Ware
A unified approach to fitting these models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed.
Multilevel analysis techniques and applications
6,055 Citations2002Joop J. Hox
BiometrikaRecovery of inter-block information when block sizes are unequal
3,792 Citations1971H. D. Patterson, R. Thompson
Journal of Educational and Behavioral StatisticsUsing SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models
2,713 Citations1998J. David Singer
This paper is written as a step-by-step tutorial that shows how to fit the two most common multilevel models: (a) school effects models, designed for data on individuals nested within naturally occurring hierarchies (e.g., students within classes); and (b) individual growth models,designed for exploring longitudinal data (on individuals) over time.
Journal of the Royal Statistical Society Series B (Statistical Methodology)Bayes Estimates for the Linear Model
2,037 Citations1972D. V. Lindley, A. F. M. Smith
Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models
1,511 Citations2004Anders Skrondal, Sophia Rabe‐Hesketh
Sociological Methods & ResearchMultilevel Covariance Structure Analysis
1,184 Citations1994Bengt Muthén
This article gives an introduction to some new techniques for multilevel covariance structure modeling with latent variables that provide a large set of new analysis possibilities and have the advantage that they only require conventional structural equation modeling software.
Journal of the Royal Statistical Society Series A (Statistics in Society)League Tables and Their Limitations: Statistical Issues in Comparisons of Institutional Performance
1,061 Citations1996Harvey Goldstein, David J. Spiegelhalter
The paper emphasizes that statistical methods exist which can contribute to an understanding of the extent and possible reasons for differences between institutions and urges caution by discussing the limitations of such methods.
BiometricsAverage Information REML: An Efficient Algorithm for Variance Parameter Estimation in Linear Mixed Models
935 Citations1995A. Gilmour, R. Thompson +1 more
BiometrikaMultilevel mixed linear model analysis using iterative generalized least squares
777 Citations1986Harvey Goldstein
Journal of the Royal Statistical Society Series B (Statistical Methodology)Multivariate Regression Analyses for Categorical Data
769 Citations1992Kung‐Yee Liang, Scott L. Zeger +1 more
BiometricsA Random-Effects Ordinal Regression Model for Multilevel Analysis
696 Citations1994Donald Hedeker, Robert D. Gibbons
A random-effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data and a maximum marginal likelihood (MML) solution is described using Gauss-Hermite quadrature to numerically integrate over the distribution of random effects.
Journal of Epidemiology & Community HealthA glossary for multilevel analysis
676 Citations2002Ana V. Diez Roux
This glossary defines key concepts and terms used in multilevel analysis, which has recently emerged as a useful analytical technique in several fields, including public health and epidemiology.
School Effectiveness and School ImprovementSchool Effectiveness and School Improvement: Sustaining Links
521 Citations1997Bert Creemers, G.J. Reezigt
Computer Methods and Programs in BiomedicineMIXOR: a computer program for mixed-effects ordinal regression analysis
412 Citations1996Donald Hedeker, Robert D. Gibbons
MIXOR provides maximum marginal likelihood estimates for mixed-effects ordinal probit, logistic, and complementary log-log regression models, used for analysis of dichotomous and ordinal outcomes from either a clustered or longitudinal design.
BiometrikaA fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects
355 Citations1987Nicholas T. Longford
Statistical ModellingMultiple membership multiple classification (MMMC) models
351 Citations2001William J. Browne, Harvey Goldstein +1 more
Bayesian methods in conjunction with suitable ‘diffuse’ prior distributions lead to similar inferences to existing frequentist techniques, as well as illustrating the diversity of models that fit into the framework.
Multilevel Modelling of Health Statistics
308 Citations2001Alastair H. Leyland, Harvey Goldstein
Repeated measures, outliers, institutional performance, and spatial analysis, which have great relevance to health and medical research, are all examined for multilevel models.
Health & PlaceIndividuals and their ecologies: analysing the geography of chronic illness within a multilevel modelling framework
284 Citations1995Kelvyn Jones, Craig Duncan
It is argued that aggregate analysis provides an inappropriate methodology for studying place differences and multilevel modelling, in contrast, allows for the simultaneous analysis of individuals and their ecologies.
School Effectiveness and School ImprovementMethods in School Effectiveness Research
280 Citations1997Harvey Goldstein
The paper outlines the appropriate multilevel statistical models and shows how these can model the complexities of school, class and student level data.
Journal of Health Services Research & PolicyMultilevel Models: Applications to Health Data
272 Citations1996Nigel Rice, Alastair H. Leyland
An introductory account of multilevel models is presented, highlighting the potential benefits that may be gained by the use of these methods and key areas that could benefit greatly from these techniques include the exploration of variations in clinical practice, comparisons of institutional performance and resource allocation.
Computer Methods and Programs in BiomedicineMIXREG: a computer program for mixed-effects regression analysis with autocorrelated errors
264 Citations1996Donald Hedeker, Robert D. Gibbons
MIXREG is a program that provides estimates for a mixed-effects regression model (MRM) for normally-distributed response data including autocorrelated errors, utilizing both the EM algorithm and a Fisher-scoring solution.
Medical Entomology and ZoologyDisease Mapping with WinBUGS and MLwiN
264 Citations2003AB Lawson, William J. Browne +1 more
Journal of Mathematical SociologyA Multilevel Network Study of the Effects of Delinquent Behavior on Friendship Evolution
252 Citations2003Tom A. B. Snijders, Chris Baerveldt
Statistics in MedicineAn introduction to hierarchical linear modelling
248 Citations1999Lisa Sullivan, Kimberly A. Dukes +1 more
This tutorial provides an introduction to the hierarchical linear models technique in general terms, and then specifies model notation and assumptions in detail, and elaborate on model interpretation and provide guidelines for model checking.
Personal RelationshipsThe social relations model for family data: A multilevel approach
243 Citations1999Tom A. B. Snijders, David A. Kenny
Social NetworksMultilevel analysis of personal networks as dependent variables
232 Citations1999Marijtje A. J. van Duijn, Jooske T. van Busschbach +1 more
It is shown that multilevel methods are particularly well-suited for the analysis of relations in personal networks and the changes in these relations.
Social Science & MedicineThe relevance of multilevel statistical methods for identifying causal neighborhood effects
228 Citations2003S. V. Subramanian
Journal of Educational and Behavioral StatisticsEfficient Analysis of Mixed Hierarchical and Cross-Classified Random Structures Using a Multilevel Model
228 Citations1994Jon Rasbash, Harvey Goldstein
An efficient and straightforward procedure is described for specifying and estimating parameters of general mixed models which contain both hierarchical and crossed random factors.
Journal of Educational StatisticsA Crossed Random Effects Model for Unbalanced Data With Applications in Cross-Sectional and Longitudinal Research
225 Citations1993Stephen W. Raudenbush
British Educational Research JournalNew Statistical Methods for Analysing Social Structures: an introduction to multilevel models
210 Citations1991Lindsay Paterson, Harvey Goldstein
It is suggested that multilevel techniques and associated software packages have reached the stage when they can and should be applied routinely in the analysis of social data, and that failure to do so can result in potentially serious misinterpretations.
Sociological Methods & ResearchMultilevel Cross-Classified Models
202 Citations1994Harvey Goldstein
The issues of efficiently modeling random cross-classifications of units can arise at any level of a data hierarchy are explored and an example from a study of parental choice of schools is given.
Scandinavian Journal of Public HealthMultilevel modelling and public health policy
187 Citations2003Alastair H. Leyland, Peter Groenewegen
This paper lays out the a basic description of multilevel modelling, discusses the problems of alternative approaches, and details the relevance for public health policy before describing which levels are relevant and illustrating the different kinds of hypotheses that can be tested using multileVEL modelling.
Oxford Review of EducationA Multilevel Analysis of School Examination Results
181 Citations1993Harvey Goldstein, Jon Rasbash +5 more
Medical EducationGeneralisability: a key to unlock professional assessment
170 Citations2002Jim Crossley, Helena Davies +2 more
There are few objective tests for the most important aspects of the professional role because they are complex and intangible and professional performance varies markedly from setting to setting and case to case.
Journal of the Royal Statistical Society Series C (Applied Statistics)Multilevel Modelling of the Geographical Distributions of Diseases
169 Citations1999Ian H. Langford, Alastair H. Leyland +2 more
Developmental PsychologyThe role of the shared family context in differential parenting.
158 Citations2002Jennifer M. Jenkins, Jon Rasbash +1 more
Journal of Educational and Behavioral StatisticsCross-Classification Multilevel Logistic Models in Psychometrics
150 Citations2003Wim Van Den Noortgate, Paul De Boeck +1 more
Economic GeographyContextual Models of Urban House Prices: A Comparison of Fixed- and Random-Coefficient Models Developed by Expansion
145 Citations1994Kelvyn Jones, Nina Bullen
Journal of the Royal Statistical Society Series A (Statistics in Society)A Multilevel Cross-Classified Modelling Approach to Peer Review of Grant Proposals: The Effects of Assessor and Researcher Attributes on Assessor Ratings
138 Citations2003Upali W Jayasinghe, Herbert W. Marsh +1 more
Statistics in MedicineOn the appropriateness of marginal models for repeated measurements in clinical trials
136 Citations1998J. K. Lindsey, Philippe Lambert
It is concluded that marginal models may sometimes be appropriate for descriptive observational studies, but should only be used with great care in causal experimental settings, such as clinical trials.
Journal of the Royal Statistical Society Series A (Statistics in Society)The Relative Impact of Interviewer Effects and Sample Design Effects on Survey Precision
136 Citations1998Colm O’Muircheartaigh, Pamela Campanelli
Statistical ModellingA general multilevel multistate competing risks model for event history data, with an application to a study of contraceptive use dynamics
133 Citations2004Fiona Steele, Harvey Goldstein +1 more
A general discrete time model for multilevel event history data is proposed for the analysis of longitudinal repeated episodes within individuals where there are multiple states and multiple types of event (competing risks) which may vary across states.
Journal of the Royal Statistical Society Series C (Applied Statistics)Meta-Analysis Using Multilevel Models with an Application to the Study of Class Size Effects
133 Citations2000Harvey Goldstein, Min Yang +3 more
Journal of the Royal Statistical Society Series A (Statistics in Society)A Multilevel Exploration of the Role of Interviewers in Survey Non-Response
120 Citations1999Colm O’Muircheartaigh, Pamela Campanelli
Journal of Agronomy and Crop ScienceAnalysis of Unbalanced Data by Mixed Linear Models Using the <scp>mixed</scp> Procedure of the SAS System
119 Citations2005Joachim Spilke, Hans‐Peter Piepho +1 more
The use of the mixed procedure of the SAS System for the analysis of designed experiments and the specification of options as depending on the assumed mixed model and on the unbalancedness in the data is described.
Sociology of EducationEffects of Neighborhood and School Environments on Transitions to First Sexual Intercourse
118 Citations2000Julien O. Teitler, Christopher C. Weiss
School Effectiveness and School ImprovementThe Influence of Secondary and Junior Schools on Sixteen Year Examination Performance: A Cross‐classified Multilevel Analysis∗
116 Citations1997Harvey Goldstein, Pam Sammons
Transportation Research Part B MethodologicalA multi-level cross-classified model for discrete response variables
113 Citations2000Chandra R. Bhat
Sociological Methods & ResearchThe Effects of Interviewer and Respondent Characteristics on Response Behavior in Panel Surveys
95 Citations2001Jan Pickery, Geert Loosveldt +1 more
The American StatisticianReview of Five Multilevel Analysis Programs: BMDP-5V, GENMOD, HLM, ML3, VARCL
92 Citations1994Ita G. G. Kreft, Jan de Leeuw +1 more
Environment and Planning A Economy and SpaceModelling Complexity: Analysing Between-Individual and Between-Place Variation—A Multilevel Tutorial
85 Citations1997Nina Bullen, Kelvyn Jones +1 more
Attention is drawn to the important contrasts between the modelling of categorical and continuous predictors and the emphasis is placed on the simultaneous consideration of complex variation at all levels.
Journal of Statistical Software<b>MIXNO</b>: A Computer Program for Mixed-Effects Nominal Logistic Regression
80 Citations1999Donald Hedeker
Journal of the Royal Statistical Society Series A (Statistics in Society)Statistical Analysis of Performance Indicators in UK Higher Education
79 Citations2004David Draper, Mark Gittoes
The large sample functional equivalence between a method based on indirect standardization and an approach based on fixed effects hierarchical modelling is demonstrated, and simulation results on the performance of the standardization method in null and non-null settings are offered.
Wiley series in probability and statisticsThe Effect of Interviewer and Respondent Characteristics on the Quality of Survey Data: A Multilevel Model
79 Citations2004Joop J. Hox, Edith D. de Leeuw +1 more
Journal of the Royal Statistical Society Series A (Statistics in Society)Adjusting for Measurement Error in Multilevel Analysis
79 Citations1996Geoffrey Woodhouse, Min Yang +2 more
Oxford Review of EducationThe Use of Assessment Data for School Improvement Purposes
71 Citations1999Min Yang, Harvey Goldstein +2 more
Statistical ModellingMultilevel ordinal models for examination grades
59 Citations2003Antony Fielding, Min Yang +1 more
Evaluation & Research in EducationSocio‐economic status and educational attainment: A multi‐dimensional and multi‐level study
59 Citations1991Lindsay Paterson
Statistica NeerlandicaThe analysis of unbalanced linear models with variance components
55 Citations1990B. Engel
The American StatisticianComparisons of Software Packages for Generalized Linear Multilevel Models
50 Citations1999Xiao‐Hua Zhou, Anthony J. Perkins +1 more
Computational Statistics & Data AnalysisEfficient computational procedures for the estimation of parameters in multilevel models based on iterative generalised least squares
50 Citations1992Harvey Goldstein, Jon Rasbash
Statistical ModellingUsing cross-classified multivariate mixed response models with application to life history traits in great tits (Parus major)
49 Citations2007William J. Browne, R. H. McCleery +2 more
This paper focuses on the reproductive behaviour and survival of a small passerine bird, the great tit, and fits multivariate cross-classified random effects models using a Markov chain Monte Carlo (MCMC) estimation algorithm described in the paper.
British Educational Research JournalProgress from GCSE to A and AS Level: Institutional and gender differences, and trends over time
49 Citations2001Min Yang, Geoffrey Woodhouse
Health Services ResearchPlan, Geographical, and Temporal Variation of Consumer Assessments of Ambulatory Health Care
41 Citations2004Alan M. Zaslavsky, Lawrence Zaborski +1 more
The findings suggest that ratings of plans and reports about customer service and prescription access are affected by plan policies, benefits design, and administrative structures that can be changed relatively quickly, whereas assessments of other aspects of care are largely determined by characteristics of provider networks that are relatively stable.
European Journal of Population / Revue européenne de DémographieMultilevel Models in the Study of Dynamic Household Structures
41 Citations2000Harvey Goldstein, Jon Rasbash +3 more
Journal of the Royal Statistical Society Series A (Statistics in Society)Estimation in Large Cross Random-Effect Models by Data Augmentation
40 Citations1999David Clayton, Jon Rasbash
A data augmentation approach to computational difficulties in which the algorithm is repeatedly fit an overlapping series of submodels, incorporating the missing terms in each submodel as ‘offsets’.
Quality & QuantityThe Impact of Respondent and Interviewer Characteristics on the Number of “No Opinion” Answers
40 Citations1998Jan Pickery, Geert Loosveldt
Elsevier eBooksAn Introduction to Multilevel Modelling
36 Citations1991Lindsay Paterson
This note is a guide to the basics of multilevel modelling, which outlines the principles rather than technical details.
Bristol Research (University of Bristol)Multilevel factor analysis modelling using Markov Chain Monte Carlo (MCMC) estimation
36 Citations2002Harvey Goldstein, William J. Browne
A very general class of multileVEL factor analysis and structural equation models is proposed which are derived from considering the concatenation of a series of building blocks that use sets of factor structures defined within the levels of a multilevel model.
eScholarship (California Digital Library)Software for Multilevel Analysis
33 Citations2011Jan de Leeuw, Ita G. G. Kreft
This paper reviews some of the more important software programs and packages that can are designed for, or can be used for, multilevel analysis and describes how these programs differ in many respects.
Journal of the American Statistical AssociationCrossed Random Effect Models for Multiple Outcomes in a Study of Teratogenesis
28 Citations2001Brent A. Coull, James P. Hobert +2 more
This article proposes the use of a logistic regression model with crossed random effect structure to address all three questions simultaneously and uses the proposed models to analyze data from a study investigating the effects of in utero antiepileptic drug exposure on fetal development.
School Effectiveness and School ImprovementTeaching Groups as Foci for Evaluating Performance in Cost-Effectiveness of GCE Advanced Level Provision: Some Practical Methodological Innovations1
28 Citations2002Antony Fielding
University of Hertfordshire Research Archive (University of Hertfordshire)An instrumental variable consistent estimation procedure to overcome the problem of endogenous variables in multilevel models
26 Citations2000Neil H. Spencer, A. Fielding
Statistics in MedicineMulti-level modelling of conception in artificial insemination by donor
24 Citations1998René Écochard, David Clayton
An efficient algorithm is presented for fitting crossed random multi-level logistic models and the inclusion of compositional covariates to determine what information the quality of a donation conveys regarding the donor basal fecundability and on the specific sperm donation.
Journal of Dairy ScienceEstimated Heterogeneity of Phenotypic Variance of Test-Day Yield with a Structural Variance Model
24 Citations2004Nicolas Gengler, G.R. Wiggans +1 more
First-lactation test-day milk, fat, and protein yields from New York, Wisconsin, and California herds from 1990 through 2000 were adjusted additively for age and lactation stage to provide herd-specific lactation curves that can change every 2 yr.
Journal of the Royal Statistical Society Series A (Statistics in Society)Generalized Linear Mixed Models for Ordered Responses in Complex Multilevel Structures: Effects Beneath the School or College in Education
19 Citations2004Antony Fielding, Min Yang
Computational StatisticsA Comparison of Modelling Strategies for Value-Added Analyses of Educational Data
16 Citations2002Neil H. Spencer, Antony Fielding
It is concluded that the approach offered by the BUGS software has advantages over more classical estimation methods for value-added multilevel models.
Journal of the Royal Statistical Society Series A (Statistics in Society)Estimation of a Large Cross-Classified Multilevel Model to Study Academic Achievement in a Modular Degree Course
13 Citations2003Vanessa Simonite, William J. Browne
An algorithm for fitting a cross-classified model that includes random effects and complex or heterogeneous variance functions is described and the results of applying this model to student transcript data for a first-degree course are used to demonstrate the importance of employing aCross- classified model and the value of the information that is obtained.
A Longitudinal Study of the Impact of America's Choice on Student Performance in Rochester, New York, 1998-2003
10 Citations2004Henry May, Jonathan Supovitz +1 more
PsychometrikaInferential Procedures for Multifaceted Coefficients of Generalizability
10 Citations1990Marsha L. Schroeder, A. Ralph Hakstian
MULTILEVEL MODELS WHERE THE RANDOM EFFECTS ARE CORRELATED WITH THE FIXED PREDICTORS
8 Citations2002Nigel Rice, Mark Andrew +1 more
…