Measurement invariance is usually tested using Multigroup Confirmatory Factor Analysis, which examines the change in the goodness-of-fit index (GFI) when cross-group constraints are imposed on a measurement model. Although many studies have examined the properties of GFI as indicators of overall model fit for single-group data, there have been none to date that examine how GFIs change when between-group constraints are added to a measurement model. The lack of a consensus about what constitutes significant GFI differences places limits on measurement invariance testing. We examine 20 GFIs based on the minimum fit function. A simulation under the two-group situation was used to examine changes in the GFIs (ΔGFIs) when invariance constraints were added. Based on the results, we recommend using Δcomparative fit index, ΔGamma hat, and ΔMcDonald's Noncentrality Index to evaluate measurement invariance. These three ΔGFIs are independent of both model complexity and sample size, and are not correlated with the o...

Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance

Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.

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Missing data: Our view of the state of the art.

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Two Monte Carlo studies were conducted to examine the sensitivity of goodness of fit indexes to lack of measurement invariance at 3 commonly tested levels: factor loadings, intercepts, and residual variances. Standardized root mean square residual (SRMR) appears to be more sensitive to lack of invariance in factor loadings than in intercepts or residual variances. Comparative fit index (CFI) and root mean square error of approximation (RMSEA) appear to be equally sensitive to all 3 types of lack of invariance. The most intriguing finding is that changes in fit statistics are affected by the interaction between the pattern of invariance and the proportion of invariant items: when the pattern of lack of invariance is uniform, the relation is nonmonotonic, whereas when the pattern of lack of invariance is mixed, the relation is monotonic. Unequal sample sizes affect changes across all 3 levels of invariance: Changes are bigger when sample sizes are equal rather than when they are unequal. Cutoff points for t...

Sensitivity of Goodness of Fit Indexes to Lack of Measurement Invariance

The establishment of measurement invariance across groups is a logical prerequisite to conducting substantive cross-group comparisons (e.g., tests of group mean differences, invariance of structura...

A Review and Synthesis of the Measurement Invariance Literature: Suggestions, Practices, and Recommendations for Organizational Research

A Psychotelemetry Experiment in Fluid Intelligence

John Leonard Horn was born in St. Joseph, Missouri, on September 7, 1928, and he died in Los Angeles, California, on August 18, 2006. John Horn was a world-renowned scholar of immense intellect, and he was highly respected in his time. I believe his major contributions to psychology, as well as his influence on psychologists, will continue to grow. His challenging factor-analytic methods of the 1960s, the important methodological debates of the 1970s and 1980s, and his continuing resistance to faddish trends in psychological research all represent fundamental contributions. Through his research and teaching he forced people to question popular assumptions and to evaluate all the data available. He challenged us to think longer, harder, and better. His work will continue to inspire important research in the fields of multivariate analysis and human cognitive abilities for many decades to come.

John L. Horn (1928-2006).

Human beings are dynamic organisms. We exist in time and space and change in many ways in space-time. Questions about these changes represent some of the most important questions in obesity research. We ask questions about what changes occur, such as, “How variable are people’s weights over time?” We ask questions about the causes of changes, such as, “What factors cause people’s weights to vary over time?” We ask questions about the effects of these changes, such as, “How do changes in weight affect longevity?”

Regression Change Models with Incomplete Repeated Measures Data in Obesity Research

Predicting Mortality from Demographics and Speciﬁc Cognitive Abilities in the Hawaii Family Study of Cognition

The goal of genetic research on behavior is to understand how genetic variation influences behavioral variation. Multiple methods have been used, from genetic influences inferred from familial resemblance to measured genes using molecular genetic methods. In this article, first, we discuss some historical background in genetic studies of behavior. Second, we focus on contemporary issues in the study of gene structure and function, emphasizing the methodological unity of most approaches. Contemporary issues include (1) measuring variation, (2) experimental methods, and (3) statistical methods. Finally, we discuss methodological challenges likely to continue in future genetic studies of behavior.

John J. McArdle

Papers

A Psychotelemetry Experiment in Fluid Intelligence

John L. Horn (1928-2006).

Regression Change Models with Incomplete Repeated Measures Data in Obesity Research

Predicting Mortality from Demographics and Speciﬁc Cognitive Abilities in the Hawaii Family Study of Cognition

Genetic Studies of Behavior: Methodology