The SAGE Handbook of Quantitative Methods in Psychology


Edited by: Roger E. Millsap & Alberto Maydeu-Olivares

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  • Chapters
  • Front Matter
  • Subject Index
  • Part I: Design and Inference

    Part II: Measurement Theory

    Part III: Scaling

    Part IV: Data Analysis

    Part V: Structural Equation Models

    Part VI: Longitudinal Models

    Part VII: Specialized Methods

  • Editorial Advisory Board

    • David Bartholomew (Sudbury, UK)
    • Peter Bentler (University of California-Los Angeles, CA)
    • Linda Collins (The Pennsylvania State University, PA)
    • Susan Embretson (Georgia Institute of Technology, GA)
    • Willem Heiser (Leiden University, The Netherlands)
    • Lawrence J. Hubert (University of Illinois, IL)
    • Karl G Joreskog (Uppsala University, Sweden)
    • Yutaka Kano (Osaka University, Japan)
    • Ivo Molenaar (Groningen University, The Netherlands)
    • John R. Nesselroade (University of Virginia, VA)
    • Albert Satorra (Universitat Pompeu Fabra, Spain)
    • Klaas Sijtsma (Tilburg University, The Netherlands)
    • Yoshio Takane (McGill University, Canada)
    • Stephen G. West (Arizona State University, AZ)


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    To Sofi, Alba and Alberto, with love, for all the hours I have been away.


    With love to Michele and our children, Mason, Laura, Simone, and Aiden. It is finally done. Thanks for being there for me.



    Quantitative psychology is the study of psychological phenomena using mathematical or statistical methods. Among fields within psychology, quantitative psychology is not recognized by the general public as part of psychology, despite its relatively long history within psychology. This lack of identity is in part due to the dual character of quantitative psychology. The field includes both the application of quantitative methods in studying psychological phenomena and the development of new quantitative methods as tools for research. Quantitative psychologists divide their time between each of these two general activities, or may pursue one activity exclusively. For example, some quantitative psychologists are associated with a particular research area (e.g., cognitive psychology) and apply quantitative tools with the goal of acquiring new knowledge about that area of inquiry. Other quantitative psychologists focus on the development of particular quantitative tools, which could later be applied across multiple research areas. From the viewpoint of psychology in general, the most valuable contributions made by quantitative psychologists are those that have enduring applicability to real psychological research or practice. These contributions usually rest on a foundation of prior theoretical work however, and this theoretical work may have had no obvious application initially.

    The precise historical origins of quantitative psychology are difficult to pinpoint. Two broad influences were the experimental psychological tradition from the nineteenth century, and the rise of mental testingin the late nineteenth and early twentieth centuries. The psychophysical research of nineteenth century psychologists such as Gustav Fechner and William Wundt introduced the application of mathematical methods to the study of sensation and perception. The idea that psychological phenomena might be accurately described using mathematical functions was new, and it inspired later generalizations to other domains of psychology, such as the measurement of attitudes (Thurstone, 1928). With regard to measurement, the development of measures of intelligence by Alfred Binet (Binet and Simon, 1905) and by James McKeen Cattell (Cattell, 1890) are early examples of influential psychometric research. Cattell first used the term mental test to describe a set of common tasks used to assess the examinees intelligence. In truth, the idea of tests as indicators of psychological traits was much older, going back to the use of written examinations in early China (Thorndike and Lohman, 1990).

    Motivations for new developments in quantitative psychology have often come from applications of quantitative methods to practical problems. For example, the application of testing to problems in educational measurement and in employment selection has led to new developments and extensions. The entire field of item response theory arose in part as a response to the practical inadequacies in classical models of measurement, for example (van der Linden and Hambleton, 1997). In educational measurement, the need for multiple forms of the same test and the resulting problems of equivalence in such tests led to new developments in test equating methods (Kolen and Brennan, 1995). In the area of research design, the inability to apply randomization principles in some domains of psychological research has led to new developments in causal modeling and quasi-experimental design (Shadish, Cook, and Campbell, 2002). However, some quantitative developments are slow to be adopted by practicing researchers, even when doing so might enhance research quality. Borsboom (2007) noted that important quantitative developments go unnoticed by psychologists in some cases. One obvious barrier to dissemination is that new quantitative developments often appear first in technical form, which discourages immediate adoption by the wider psychological community. The need then arises for work that will translate the technical details into a form that can be understood by a wider audience.

    The present book is an attempt to meet this need. Here we survey the field of quantitative psychology as it exists today, providing an overview with some depth while still making the contents accessible to readers who are not experts in statistics. We do assume that the reader has been exposed to fundamental concepts in statistics. Nearly all psychologists acquire some familiarity with statistical reasoning as part of their training. Some of the quantitative topics discussed in the book are necessarily more technical than others. We have tried to achieve relative uniformity in the level of discourse across the different contributed chapters, and where possible, to limit the technical level without sacrificing information. In choosing the topics to be covered, we have admittedly been influenced by our own perceptions of the important trends in the field. We do not claim to be exhaustive in our coverage. Arguably, there are additional quantitative topics that could have been covered as part of quantitative psychology. To our knowledge, this book is the first attempt to bring together the many different topics within quantitative psychology in a single volume.

    Turning now to the contents, Part I of the book addresses issues in research design and causal inference. Chapter 1, by Michael Sobel, describes the current thinking on the conditions needed for inferences of causality from empirical studies: What evidence is needed to conclude that A causes B? As noted in the chapter, the interest among researchers in developing formal principles of causal inference from real data has greatly increased in recent decades. Chapter 2, by Roger Kirk, on experimental design describes the basic principles of design for true experiments in which randomization ispossible forat least one independent variable. While most psychologists are exposed at some point in their training to statistical methods for the analysis of experimental data, research design principles are now less frequently taught in graduate schools of psychology (Aiken, West, and Millsap, 2008). Chapter 3, by Charles Reichardt, continues the design discussion by describing issues in the design of quasi-experiments, or studies in which interventions are made without full randomization. This topic is of deep interest to the many researchers who, for various practical reasons, cannot conduct true experiments. Chapter 4, by Paul D. Allison, addresses the problem of missing data, a topic that is now considered essential in the education of nearly any researcher in psychology, and is particularly important for longitudinal researchers. We know now that some informal methods of handling missing data can distort conclusions, and that better methods are available. We have placed this chapter in Part I because effective handling of missing data usually requires careful research design, especially with regard to the choice of which variables are measured.

    Part II of the book considers topics in psychological measurement, which has been an essential part of quantitative psychology from its early beginnings. Chapter 5, by James Algina and Randall Penfield, describes classical test theory (CTT). CTT has roots in work done in the late nineteenth century, yet it still guides much thinking about measurement in psychology today. An understanding of CTT is essential for psychologists who must critically evaluate tests and measures used in psychological researchor in applied settings. Chapter 6, by Robert MacCallum, discusses the traditional common factor analysis model, which bears a close relationship to models used in CTT. The linear factor model is the most commonly used latent variable model in psychology. It is used primarily to explore or confirm the number of latent dimensions that underlie a set of measures. Chapter 7, by David Thissen and Lynne Steinberg, concerns item response theory (IRT), which is a set of models for how people respond to test items. IRT models are latent variable models that make stronger assumptions than do models in CTT, but these stronger assumptions also permit useful applications such as computerized adaptive testing. This chapter gives an overview of IRT models and assumptions. Chapter 8, by Michael Edwards and Maria Orlando Edelen, addresses three special topics within IRT: computerized adaptive testing, the detection of differential item functioning, and multidimensional IRT. Computerized adaptive testing represents an important innovation in actual testing practice. Differential item functioning refers to group or temporal differences in the probabilities of various responses to test items, given scores on the latent variables. Multidimensional IRT is a collection of models for items in which more than one latent variable affects the response probabilities. The last chapter in this section, Chapter 9, by David Rindskopf, addresses latent class analysis, which is a latent variable model that applies when the latent variable is categorical rather than continuous in scale. These models have important applications within areas of psychology that posit multiple subpopulations defined by psychological status. For example, latent class models are the focus of recent debates about taxons versus continuous dimensions as models for personality measurements (e.g., Waller and Meehl, 1998).

    Part III of the book addresses psychological scaling methods. Whereas Part II focused on measurement models for the psychological attributes of people, Part III focuses on the scaling of psychological stimuli. To illustrate, we may want to understand how people evaluate political figures on a set of attributes. Psychological scaling methods can be used to help understand: (1) the dimensions along which people evaluate the political figures; and (2) the estimated location for each political figure on the dimensions. To begin, Chapter 10, by Yoshio Takane, Sunho Jung, and Yuriko Oshima-Takane, describes procedures for metric and non-metric scaling of stimuli. The distinction between these two forms of scaling lies in the initial measures that form the input for the scaling procedure, and whether those measures can be viewed as metric or simply ordinal in scale. Chapter 11, by Heungsun Hwang, MarcA. Tomiuk, and Yoshio Takane, addresses correspondence analysis and multiple correspondence analysis. Correspondence analysis provides exploratory representations of data in two-way cross-tabulation tables in terms of several latent dimensions. Under this representation, it is possible to calculate distances between rows and columns in the original table on the latent dimensions. This group of methods is not yet widely known in North America. Finally, Chapter 12, by Alberto Maydeu-Olivares and Ulf Böckenholt, describes scaling methods for preference data. Preference data are the data gathered by asking participants to indicate their choices or preferences among a set of stimuli. Thurstone (1927) presented models for such data that provided a basis for scaling the stimuli on psychological dimensions using the relative frequencies with which one stimuli is preferred to the other stimuli. Recent developments have greatly expanded the number of models that can be applied to preference data, as illustrated in the chapter.

    Part IV of the book presents chapters on topics within the general subject of data analysis and statistics. The section begins with Chapter 13, by Razia Azen and David Budescu, on the use of multiple regression in psychological research. Multiple regression is the most widely used multivariate statistical method in psychology, and it serves as a kind of gateway to more elaborate forms of multivariate statistics. A clear understanding of regression methods is thus essential for any researcher who wishes to use multivariate statistics. Chapter 14, by Carolyn Anderson, addresses the analysis of categorical data. Given that most measurement in psychology is done with items that have discrete response scales, categorical data analysis is vital to the study of psychological measures, as noted in the chapter. Also, substantial advances in categorical analysis methods have been made in the last 30 years. Chapter 15, by Jee-Seon Kim, concerns the analysis of multilevel data, or data in which some hierarchical structure is present among the individuals who provide the data. Multilevel data analysis is now regarded as a standard tool for psychologists who study data containing pre-existing groups, such as families, siblings, couples, work groups, schools, or organizations. In Chapter 16, William H. Beasley and Joseph L. Rodgers describe methods of analysis that employ resampling in various forms, such as the bootstrap or the jackknife. Resampling methods are highly useful for the analysis of psychological data because standard distributional assumptions are often violated in such data. In these cases, resampling methods offer one approach to obtaining accurate standard errors and confidence intervals. Chapter 17, by Rand Wilcox, addresses robust data analysis, or methods of data analysis that permit accurate estimation and statistical inference when distributional assumptions are violated. Psychologists who are unfamiliar with recent developments in this area will be surprised to learn of what is known about the negative impact of distributional problems on standard inference procedures, and what new alternatives are available. Chapter 18, byAndy Field, examines methods of meta-analysis, or the statistical integration of the results of many independent empirical studies. Meta-analytic methods have undergone rapid growth in the last 25 years, and have led to important advances in some areas of psychology, such as industrial-organizational psychology. Chapter 19, by Herbert Hoijtink, describes developments in data analysis that are motivated from a Bayesian perspective, in contrast to the frequentist perspective that has dominated much statistical practice in psychology. Psychologists as a whole are unaware of the impact of Bayesian statistical methods in the field of statistics generally. The chapter provides an introduction to many ideas that are now standard in the field of statistics, and that will become more widely used in psychology. The last chapter in this section is Chapter 20, by Lawrence J. Hubert, Hans-Friedrich Köhn, and Douglas Steinley, on cluster analysis. Cluster analysis is a collection of methods for grouping objects using some measures of distance or similarity between the objects. The chapter focuseson two broad clustering methods, hierarchical clustering and K-means partitioning. Software routines written in MATLAB are used throughout to illustrate the methods.

    Part V of the book is devoted to structural equation modeling. Structural equation models (SEMs) are found in nearly every area of psychology at present, moving in 30 years from a topic largely confined to technical journals to a part of the standard statistical training in many graduate schools of psychology. At present, the topic is too large to be covered in a single chapter, and so we have included several chapters in this section. Chapter 21, by Robert Cudeck and Stephen H.C. du Toit, gives an overview of general SEM theory and practice. This chapter covers the specification and identification of structural models, parameter estimation methods, and the evaluation of fit, using regression theory as a basic building block leading to the full SEM. In fact, many of the statistical models that are already familiar to psychologists, such as the analysis of variance model and regression models, can be represented as SEMs. Chapter 22, by Melanie M. Wall, addresses nonlinear structural equation models, in contrast to the linear models that form the basis for many applications of structural modeling. The need for such nonlinear models becomes apparent, for example, when theory suggests that two latent variables might interact in their causal effects on a third variable. Interactions at the latent level provide one application for these nonlinear models, and the chapter mentions other potential applications while also describing several broad approaches to estimation and fit evaluation in nonlinear SEM. Chapter 23, by Conor Dolan, addresses the topic of mixture modeling in the context of SEM. Mixture models arise from the combination of several distinct statistical models corresponding to distinct subpopulations within a general population. Mixture SEM models exist when the component models are SEM models in the various subpopulations. For example, in clinical applications, a mixture model might posit several distinct subpopulations corresponding to different levels of psychopathology in the general population. The last chapter in this section, Chapter 24, by David Kaplan, Jee-Seon Kim, and Su-Young Kim, describes developmentsinmultilevel latent variable modeling. This chapter sharesamultilevel perspective with the earlier Chapter 15, but focuses here on latent variable modeling in multilevel data. Given the frequent use of latent variable models in psychology to describe psychological measures, the extension to multilevel data structures is important in expanding the scope of these latent variable models.

    Part VI of the book examines statistical models for longitudinal data. The analysis of longitudinal data has undergone many new developments in the last 30 years, resulting in new approaches that are unfamiliar to most psychologists. Chapter 25, by Suzanne E. Graham, Judith D. Singer, and John B. Willett, provides an overview of longitudinal methods by focusing on models for individual change over time. The shift in recent years from modeling averages across time to developing random effects models for individual change trajectories is an important theme here. The problem of modeling change is a long-standing one in psychology (e.g., Harris, 1963) and will certainly continue to be of interest. Chapter 26, by Emilio Ferrer and Guangjian Zhang, examines the use of time series models in psychological research. Time series analysis is traditionally an important topic in longitudinal data analysis, but panel studies in psychology often include too few measurementsto enable the use ofsuch analyses. This situation has changed however with newer methods of data collection that seek many repeated measurements (Walls and Schafer, 2006), such as the use of electronic devices to record repeated self-reports of mood or stress levels. These methods have provided new scope for the application of times series analysis. The final chapter of this section is Chapter 27, by Jeroen K. Vermunt, that describes methods for event history analysis. Event history analysis includes methods for modeling the occurrence and timing of discrete events in a longitudinal sequence. For example, we may want to study causal influences on the elapsed time between the initial hiring of an employee and that employees departure from a job. As another example, we may study the time spent in recovery following a major psychological trauma. Event history analysis methods are less familiar to psychologists than are other longitudinal methods based on regression models.

    The last section of the book examines some specialized quantitative methods that are important, but are not easily classified in any of the preceding categories. Chapters 28 and 29 are related by a common emphasis on quantitative methods for the analysis of neuroimaging data. Chapter 28, by Josep Marco-Pallerés, Estela Camara, Thomas F. Münte, and Antoni Rodríguez-Fornells, describes methods for handling data provided by electroencephalography (EEG). EEG measurements typically provide a wealth of time-related data from multiple channels, and are often recorded in response to various stimuli to study variation in peoples responses. Some form of data reduction is often necessary (e.g., principal components analysis). Methods for looking at cross-series relations in multiple time series are also important. The chapter describes the statistical methods that are most often used for these data. Chapter 29, by Estela Camara, Josep Marco-Pallerés, Thomas F. Münte, and Antoni Rodríguez-Fornells, describes methods for handling magnetic resonance imaging (MRI) data. Like EEG data, the data provided by MRI is extensive and complex, requiring careful multivariate analyses that both simplifies and brings important trends into relief. MRI is an extraordinary tool for the analysis of brain processes, but methods for the analysis of these data are still under development. Please note that color versions of the plates in Chapters 28 and 29 are available at the end of the Handbook. The final chapter in this section is Chapter 30, by James O. Ramsay, on functional data analysis. Functional data analysis is a collection of methods for working with functions of data as the basic object of analysis. These functions ordinarily operate on individual-level data, as in a collection of individual growth curves over time. Once the functions to be used are specified, it is possible to also model selected features of these functions, such as differentials or acceleration. Functional data analysis makes it possible to model data in ways that would be difficult with more conventional approaches.

    While it is difficult to span the entire field of quantitative psychology in 30 chapters, we feel that the chapters in this volume represent a fair sampling of the many contributions made by quantitative psychologists to design, measurement, and analysis. We hope that people who are interested in learning more about quantitative psychology will find these chapters to be informative, and that psychologists who seek to use quantitative methods will find the book to be a useful resource.

    Roger E.Millsap and AlbertoMaydeu-Olivares
    Aiken, L.S., West, S.G., and Millsap, R.E. (2008) Doctoral training in statistics, measurement, and methodology in psychology: replication and extension of the Aiken, West, Sechrest, and Reno (1990) Survey of PhD Programs in North America, American Psychologist, 63 (1): 32–50.
    Binet, A., and Simon, T. (1905) Application of the new methods of the diagnosis of the intellectual level among normal and subnormal children in institutions and in the primary schools, L Année Psychologique, 11: 245–336.
    Borsboom, D. (2006) The attack of the psychometricians, Psychometrika, 71: 425–440.
    Cattell, J.M. (1890) Mental tests and measurements, Mind, 15: 373–381.
    Harris, C.W. (1963) Problems in Measuring Change. Madison, WI: University of Wisconsin Press.
    Kolen, M.J., and Brennan, R.L. (1995) Test Equating: Methods and Practices. New York: Springer.
    Shadish, W.R., Cook, T.D., and Campbell, D.T. (2002) Experimental and Quasi-experimental Designs for Generalized Causal Inference. Boston, MA: Houghton-Mifflin.
    Thorndike, R.L., and Lohman, D.F. (1990) A Century of Ability Testing. Chicago: Riverside Publishing.
    Thurstone, L.L. (1927) A law of comparative judgment, Psychological Review, 34: 273–286.
    Thurstone, L.L. (1928) The Measurement of Values. Chicago: University of Chicago Press.
    Van der Linden, W.J., and Hambleton, R.K. (1997) Handbook of Modern Item Response Theory. New York: Springer.
    Waller, N.G., and Meehl, P.E. (1998) Multivariate Taxometric Procedures: Distinguishing Types from Continua. Thousand Oaks, CA: Sage Publications.
    Walls, T.A., and Schafer, J.L. (2006) Models for Intensive Longitudinal Data. New York: Oxford University Press.

    Notes on Contributors

    James Algina is Professor and Coordinator of the Program in Research and Evaluation Methodology at the University of Florida. His scholarly interests are in statistics and psychometrics. His recent research interests have been in robust univariate and multivariate hypothesis tests about means, effect sizes and robust confidence intervals for effect size, methods for missing data, sample size selection, and differential item functioning and he is co-author of the widely used text Classical and modern test theory (Wadsworth, 1986). His work has appeared journals such as British Journal of Mathematical and Statistical Psychology, Communications in Statistics Simulation and Computation, Educational and Psychological Measurement, Journal of Educational Measurement, Journal of Educational and Behavioral Statistics, Journal of ModernApplied Statistical Methods, Multivariate Behavioral Research,Psychological Methods, and Psychometrika.

    Paul D. Allison is a Professor of Sociology at the University of Pennsylvania, where he teaches graduate methods and statistics. He is the author of numerous articles on regression analysis, log-linear analysis, logit analysis, latent variable models, missing data, and inequality measures. He has also publishedanumberofbooks, among themMissing data (Sage 2001), Logistic regression using SAS: theory and application (SAS Institute 1999), Multiple regression: a primer (Pine Forge 1999), Survival analysis using SAS: a practical guide (SAS Institute 1995), and Event history analysis (Sage 1984). A former Guggenheim Fellow, he is also on the editorial board of Sociological Methods and Research. In 2001 he received the Paul Lazarsfeld Memorial Award for Distinguished Contributions to Sociological Methodology.

    Carolyn J. Anderson is a Professor in the Departments of Educational Psychology, Psychology, and Statistics at the University of Illinois, Urbana-Champaign. Her research interests lie at the intersection of statistical models for categorical data analysis and psychometrics. Her major line of research deals with the development of flexible models for multivariate categorical data that have latent variable interpretations. Although the models are derived from different starting points, they are essentially equivalent to item response theory models. Some of the advantages of her approach are that models for observed data are derived, they can handle multiple correlated latent variables, various types of covariates in many different ways, and the models have graphical representations. She has published articles on this topic in Psychometrika, Psychological Methods, Sociological Methodology, Journal of Statistical Software, and Contemporary Educational Psychology.

    Razia Azen is currently an Associate Professor of Research Methodology in the Department of Educational Psychology at the University of Wisconsin Milwaukee. Dr Azen received her MS in Statistics and PhD in Quantitative Psychology from the University of Illinois at Urbana-Champaign. Her main research interests include the investigation and improvement of statistical methods for comparing predictors in multiple regression models, the extension of these methods to other general linear models, and the bootstrap technique. The goals of this research are to develop methods that can address research questions in a wide variety of disciplines and to aid researchers in the application of statistical methods and the interpretation of statistical information. Dr Azen has published research in journals such as Psychological Methods, Journal of Educational and Behavioral Statistics, and the British Journal of Mathematical and Statistical Psychology. She teaches research methods, experimental design, and advanced statistical analysis courses.

    William H. Beasley is a Quantitative Psychology graduate student at the University of Oklahoma. He is interested in graphical data analysis and computationally intensive procedures, including resampling methods and Bayesian statistics. He has a BA in Psychology from Davidson College, and an MA in Quantitative Psychology from the University of Oklahoma. He owns Howard Live Oak, Inc., a small statistical software and consulting company. Will has conducted simulation studies of bootstrapping, IRT DIF analysis, and multilevel models with multiple dependent variables. He has worked on applied problems involving behavior genetics, cardiovascular rehabilitation, adolescent development, and screening test validity. For the past two years, he has been the data management coordinator of an NIH grant titled Biometrical Modeling of Fertility using the NLSY.

    Ulf Böckenholt is a Professor at the Desautels Faculty of Management at McGill University. His research activities focus on the development and application of statistical and econometric methods for understanding judgment and choice behavior. He is a past Editor of Psychometrika, a past President of the Psychometric Society, and a Fellow of the Association of Psychological Science.

    David Budescu is the Anne Anastasi Professor of Psychometrics and Quantitative Psychology at Fordham University in New York. His research is in the areas of human judgment, individual and group decision making under uncertainty and with incomplete and vague information, and statistics for the behavioral and social sciences. He is on the editorial boards of Applied Psychological Measurement, Journal of Behavioral Decision Making, Journal of Mathematical Psychology, Journal of Experimental Psychology: Learning, Memory&Cognition(20002003), Multivariate Behavioral Research, Organizational Behavior and Human Decision Processes (19922002), Psychological Methods (19962000). He is a past-President of the Society for Judgment and Decision Making (20002001), Fellow of the American Psychological Society, and an elected member of the Society of Multivariate Experimental Psychologists.

    Estela Camara is currently a post-doc researcher at the Otto von Guericke University of Magdeburg (Germany) (Neuropsychology and Center for Advanced Imaging departments). She has obtained her bachelor degree in Physics and her PhD in Cognitive Science at the University of Barcelona. Her dissertation has been devoted to the study of brain connectivity and brain dynamics of the human reward system using MRI neuroimaging techniques. She has several studies in which information from white-matter brain pathways, using obtained Diffusion Tensor Imaging, functional magnetic resonance imaging and event-related brain potentials have been combined. Her research interests are focussedon the integrationoffunctional and microstructural information using advanced neuroimaging techniques in order to reach a better understanding of the organization and dynamics of the distributed networks that subserve neural functions and human behaviour.

    Robert Cudeck received his PhD from the University of Southern California and is currently a member of the Faculty in Psychology at Ohio State University. His research interests are in applications of factor analysis, structural equation models, and hierarchical models in the behavioral sciences.

    Conor V. Dolan is an Associate Professor in the Department of Psychology at the University of Amsterdam. His research interests, which center around structural equation modeling (SEM), include finite mixture SEM of cognitive development, the analysis of individual and group differences in IQ test scores, the analysis of twin and family data, the SEM approach to time series modeling, and modeling heterogeneity in the common factor model.

    Stephen H.C. du Toit is presently a Vice-President at Scientific Software International. He received his PhD in statistics from the University of South Africa and was formerly a Professor of Statistics atPretoria University. His research activities have covered a numberoftopics in mul-tivariate statistics and computational statistics, especially time series analysis, hierarchical linear models, item response theory, structural equation models, and the analysis of complex samples.

    Maria Orlando Edelen received her PhD from the University of North Carolina at Chapel Hill and is currently a Behavioral Scientist and Psychometrician at the RAND Corporation. As a quantitative psychologist, she has extensive knowledge of test theory including item response theory (IRT) and of advanced multivariate methods, such as structural equation modeling (SEM) and latent growth mixture modeling. Dr Edelen has applied her measurement and methodological skills in a variety of behavioral health research contexts; IRT applications include linking scores from overlapping versions of the CES-D, assisting in the development of short screeners aimed to decrease respondent burden and cost of administration, detecting differential item functioning in scales based on language and mode of administration (e.g., mail vs. phone interviews), as well as other potentially biasing characteristics, using factor analysis and IRT in the evaluation and refinement of instruments designed to measure quality of care for substance abuse treatment, and using IRT to refine the assessment of adolescent depression.

    Michael C. Edwards received his PhD from the University of North Carolina at Chapel Hill and is currently an Assistant Professor in the quantitative area of the Psychology Department at The Ohio State University. His dissertation, A Markov chain Monte Carlo approach to confirmatory item factor analysis, received the 2006 Psychometric Society Dissertation Award. As part of this line of research he created a software program called MultiNorm, which performs MCMC estimation of a wide range of item factor analysis models. This interest in item factor analysis has resulted in several publications, examining the differences (or more often similarities) between the item response theory and factor analytic frameworks. Other methodological interests include subscore augmentation, local dependence detection, measurement solutions for multiple reports, and computerized adaptive testing.

    Emilio Ferrer is an Associate Professor in the Department of Psychology at the University of California, Davis. His research interests include methods to analyze change and intra-individual variability, in particular latent growth analysis and dynamical systems. His current research in this area involves techniques for modeling dyadic interactions using dynamic factor analysis, structural equation modeling, and exploratory methods. He received his PhD in quantitative psychology from the University of Virginia.

    Andy P. Field is a Reader in Experimental Psychopathology at the University of Sussex, UK. He researches the development of anxiety in children and dabbles in statistics when the mood takes him. He has published around 50 research papers, mostly on child anxiety and human conditioning but some on meta-analysis too. He has written or edited nine books (and contributed to many more), including the bestselling textbook Discovering statistics using SPSS: and sex and drugs and rock n roll, for which he won the British Psychological Society book award in 2007. His uncontrollable enthusiasm for teaching statistics to psychologists has led to teaching awards from the University of Sussex (2001) and the British Psychological Society (2006). He is currently anAssociate Editor for the British Journal of Mathematical and Statistical Psychology and Cognition and Emotion. In his spare time he plays the drums very noisily, which he finds very therapeutic.

    Suzanne E. Graham isanAssistant Professor of Education at the University of New Hampshire. She received her doctorate in Human Development and Psychology, with a focus on quantitative methodology, from the Harvard Graduate School of Education, where she subsequently taught applied courses in regression analysis, covariance structure analysis, research design, and longitudinal data analysis for several years. At the University of New Hampshire, Graham continues to teach courses in applied statistics and research design. In addition, she is affiliated with the University of New Hampshires Carsey Institute, as both a Faculty Research Fellow and a member of the Research Development Working Group. Professor Grahams primary research interests center on the application of quantitative methods, such as individual growth modeling, survival analysis, multilevel modeling, and propensity score analysis to research in education and other social sciences.

    Herbert Hoijtink is a Professor in Applied Bayesian Statistics at Utrecht University in the Netherlands. During his PhD he researched item response models for proximity data. After a visit to the Harvard Statistics Department, his research focus changed to applied Bayesian statistics. Currently he is executing a VICI project funded by the Netherlands Organization for Scientific Research in which Bayesian evaluation of informative hypothesis is proposed as an alternative for null-hypothesis significance testing. Some detailsof the proposed approach can be found in his chapter in this book. Those who want to pursue this topic are referred to Hoijtink, H., Klugkist, I. and Boelen, P.A. (2008) Bayesian evaluation of informative hypotheses. New York: Springer.

    Lawrence J. Hubert is the Lyle H. Lanier Professor of Psychology, and Professor of Statistics and of Educational Psychology at the University of Illinois, Champaign, Illinois. His research program has concentrated on the development of exploratory methods for data representation in the behavioral sciences. Specifically, he has emphasized cluster analysis methods (hierarchical, nonhierarchical, and those allowing overlapping cluster options), a range of spatially oriented multidimensional scaling techniques (both metric and nonmetric), and a number of network representation procedures (through tree models as well as more general graph-theoretic entities). Much of this work within the field of Combinatorial Data Analysis is summarized in two research monographs with the Society of Industrial andApplied Mathematics (with co-authors P. Arabie and J. Meulman): Combinatorial data analysis: optimization by dynamic programming(2001);The structural representation of proximity matriceswith MATLAB (2006).

    Heungsun Hwang is currently an Assistant Professor of Psychology at McGill University, Montreal, Canada. He has also been an Assistant Professor of Marketing at HEC Montreal, Montreal, Canada. Before a full career transition at the academic level, he worked as a research analyst at an international marketing consulting company called Claes Fornell International Group at Ann Arbor, Michigan, USA. He received his PhD in Quantitative Psychology from McGill University. In general, his research interests lie in the development and applications of quantitative methods and advanced modeling methodologies to a variety of issues and topics in psychology, marketing, and other fields of inquiry. More specifically, his recent interests include component-based structural equation modeling, growth curve models, generalized linear models, cluster analysis, and data-reduction techniques.

    SunhoJung isaPhD studentinthe DepartmentofPsychologyatMcGill University. His research interests include statistical computing, structural equation models, and the development of new statistical methods for multivariate models for situations with a variety of difficulties such as small samples or non-normal data.

    David Kaplan received his PhD from UCLAin 1987 and joined the faculty of the University of Delaware where he remained until 2006. He is now a Professor in the Department of Educational Psychology at the University of Wisconsin-Madison and holds an affiliate appointment in the Department of Population Health Sciences in the School of Medicine and Public Health at UW-Madison. His present research interests concern Bayesian latent variable models and casual inference in observational studies. He has been a consultant on numerous projects sponsored by the U.S. Department of Education (IES and NCES), the National Science Foundation, and the Organization for Economic Cooperation and Development (OECD). He is currently a member of the Technical Advisory Group and the Questionnaire Expert Group for the OECD/Program for International Student Assessment (PISA). He has been a Visiting Professor at the Hebrew University of Jerusalem and the University of Milano-Bicocca. During the 20012002 academic year, he was the Jeanne Griffith Fellowatthe National Center for Education Statistics.

    Jee-Seon Kim is an Associate Professor in the Department of Educational Psychology at the University of Wisconsin-Madison. Her research interests concern the development and application of quantitative methods in the social sciences, focusing on multilevel models, latent variable models, methods for modeling change, learning, and human development, using longitudinal data, test equating, and issues related to omitted variables and school effectiveness. She received her BS and MS in Statistics and her PhD in Quantitative Psychology from the University of Illinois at Urbana-Champaign in 2001. Following her graduate study, she received the Outstanding Dissertation Award for Quantitative Methods from the American Educational Research Association in 2002. She was selected as a Fellow by the National Academy of Educational and Spencer Foundation in 2004. Her scholarly work has been published in Psychometrika, Multivariate Behavioral Research, the Journal of Educational Measurement, the British Journal of Mathematical and Statistical Psychology, Applied Psychological Measurement, and Psychological Methods.

    Su-Young Kim is a PhD student in the Quantitative Methods area of the Educational Psychology Department at the University of Wisconsin-Madison. He has worked with Jee-Seon Kim on statistical methodologies for longitudinal data analysis based on latent growth mixture models and covariance structure models. He has also pursued applications of these methodologies to data collected in smoking cessation studies. Currently, Su-Young works as a project assistant at the Center for Tobacco Research and Intervention at the University of Wisconsin-Madison.

    Roger E. Kirk received his PhD in Experimental Psychology from the Ohio State University and did post doctoral study in Mathematical Psychology at the University of Michigan. He is a Distinguished Professor of Psychology and Statistics and Master Teacher at Baylor University. He has published over a hundred scholarly papers and five statistics books. His first book, Experimental design: procedures for the behavioral sciences (Brooks/Cole, 1968), was named a Citation Classic by the Institute of Scientific Information. Dr Kirk is a Fellow of the American Psychological Association, Association for Psychological Science, and the American Educational Research Association. He is a past-President of the Society for Applied Multivariate Research, Division 5 of the American Psychological Association, and the Southwestern Psychological Association. In recognition of his many contributions to the teaching of statistics, Division 5 of the American Psychological Association honored him with the 2005 Jacob Cohen Award for Distinguished Contributions to Teaching and Mentoring.

    Hans-Friedrich Köhn is an Assistant Professor of Quantitative Psychology in the Department of Psychological Sciences at the University of Missouri-Columbia. He earned his Doctoral degree in Quantitative Psychology from the University of Illinois, Champaign, Illinois. His research concerns applications of combinatorial optimization methods to scaling/unfolding, clustering/tree-fitting, and order-constrained matrix decomposition problems, with particular focus on the analysis of individual differences based on sets of multiple proximity matrices, as might be collected from different data sources in the context of cross-sectional or longitudinal studies. He has also worked on algorithms for the p-median clustering of large data sets and the clique partitioning problem.

    Robert C. MacCallum is a Professor of Psychology and Director of the L.L. Thurstone Psychometric Laboratory at the University of North Carolina at Chapel Hill. He assumed these positions in 2003 following 28 years on the faculty at Ohio State University. He received his graduate training at the University of Illinois under the direction of Ledyard R Tucker, the most prominent protégé of L.L. Thurstone. His research interests focus on methods for analysis and modeling of correlational and longitudinal data, including factor analysis, structural equation modeling, and latent curve models. Within these areas he has worked on various issues, including model estimation and evaluation, power analysis for testing models, and the nature and management of sources of error in modeling.

    Josep Marco-Pallarés is a researcher in the Biomedical Research Institute and Department of Physiology at the Faculty of the Medicine (University of Barcelona). He obtained his bachelor degree in Physics in the University of Barcelona and pursued his PhD in the same university on the application of advanced mathematical methods in the study of electroencephalography (EEG) and event-related brain potentials (ERPs). He then moved to the Otto von Guericke University of Magdeburg (Germany) (Neuropsychology and Center for Advanced Imaging departments). His current research is focused in the study of executive functions, especially in action monitoring and error, reward and punishment processing. To study them, he uses advanced neuroimaging techniques, such as functional magnetic resonance imaging, electroencephalography, magnetoencephalography, and intracranial recordings. Moreover, he studies the alteration of these systems in neurological and psychiatric populations.

    Alberto Maydeu-Olivares is an Associate Professor of Psychology at the University of Barcelona. His research interests focus on structural equation modeling and item response theory, and more generally on developing new quantitative methods for Psychology and Marketing applications. Among other awards, he has received the American Psychological Association dissertation award (Division 5), the Catalan Young Investigator Award, and the Society of Multivariate Experimental Psychology Cattells award. He is currently Section Editor of Psychometrika.

    Roger E. Millsap is a Professor in the doctoral program in Quantitative Psychology in the Department of Psychology at Arizona State University. His research interests include latent variable modeling, psychometric theory, and multivariate statistics. His recent publications have addressed problems in the evaluation of measurement invariance, either in multiple group data or in longitudinal data. Some of this work has concerned relationships between invariance in measurement and invariance in prediction. He served as the Editor of Multivariate Behavioral Research from 1996 to 2006, and is the current Executive Editor of Psychometrika. He is a past-President of the Society of Multivariate Experimental Psychology, the Psychometric Society, and Division 5 of the American Psychological Association.

    Thomas F.Münte is currentlya Professorof Neuropsychology in the Department of Psychology, Otto-von-Guericke University and one of the directors of the Center for Behavioral Brain Sciences, both in Magdeburg, Germany. He studied medicine in Göttingen, Germany, and neuroscience in San Diego, USA, and subsequently was trained as a neurologist while at the same time developing several lines of research addressing the neural underpinnings of cognitive processes (language, attention, executive functions) and their changes in neuropsychiatric disorders. To delineate the spatiotemporal signature of these processes, he employs electroencephalography, magnetoencephalography, and functional neuroimaging. More recently, he has also used invasive intracranial recordings in awake patients performing cognitive tasks while undergoing implantation of deep brain stimulation electrodes. His aim for the next 10 years is to increasingly bridge the gap between systems level and molecular level neuroscience, for example by using participants differing in certain genetic traits.

    Yuriko Oshima-Takane is a Professor of Psychology at McGill University. Her main interest of research lies in the area of language development in children. She has published widely in this area. Her recent interest in word learning (particularly, object noun learning, and verb learning) called for similarity judgments and multidimensional scaling to analyze the visual and auditory/linguistic stimuli.

    Randall D. Penfield is an Associate Professor of Measurement and Applied Statistics in the School of Education at the University of Miami where he currently serves as the Director of the Graduate Program in Research, Measurement, and Evaluation. His primary research concentration is in the areas of measurement and assessment. Much of his research concentrates on advancing methodology pertaining to item response theory, differential item functioning, and computerized adaptive testing. Other research interests include fairness issues associated with high-stakes testing, legal and professional standards of educational and psychological testing, and the use of high-stakes testing in educational accountability systems. His research has appeared in journals, such as the Journal of Educational Measurement, Applied Psychological Measurement, Educational and Psychological Measurement, Applied Measurement in Education, Psychological Methods, and Educational Measurement: Issues and Practice.

    James O. Ramsay isa retired Professor of Psychology andAssociate Member in the Department of Mathematics and StatisticsatMcGill University. He receiveda PhD from Princeton University in 1966 in quantitative psychology. He served as Chair of the Department from 1986 to 1989. Jim has contributed research on various topics in psychometrics, including multidimensional scaling and test theory. His current research focus is on functional data analysis, and involves developing methods for analyzing samples of curves and images. The identification of systems of differential equations from noisy data plays an important role in this work. He has been the President of the Psychometric Society and the Statistical Society of Canada. He received the Gold Medal of the Statistical Society of Canada in 1998 and the Award for Technical or Scientific Contributions to the Field of Educational Measurement of the U. S. National Council on Measurement in Education in 2003.

    Charles S. Reichardt is a Professor of Psychology at the University of Denver. His research concerns statistics, research methods, and program evaluation, most often with a focus on the logic of assessing cause and effect outside the laboratory. He has published three edited volumes in the field of program evaluation, served as a statistical consultant on dozens of federally funded evaluations, and given numerous workshops on statistics and research design. He has served on the Board of Directors of the American Evaluation Association, is a Fellow of the American Psychological Society, is an elected member of the Society for Multivariate Experimental Psychology, and received the Perloff award from the American Evaluation Society and the Tanaka award from the Society for Multivariate Experimental Psychology.

    David Rindskopf is a Distinguished Professor of Educational Psychology and Psychology at the City University of New York Graduate Center. He is a Fellow of the American Statistical Association, the American Educational Research Association, and is past-President of the New York Chapter of the American Statistical Association. Currently he serves as an Editor of the Journal of Educational and Behavioral Statistics. His research interests are categorical data, latent variable models, and multilevel models. Among his current projects are: (1) showing how people subconsciously use complex statistical methods to make decisions in everyday life, (2) introducing floor and ceiling effects into logistic regression to model response probabilities constrained to a limited range, (3) using multilevel models to analyze data from single case designs.

    Joseph L. Rodgers is a Quantitative Psychologist in the Department of Psychology at the University of Oklahoma, where he has been the Robert Glenn Rapp Foundation Presidential Professor since 2000. He received his PhD from the University of North Carolina in 1981, and began his faculty career at OU in that year. He has held visiting teaching/research positions at Ohio State, UNC, Duke, the University of Southern Denmark, and the University of Pennsylvania. He has maintained continuous NIH funding since 1987 to develop mathematical models of adolescent development and family/friendship interactions. His methodological interests include resampling theory, linear statistical models, quasi-experimental design methods, exploratory data analysis, and multidimensional scaling. He has been the Editor of the applied methods journal Multivariate Behavioral Research since 2005, and is a past-President of the Society of Multivariate Experimental Psychology, the Society for the Study of Social Biology, and the APAs Division 34 (Population and Environmental Psychology).

    Antoni Rodríguez-Fornells is currently a Research Professor at the Department of General Psychology, University of Barcelona and belongs to the Catalan Institute for Research and Advanced Studies (ICREA, Spain). One of his main current interests has been the application of event-related brain potentials (ERPs) and functional magnetic resonance imaging (fMRI) to several research lines. For example, his doctoral (University of Barcelona) and post-doctoral research periods (at the University of Hannover/Magdeburg) were devoted to the study of cognitive control (impulsiveness, error processing, and bilingualism) using neurophysiological measures. He is currently involved in studying the neurophysiological mechanisms involved in word learning and language acquisition and the interface between cognitive control and language learning. In relation to his neuroimaging work, he has been very interested in trying to combine acquired information using different neuroimaging techniques which could provide a complementary picture of the studied phenomena.

    Judith D. Singer is the James Bryant Conant Professor of Education and Senior Vice-Provost for Faculty Development and Diversity at Harvard University. An internationally renowned statistician and social scientist, Singers scholarly interests focus on improving the quantitative methods used in social, educational, and behavioral research. She is primarily known for her contributions to the practice of multilevel modeling, survival analysis, and individual growth modeling, and to making these and other statistical methods accessible to empirical researchers. Singers wide-ranging interests have led her to publish across a broad array of disciplines, including statistics, education, psychology, medicine, and public health. In addition to writing and co-writing nearly 100 papers and book chapters, often with longtime collaborator John B. Willett, she has also co-written three books, most recently Applied longitudinal data analysis: modeling change and event occurrence (Oxford University Press 2003). Already a classic, the book received honorable mention from the American Publishers Association for the best mathematics and statistics book of 2003.

    Michael E. Sobel is a Professor at Columbia University. He has published extensively in statistics and in the social and behavioral sciences, and is a past Editor of Sociological Methodology. His current research interests include assessing the relative performance of various election forecasting methodologies as well as a number of topics related to causal inference, for example, mediation and causal inference in the presence of interference between units.

    Lynne Steinberg is an Associate Professor in the Department of Psychology at the University of Houston. Her research interests involve applications of the psychometric methods of item response theory (IRT) to issues that arise in personality and social psychological measurement. She investigates processes underlying responses to self-report questions, context effects in personality measurement, and the effects of alternate response scales on item responses for social and personality measures. She has been active in the development and validation of new instruments for personality, social, and clinical research. She is also one of the authors of Computerized adaptive testing: a primer (Lawrence Erlbaum), published in 1990 and republished in a second edition in 2000.

    Douglas L. Steinley is an Assistant Professor of Psychological Sciences at the University of Missouri, Columbia. His research program concentrates on the development and refinement of modern cluster analytic procedures, including variable selection, variable weighting, and data reduction. In conjunction with traditional cluster analytic methodologies (with primary focus being on nonhierarchical procedures), he also focuses on partitioning problems from a social network analysis perspective.

    Yoshio Takane is a Professor of Psychology at McGill University. He is interested in structured multivariate analysis (MVA) in general, wherea variety of structural hypotheses are incorporated in the analysis of multivariate data. His most recent contributions in this area include regularized estimations in various MVA techniques, acceleration techniques for iterative algorithms, and neural network simulations.

    David Thissen is a Professor in the Department of Psychology and the L.L. Thurstone Psychometric Laboratory at the University of North Carolina at Chapel Hill. His research interests are in the areas of psychological testing, measurement, and item response theory (IRT). His 2001 book with Howard Wainer,Test scoring (Lawrence Erlbaum), describes both traditional and novel uses of IRT to compute scores for conventional linear tests, tests comprising mixtures of item types, and multi-stage and computerized adaptive tests (CATs). He is also one of the authors of Computerized adaptive testing: a primer (Lawrence Erlbaum), published in 1990 and republished in a second edition in 2000. He is primary creator of the widely used computer software Multilog, a flexible system for item calibration using any of several IRT models, and a number of other general- and special-purpose software applications. He is currently involved in research programs that use item response theory to measure aspects of health-related quality of life, and adaptive behavior for individuals with intellectual disabilities; he also works in various roles with a number of educational assessment programs.

    Marc A. Tomiuk is an Associate Professor of Marketing at HEC Montréal. His substantive research interest revolves around the assessment of services, consumer behavior, and retailing. He has published a number of papers in journals, such as the Journal of Cross-Cultural Psychology, the Journal of International Consumer Marketing, Group and Organization Management, etc.

    Jeroen K. Vermunt isa full Professorinthe Department of Methodology and StatisticsatTilburg University, the Netherlands. He holds a PhD in Social Sciences from Tilburg University. He has published extensively on categorical data techniques, methods for the analysis of longitudinal and event history data, latent class and finite mixture models, and latent trait models. He is the co-developer (with Jay Magidson) of the Latent GOLD software package. His full CV and publications can be found at:vermunt.

    Melanie M. Wall is an Associate Professor in the Division of Biostatistics within the School of Public Health at the University of Minnesota. Her research interests are in statistical methods for latent variable modeling and extending traditional latent variable models (e.g., to include nonlinearities, spatial structure, and to include both categorical and continuous latent variables) making them more attractive to a variety of researchers. In particular, she works on applying latent variable models to answer research questions relevant for behavioral public health.

    Rand R. Wilcox is a Professor in the Department of Psychology at the University of Southern California. His main interests are robust methods. His work deals with a range of problems that include methods for comparing groups and studying associations. Some of his work also deals with multivariate issues and various nonparametric methods. Briefly, there have been major insights regarding classic techniques based on means and least squares regression that show the techniques to be unsatisfactory under general conditions. Many new and improved methods have been devised and compared.

    John B. Willett is the Charles William Elliot Professor at the Harvard University Graduate School of Education. He holds a doctorate in Quantitative Methods from Stanford University, masters degrees in Statistics and Psychometrics from Stanford and Hong Kong Universities, and an undergraduate degree in Physics from Oxford University, respectively. Professor Willett teaches coursesin applied statistics and specializesinquantitative methods for measuring change over time and for analyzing the occurrence, timing, and duration of events. His most recent book, authored with longtime collaborator and colleague Professor Judith D. Singer, is entitled Applied longitudinal data analysis: modeling change and event occurrence (Oxford University Press, 2003). He and Professor Singer are currently working on a companion volume on multilevel modeling.

    Guangjian Zhang is currently an Assistant Professor of Quantitative Psychology in the Department of Psychology at University of Notre Dame. His research interests include dynamic factor analysis, longitudinal analysis, structural equation modeling, and statistical computing. His current research involves using resampling-based methods like the bootstrap to make valid inference when assumptions of statistical procedures are violated. He received his PhD from the Ohio State University under the supervision of Michael W. Browne in 2006. He studied Clinical Medicine, Counseling Psychology, and Social Psychology in his previous trainings. He was a licensed medical doctor in China and practiced Psychiatry for two years.

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