Book Review Multilevel Modeling Methodological Advances, Issues, and Applications

Applied Psychological MeasurementDOI: 10.1177/01466216052885552007; 31; 158 Applied Psychological Measurement Kimberly S. Maier and Raymond Mapuranga Applications Book Review: Multilevel Modeling: Methodological Advances, Issues, and The online version of this article can be found at: Published by:can be found at:Applied Psychological Measurement Additional services and information for/cgi/alerts Email Alerts:/subscriptions Subscriptions:/journalsReprints.nav Reprints:/journalsPermissions.nav Permissions:Book ReviewMultilevel Modeling:MethodologicalAdvances,Issues,and ApplicationsEdited by Stephen Reise and Naihua DuanMahwah,NJ:Lawrence Erlbaum,2003,314pp.,$37.50(paperback)ISBN0-8058-5170-4Interest in multilevel modeling has exploded over the past two decades,and research applying these statistical models has become more common in educational measurement contexts.Several textbooks have emerged that introduce both the theory and application of these models and are quite useful for providing a broad overview of the model and estimation techniques as well as illustrating applications to educational research(Goldstein,2002;Hox,2002;Kreft&de Leeuw, 1998;Raudenbush&Bryk,2001;Snijders&Bosker,1999).Many of these introductory texts tend to focus on linear models(e.g.,Kreft&de Leeuw,1998;Raudenbush&Bryk,2001)and illustrate the concept of model building with linear models.Nonlinear models and novel applications of multilevel models are addressed in these books,but these topics are typically not explored to the extent of linear multilevel models.This book augments these introductory texts by providing a collection of works outlining the recent statistical advances,methodological issues,and applications that have been identified in multilevel modeling.The topic of multilevel modeling is considered more broadly,including topics in structural equation modeling,latent trait models,meta-analysis,and growth models.Fur-thermore,the methodological topics treated are diverse and cover such areas as missing data, Bayesian data analysis,the EM algorithm,and detection and treatment of outliers.The book is composed of13chapters that are written by internationally recognized researchers. Each chapter provides a description of the problem considered as well as helpful examples that illustrate each application.As the preface states,many of the book chapters involve discussions that would necessitate the reader to have a fairly sophisticated level of knowledge of not only mul-tilevel models but mathematical statistics as well.The authors suggest that this text could be useful as a supplemental text for an introductory multilevel models course.This might be a little optimis-tic,especially if the focus is on application in such a course;these students would likely have a dif-ficult time with the majority of the material.However,this book would be right at home in an advanced seminar on multilevel models and would provide the basis of discussion for a good many topics that would arise in such a seminar.Chapter1.Cudeck and du Toit present nonlinear multilevel models that are specifically used with repeated-measures data in describing individual change.The manner in which the parameters Applied Psychological Measurement,Vol.31No.2,March2007,158–160 158DOI:10.1177/0146621605288555Ó2007Sage PublicationsK.S.MAIER and R.MAPURANGABOOK REVIEW159 are estimated is presented both theoretically and with illustrative examples provided from a longi-tudinal study and a repeated-measure experiment.Chapter2.This chapter presents a method for the sensitivity analysis of hierarchical linear models.Seltzer and Choi discuss how to check the adequacy of hierarchical models under t distri-butional assumptions.This sensitivity analysis technique is illustrated using several examples through a fully Bayesian analysis approach.This analysis uses Markov chain Monte Carlo (MCMC)techniques such as Gibbs sampling and is implemented using the software packages WinBUGS and CODA(syntax available from the authors).Chapter3.A method for analyzing two-level mean and covariance structures using structural equation modeling is presented by Bentler and Liang.The maximum likelihood analysis of the two-level structural equation model is implemented via an EM algorithm as a missing data prob-lem.The authors derive the EM algorithm and describe the computation of asymptotic standard errors of the model parameters as well as the chi-squared test for modelfit.Empirical examples are provided,and a discussion of convergence and possible improvements of the algorithm are suggested.Chapter4.In this chapter,the use of growth mixture modeling for studying achievement and learning progress is presented.Muthe´n,Khoo,Francis,and Boscardin discuss the random coeffi-cient growth model and the statistical software that can be used in its analysis(e.g.,SAS PROC MIXED,MLn,HLM).In addition,a latent variable framework for modeling growth processes and multiple trajectory classes in growth mixture modeling is described.Chapter5.Multilevel models for meta-analysis are described by Hox and de Leeuw.The ran-dom effects model is presented as a general model for meta-analysis.An example and comparison with classical meta-analysis is provided.A detailed explanation of how to correct for artifacts is also given.In addition,this chapter explains how to conduct meta-analyses using the multilevel software HLM and MLwiN.Chapter6.In what may be considered an extension of Chapter4,Jo and Muthe´n explain how causal effects are estimated in growth mixture modeling of longitudinal studies that include an intervention and noncompliance using the compiler average causal effect(CACE)approach.Spe-cifically,this estimation method uses latent growth trajectories over time and covariates,which often improves precision in determining the compliance type of individuals.The assumptions of the CACE model and its modeling are presented using a maximum likelihood EM algorithm approach.In addition,empirical and simulated data illustrate the CACE estimation procedure.Chapter7.An analysis of repeated-measures data with the multilevel repeated-measures model is presented by Baumler,Harist,and Carvajal.Unlike ANOVA,which uses least squares estima-tion,the multilevel model uses maximum likelihood estimation and can be used for analyzing unbalanced designs or irregularly spaced observations.An illustrative example is included.Chapter8.A multilevel analysis of the development of social resources in a university setting is described by Bachmann and Hornung.In contrast to the other chapters,this one takes on an entirely applied statistical analysis approach.A two-level hierarchical linear model was used to analyze a longitudinal study on the use of social resources by college students.The study suggests several interestingfindings on the relationship between student resources and student characteristics.Chapter9.The use of multilevel modeling for analyzing data that is composed of ordered cate-gories and random effects is described by Fielding.The author discusses methodological develop-ments and gives related applications of these methods.In addition,model estimation using software such as MIXOR,MlwiN,and HLM is discussed in the context of generalized linear mixed models(GLMMs).In his conclusion,the author notes the need for improved estimation procedures.Chapter10.Bootstrapping is employed as a methodology to account for the effect of measure-ment error on aggregated group-level effects.Hutchison describes various methods that are used when implementing the bootstrap on errors in multilevel models.Specifically,he discusses how to resample residuals,conducting a parametric bootstrap,methods for resampling units,and a general approach to bias correction.An applied example that uses data from a longitudinal study is also given.Chapter11.Ecob and Der present an iterative method for detecting outliers in longitudinal growth analyses that use multilevel modeling.This method uses the method of empirical Bayesian estimation.The authors describe models that are used with this method and provide an illustrative example.In the example,the method converges in a few iterations,but the authors also offer sug-gestions for convergence improvement in more complex applications,and several extensions are suggested.Chapter12.Rowe demonstrates multilevel structural equation modeling as a technique that can be used when modeling hierarchically structured data in organizational psychology research. He provides an empirical example using LISREL and PRELIS.In addition,the author explains how tofit two-level variance components,conditional multilevel regression models,and multi-level structural equation st,a discussion of the strengths and limitations of multilevel and structural equation models is given.Chapter13.Reise and Duan discuss design issues in multilevel studies,focusing on the topics of sampling,experimental design,and the estimation of power.The purpose of thisfinal chapter is to describe how to improve the planning and design of multilevel studies.Interesting issues that are raised relate to allocating samples across levels,choice of estimand,cohort design,and level of randomization.Overall,the chapter emphasizes that the quality of the analysis is dependent on the quality of data collected.This text is highly recommended for methodologists and students knowledgeable of advanced statistical topics.It provides a good survey of recent statistical advances and applied approaches in multilevel modeling.One of the strengths of the book is the empirical examples given in each chapter.Kimberly S.MaierRaymond MapurangaMichigan State UniversityReferencesGoldstein,H.(2002).Multilevel statistical models (3rd ed.).London:Arnold.Hox,J.(2002).Multilevel analysis:Techniques and applications.Mahwah,NJ:Lawrence Erlbaum. Kreft,I.,&de Leeuw,J.(1998).Introducing multi-level modeling.Thousand Oaks,CA:Sage. Raudenbush,S.W.,&Bryk,A.S.(2001).Hierarchi-cal linear models:Applications and data analysis methods(2nd ed.).Thousand Oaks,CA:Sage.Snijders,T.,&Bosker,R.(1999).Multilevel analy-sis:An introduction to basic and advanced multi-level modeling.Thousand Oaks,CA:Sage.Author’s AddressAddress reprint requests to Kimberly S.Maier,451 Erickson Hall,Michigan State University,East Lan-sing,MI48824;e-mail:kmaier@.160Volume31Number2March2007APPLIED PSYCHOLOGICAL MEASUREMENT。