Measurement Invariance

This user-friendly guide illustrates how to assess measurement invariance using computer programs, statistical methods, and real data.

This book reviews the statistical procedures used to detect measurement bias. Measurement bias is examined from a general latent variable perspective so as to accommodate different forms of testing in a variety of contexts including cognitive or clinical variables, attitudes, personality dimensions, or emotional states. Measurement models that underlie psychometric practice are described, including their strengths and limitations. Practical strategies and examples for dealing with bias detection are provided throughout. The book begins with an introduction to the general topic, followed by a review of the measurement models used in psychometric theory. Emphasis is placed on latent variable models, with introductions to classical test theory, factor analysis, and item response theory, and the controversies associated with each, being provided. Measurement invariance and bias in the context of multiple populations is defined in chapter 3 followed by chapter 4 that describes the common factor model for continuous measures in multiple populations and its use in the investigation of factorial invariance. Identification problems in confirmatory factor analysis are examined along with estimation and fit evaluation and an example using WAIS-R data. The factor analysis model for discrete measures in multiple populations with an emphasis on the specification, identification, estimation, and fit evaluation issues is addressed in the next chapter. An MMPI item data example is provided. Chapter 6 reviews both dichotomous and polytomous item response scales emphasizing estimation methods and model fit evaluation. The use of models in item response theory in evaluating invariance across multiple populations is then described, including an example that uses data from a large-scale achievement test. Chapter 8 examines item bias evaluation methods that use observed scores to match individuals and provides an example that applies item response theory to data introduced earlier in the book. The book concludes with the implications of measurement bias for the use of tests in prediction in educational or employment settings. A valuable supplement for advanced courses on psychometrics, testing, measurement, assessment, latent variable modeling, and/or quantitative methods taught in departments of psychology and education, researchers faced with considering bias in measurement will also value this book.

Multi-item surveys are frequently used to study scores on latent factors, like human values, attitudes and behavior. Such studies often include a comparison, between specific groups of individuals, either at one or multiple points in time. If such latent factor means are to be meaningfully compared, the measurement structures including the latent factor and their survey items should be stable across groups and/or over time, that is ‘invariant’. Recent developments in statistics have provided new analytical tools for assessing measurement invariance (MI). The aim of this special issue is to provide a forum for a discussion of MI, covering some crucial ‘themes’: (1) ways to assess and deal with measurement non-invariance; (2) Bayesian and IRT methods employing the concept of approximate measurement invariance; and (3) new or adjusted approaches for testing MI to fit increasingly complex statistical models and specific characteristics of survey data. The special issue started with a kick-off meeting where all potential contributors shared ideas on potential papers. This expert workshop was organized at Utrecht University in The Netherlands and was funded by the Netherlands Organization for Scientific Research (NWO-VENI-451-11-008). After the kick-off meeting the authors submitted their papers, all of which were reviewed by experts in the field. The papers in the eBook are listed in alphabetical order, but in the editorial the papers are introduced thematically. Although it is impossible to cover all areas of relevant research in the field of MI, papers in this eBook provide insight on important aspects of measurement invariance. We hope that the discussions included in this special issue will stimulate further research on MI and facilitate further discussions to support the understanding of the role of MI in multi-item surveys.

Latent variable models are a powerful tool for measuring many of the phenomena in which developmental psychologists are often interested. If these phenomena are not measured equally well among all participants, this would result in biased inferences about how they unfold throughout development. In the absence of such biases, measurement invariance is achieved; if this bias is present, differential item functioning (DIF) would occur. This Element introduces the testing of measurement invariance/DIF through nonlinear factor analysis. After introducing models which are used to study these questions, the Element uses them to formulate different definitions of measurement invariance and DIF. It also focuses on different procedures for locating and quantifying these effects. The Element finally provides recommendations for researchers about how to navigate these options to make valid inferences about measurement in their own data.

This Element demonstrates how and why the alignment method can advance measurement fairness in developmental science. It explains its application to multi-category items in an accessible way, offering sample code and demonstrating an R package that facilitates interpretation of such items' multiple thresholds. It features the implications for group mean differences when differences in the thresholds between categories are ignored because items are treated as continuous, using an example of intersectional groups defined by assigned sex and race/ethnicity. It demonstrates the interpretation of item-level partial non-invariance results and their implications for group-level differences and encourages substantive theorizing regarding measurement fairness.

This book reviews the latest techniques in exploratory data mining (EDM) for the analysis of data in the social and behavioral sciences to help researchers assess the predictive value of different combinations of variables in large data sets. Methodological findings and conceptual models that explain reliable EDM techniques for predicting and understanding various risk mechanisms are integrated throughout. Numerous examples illustrate the use of these techniques in practice. Contributors provide insight through hands-on experiences with their own use of EDM techniques in various settings. Readers are also introduced to the most popular EDM software programs. A related website at http://mephisto.unige.ch/pub/edm-book-supplement/offers color versions of the book’s figures, a supplemental paper to chapter 3, and R commands for some chapters. The results of EDM analyses can be perilous – they are often taken as predictions with little regard for cross-validating the results. This carelessness can be catastrophic in terms of money lost or patients misdiagnosed. This book addresses these concerns and advocates for the development of checks and balances for EDM analyses. Both the promises and the perils of EDM are addressed. Editors McArdle and Ritschard taught the "Exploratory Data Mining" Advanced Training Institute of the American Psychological Association (APA). All contributors are top researchers from the US and Europe. Organized into two parts--methodology and applications, the techniques covered include decision, regression, and SEM tree models, growth mixture modeling, and time based categorical sequential analysis. Some of the applications of EDM (and the corresponding data) explored include: selection to college based on risky prior academic profiles the decline of cognitive abilities in older persons global perceptions of stress in adulthood predicting mortality from demographics and cognitive abilities risk factors during pregnancy and the impact on neonatal development Intended as a reference for researchers, methodologists, and advanced students in the social and behavioral sciences including psychology, sociology, business, econometrics, and medicine, interested in learning to apply the latest exploratory data mining techniques. Prerequisites include a basic class in statistics.

Covers the latest methodologies and research on international comparative surveys with contributions from noted experts in the field Advances in Comparative Survey Methodology examines the most recent advances in methodology and operations as well as the technical developments in international survey research. With contributions from a panel of international experts, the text includes information on the use of Big Data in concert with survey data, collecting biomarkers, the human subject regulatory environment, innovations in data collection methodology and sampling techniques, use of paradata across the survey lifecycle, metadata standards for dissemination, and new analytical techniques. This important resource: Contains contributions from key experts in their respective fields of study from around the globe Highlights innovative approaches in resource poor settings, and innovative approaches to combining survey and other data Includes material that is organized within the total survey error framework Presents extensive and up-to-date references throughout the book Written for students and academic survey researchers and market researchers engaged in comparative projects, this text represents a unique collaboration that features the latest methodologies and research on global comparative surveys.