The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities.

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model, nonnormal continuous measures, and nonlinear relationships among observed and/or latent variables. When the objective of a SEMM analysis is the identification of latent classes, these conditions should be considered as alternative hypotheses and results should be interpreted cautiously. However, armed with greater knowledge about the estimation of SEMMs in practice, researchers can exploit the flexibility of the model to gain a fuller understanding of the phenomenon under study. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The Use of Latent Trajectory Models in Psychopathology Research.

Despite the recent surge in the development of powerful modeling strategies to test questions about individual differences in stability and change over time, these methods are not currently widely used in psychopathology research. In an attempt to further the dissemination of these new methods, the authors present a pedagogical introduction to the structural equation modeling based latent trajectory model, or LTM. They review several different types of LTMs, discuss matching an optimal LTM to a given question of interest, and highlight several issues that might be particularly salient for research in psychopathology. The authors augment each section with a review of published applications of these methods in psychopathology-related research to demonstrate the implementation and interpretation of LTMs in practice. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Structural Equation Models for Interchangeable Dyads: Being the Same Makes a Difference.

Structural equation modeling (SEM) offers a flexible method for studying the patterns of interdependence in partners' behavior, which lie at the heart of interactions and relationships. Although SEM has been applied to the study of distinguishable dyads, in which partners are distinguishable by type, such as male and female, it has rarely been applied to the study of interchangeable dyads, such as male-male or female-female pairs. The authors integrate a wide range of dyadic interdependence models--including actor-partner interdependence models, mutual-influence models, and common-fate or dyadic personality models--into an SEM framework for use with interchangeable dyads. The authors also address the use of latent variables at both the dyadic and individual levels, whereby substantive relationships in these models can be corrected for errors of measurement. Furthermore, the authors discuss the conceptual underpinnings of dyadic models and give examples of their application. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Distributional Assumptions of Growth Mixture Models: Implications for Overextraction of Latent Trajectory Classes.

Growth mixture models are often used to determine if subgroups exist within the population that follow qualitatively distinct developmental trajectories. However, statistical theory developed for finite normal mixture models suggests that latent trajectory classes can be estimated even in the absence of population heterogeneity if the distribution of the repeated measures is nonnormal. By drawing on this theory, this article demonstrates that multiple trajectory classes can be estimated and appear optimal for nonnormal data even when only 1 group exists in the population. Further, the within-class parameter estimates obtained from these models are largely uninterpretable. Significant predictive relationships may be obscured or spurious relationships identified. The implications of these results for applied research are highlighted, and future directions for quantitative developments are suggested. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Latent variable analyses of age trends of cognition in the Health and Retirement Study, 1992-2004.

The present study was conducted to better describe age trends in cognition among older adults in the longitudinal Health and Retirement Study (HRS) from 1992 to 2004 (N = 17,000). The authors used contemporary latent variable models to organize this information in terms of both cross-sectional and longitudinal inferences about age and cognition. Common factor analysis results yielded evidence for at least 2 common factors, labeled Episodic Memory and Mental Status, largely separable from vocabulary. Latent path models with these common factors were based on demographic characteristics. Multilevel models of factorial invariance over age indicated that at least 2 common factors were needed. Latent curve models of episodic memory were based on age at testing and showed substantial age differences and age changes, including impacts due to retesting as well as several time-invariant and time-varying predictors. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing Mediational Models With Longitudinal Data: Questions and Tips in the Use of Structural Equation Modeling.

R. M. Baron and D. A. Kenny (1986; see record 1987-13085-001) provided clarion conceptual and methodological guidelines for testing mediational models with cross-sectional data. Graduating from cross-sectional to longitudinal designs enables researchers to make more rigorous inferences about the causal relations implied by such models. In this transition, misconceptions and erroneous assumptions are the norm. First, we describe some of the questions that arise (and misconceptions that sometimes emerge) in longitudinal tests of mediational models. We also provide a collection of tips for structural equation modeling (SEM) of mediational processes. Finally, we suggest a series of 5 steps when using SEM to test mediational processes in longitudinal designs: testing the measurement model, testing for added components, testing for omitted paths, testing the stationarity assumption, and estimating the mediational effects. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Structural Equation Modeling of Paired-Comparison and Ranking Data.

L. L. Thurstone's (1927) model provides a powerful framework for modeling individual differences in choice behavior. An overview of Thurstonian models for comparative data is provided, including the classical Case V and Case III models as well as more general choice models with unrestricted and factor-analytic covariance structures. A flow chart summarizes the model selection process. The authors show how to embed these models within a more familiar structural equation modeling (SEM) framework. The different special cases of Thurstone's model can be estimated with a popular SEM statistical package, including factor analysis models for paired comparisons and rankings. Only minor modifications are needed to accommodate both types of data. As a result, complex models for comparative judgments can be both estimated and tested efficiently. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Decomposing Person and Occasion-Specific Effects: An Extension of Latent State-Trait (LSI) Theory to Hierarchical LST Models.

An extension of latent state-trait (LST) theory to hierarchical LST models is presented. In hierarchical LST models, the covariances between 2 or more latent traits are explained by a general 3rd-order factor, and the covariances between latent state residuals pertaining to different traits measured on the same measurement occasion are explained by 2nd-order latent occasion-specific factors. Analogous to recent developments in multitrait-multimethod methodology, all factors are interpreted in relation to factors taken as comparison standards. An empirical example from test anxiety research illustrates how estimates of additive variance components due to general trait, specific trait, occasion, state residual, method, and measurement error can be obtained using confirmatory factor analysis. Advantages and limitations of these models are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Group Climate, Cohesion, Alliance, and Empathy in Group Psychotherapy: Multilevel Structural Equation Models.

This study examined the definitional and statistical overlap among 4 key group therapeutic relationship constructs--group climate, cohesion, alliance, and empathy--across member-member, member-group, and member-leader relationships. Three multilevel structural equation models were tested using self-report measures completed by 662 participants from 111 counseling center and personal growth groups. As hypothesized, almost all measures of therapeutic relationship were significantly correlated. Hypothesized 1-factor, 2-factor (Working and Bonding factors), and 3-factor (Member, Leader, and Group factors) models did not fit the data adequately. An exploratory model with Bonding, Working, and Negative factors provided the best fit to the data. Group members distinguished among relationships primarily according to relationship quality rather than the status or role of others (i.e., leader, member, or whole group). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multilevel Modeling of Two Cyclical Processes: Extending Differential Structural Equation Modeling to Nonlinear Coupled Systems.

The authors present a dynamical multilevel model that captures changes over time in the bidirectional, potentially asymmetric influence of 2 cyclical processes. S. M. Boker and J. Graham's (1998) differential structural equation modeling approach was expanded to the case of a nonlinear coupled oscillator that is common in bimanual coordination studies in which participants swing hand-held pendulums but is also applicable to social systems in general. The authors' nonlinear coupled oscillator model decomposed the fluctuations into a competitive component, unique to each individual variable, and a cooperative component that captured bidirectional influence. The authors' model also generated an index of the symmetry/asymmetry of bidirectional influence. Together, the models are useful quantitative tools for the study of interacting, changing processes. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The Persistence of Underpowered Studies in Psychological Research: Causes, Consequences, and Remedies.

Underpowered studies persist in the psychological literature. This article examines reasons for their persistence and the effects on efforts to create a cumulative science. The "curse of multiplicities" plays a central role in the presentation. Most psychologists realize that testing multiple hypotheses in a single study affects the Type I error rate, but corresponding implications for power have largely been ignored. The presence of multiple hypothesis tests leads to 3 different conceptualizations of power. Implications of these 3 conceptualizations are discussed from the perspective of the individual researcher and from the perspective of developing a coherent literature. Supplementing significance tests with effect size measures and confidence intervals is shown to address some but not necessarily all problems associated with multiple testing. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing for Suspected Impairments and Dissociations in Single-Case Studies in Neuropsychology: Evaluation of Alternatives Using Monte Carlo Simulations and Revised Tests for Dissociations.

In neuropsychological single-case studies, a patient is compared with a small control sample. Methods of testing for a deficit on Task X, or a significant difference between Tasks X and Y, either treat the control sample statistics as parameters (using z and zD) or use modified t tests. Monte Carlo simulations demonstrated that if z is used to test for a deficit, the Type I error rate is high for small control samples, whereas control of the error rate is essentially perfect for a modified t test. Simulations on tests for differences revealed that error rates were very high for zD. A new method of testing for a difference (the revised standardized difference test) achieved good control of the error rate, even with very small sample sizes. A computer program that implements this new test (and applies criteria to test for classical and strong dissociations) is made available. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Analyzing true change in longitudinal multitrait-multimethod studies: Application of a multimethod change model to depression and anxiety in children.

The authors show how structural equation modeling can be applied to analyze change in longitudinal multitrait-multimethod (MTMM) studies. For this purpose, an extension of latent difference models (McArdle, 1988; Steyer, Eid, & Schwenkmezger, 1997) to multiple constructs and multiple methods is presented. The model allows investigators to separate true change from measurement error and to analyze change simultaneously for different methods. The authors also show how Campbell and Fiske’s (1959) guidelines for analyzing convergent and discriminant validity can be applied to the measurement of latent change. The practical application of the multimethod change model is illustrated in a reanalysis of child depression and anxiety scores (N = 906 American children) that were assessed by self- and parent reports on three measurement occasions. The analyses revealed that (a) the convergent validity of change was low for both constructs and (b) sex was a significant predictor of self-reported, but not of parent reported, anxiety states. Finally, the authors discuss advantages and limitations and compare the model with other approaches for analyzing longitudinal MTMM data. (PsycINFO Database Record (c) 2010 APA, all rights reserved)