Executive function in older adults: A structural equation modeling approach.

Confirmatory factor analysis (CFA) and structural equation modeling (SEM) were used to study the organization of executive functions in older adults. The four primary goals were to examine (a) whether executive functions were supported by one versus multiple underlying factors, (b) which underlying skill(s) predicted performance on complex executive function tasks, (c) whether performance on analogous verbal and nonverbal tasks was supported by separable underlying skills, and (d) how patterns of performance generally compared with those of young adults. A sample of 100 older adults completed 10 tasks, each designed to engage one of three control processes: mental set shifting (Shifting), information updating or monitoring (Updating), and inhibition of prepotent responses (Inhibition). CFA identified robust Shifting and Updating factors, but the Inhibition factor failed to emerge, and there was no evidence for verbal and nonverbal factors. SEM showed that Updating was the best predictor of performance on each of the complex tasks the authors assessed (the Tower of Hanoi and the Wisconsin Card Sort). Results are discussed in terms of insight for theories of cognitive aging and executive function. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints.

The authors show how the use of inequality constraints on parameters in structural equation models may affect the distribution of the likelihood ratio test. Inequality constraints are implicitly used in the testing of commonly applied structural equation models, such as the common factor model, the autoregressive model, and the latent growth curve model, although this is not commonly acknowledged. Such constraints are the result of the null hypothesis in which the parameter value or values are placed on the boundary of the parameter space. For instance, this occurs in testing whether the variance of a growth parameter is significantly different from 0. It is shown that in these cases, the asymptotic distribution of the chi-square difference cannot be treated as that of a central chi-square-distributed random variable with degrees of freedom equal to the number of constraints. The correct distribution for testing 1 or a few parameters at a time is inferred for the 3 structural equation models mentioned above. Subsequently, the authors describe and illustrate the steps that one should take to obtain this distribution. An important message is that using the correct distribution may lead to appreciably greater statistical power. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On specifying the null model for incremental fit indices in structural equation modeling.

In structural equation modeling, incremental fit indices are based on the comparison of the fit of a substantive model to that of a null model. The standard null model yields unconstrained estimates of the variance (and mean, if included) of each manifest variable. For many models, however, the standard null model is an improper comparison model. In these cases, incremental fit index values reported automatically by structural modeling software have no interpretation and should be disregarded. The authors explain how to formulate an acceptable, modified null model, predict changes in fit index values accompanying its use, provide examples illustrating effects on fit index values when using such a model, and discuss implications for theory and practice of structural equation modeling. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Perceived coping as a mediator between attachment and psychological distress: A structural equation modeling approach.

This study examined perceived coping (perceived problem-solving ability and progress in coping with problems) as a mediator between adult attachment (anxiety and avoidance) and psychological distress (depression, hopelessness, anxiety, anger, and interpersonal problems). Survey data from 515 undergraduate students were analyzed using structural equation modeling. Results indicated that perceived coping fully mediated the relationship between attachment anxiety and psychological distress and partially mediated the relationship between attachment avoidance and psychological distress. These findings suggest not only that it is important to consider attachment anxiety or avoidance in understanding distress but also that perceived coping plays an important role in these relationships. Implications for these more complex relations are discussed for both counseling interventions and further research. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Mechanisms linking socioeconomic status to smoking cessation: A structural equation modeling approach.

Objective: Although there has been a socioeconomic gradient in smoking prevalence, cessation, and disease burden for decades, these disparities have become even more pronounced over time. The aim of the current study was to develop and test a conceptual model of the mechanisms linking socioeconomic status (SES) to smoking cessation. Design: The conceptual model was evaluated using a latent variable modeling approach in a sample of 424 smokers seeking treatment (34% African American; 33% Latino; 33% White). Hypothesized mechanisms included social support, neighborhood disadvantage, negative affect/stress, agency, and craving. Main Outcome Measure: The primary outcome was Week 4 smoking status. Results: As was hypothesized, SES had significant direct and indirect effects on cessation. Specifically, neighborhood disadvantage, social support, negative affect/stress, and agency mediated the relation between SES and smoking cessation. A multiple group analysis indicated that the model was a good fit across racial/ethnic groups. Conclusion: The present study yielded one of the more comprehensive models illuminating the specific mechanisms that link SES and smoking cessation. Policy, community, and individual-level interventions that target low SES smokers and address the specific pathways identified in the current model could potentially attenuate the impact of SES on cessation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Accuracy in parameter estimation for targeted effects in structural equation modeling: Sample size planning for narrow confidence intervals.

In addition to evaluating a structural equation model (SEM) as a whole, often the model parameters are of interest and confidence intervals for those parameters are formed. Given a model with a good overall fit, it is entirely possible for the targeted effects of interest to have very wide confidence intervals, thus giving little information about the magnitude of the population targeted effects. With the goal of obtaining sufficiently narrow confidence intervals for the model parameters of interest, sample size planning methods for SEM are developed from the accuracy in parameter estimation approach. One method plans for the sample size so that the expected confidence interval width is sufficiently narrow. An extended procedure ensures that the obtained confidence interval will be no wider than desired, with some specified degree of assurance. A Monte Carlo simulation study was conducted that verified the effectiveness of the procedures in realistic situations. The methods developed have been implemented in the MBESS package in R so that they can be easily applied by researchers. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

A structural equation model of expertise in college physics.

A model of expertise in physics was tested on a sample of 374 college students in 2 different level physics courses. Structural equation modeling was used to test hypothesized relationships among variables linked to expert performance in physics including strategy use, pictorial representation, categorization skills, and motivation, and these variables were examined for their influence on physics achievement. Gender was included in the model to examine how it influenced achievement indirectly through its influence on the other variables in the model. Two levels of expertise were examined by testing the model on trigonometry-based physics students and on more advanced, calculus-based physics students. Results were similar across both levels of expertise: For both courses, student motivation had a significant influence on students’ strategy use and categorization skills. Categorization skills, in turn, influenced student achievement directly, and indirectly, through strategy use. Strategy use had a significant influence on achievement. Pictorial representation played little role in the model. Gender contributed primarily through motivation, but for the more advanced level course it also directly predicted strategy use. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A new look at the big five factor structure through exploratory structural equation modeling.

NEO instruments are widely used to assess Big Five personality factors, but confirmatory factor analyses (CFAs) conducted at the item level do not support their a priori structure due, in part, to the overly restrictive CFA assumptions. We demonstrate that exploratory structural equation modeling (ESEM), an integration of CFA and exploratory factor analysis (EFA), overcomes these problems with responses (N = 3,390) to the 60-item NEO–Five-Factor Inventory: (a) ESEM fits the data better and results in substantially more differentiated (less correlated) factors than does CFA; (b) tests of gender invariance with the 13-model ESEM taxonomy of full measurement invariance of factor loadings, factor variances–covariances, item uniquenesses, correlated uniquenesses, item intercepts, differential item functioning, and latent means show that women score higher on all NEO Big Five factors; (c) longitudinal analyses support measurement invariance over time and the maturity principle (decreases in Neuroticism and increases in Agreeableness, Openness, and Conscientiousness). Using ESEM, we addressed substantively important questions with broad applicability to personality research that could not be appropriately addressed with the traditional approaches of either EFA or CFA. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An introduction to using structural equation models in rehabilitation psychology.

Objective: To provide an overview of structural equation modeling (SEM) using an example drawn from the rehabilitation psychology literature. Design: To illustrate the 5 steps in SEM (model specification, identification, estimation methods, interpretation of results, and model modification), an example is presented, with details on determining whether alternative models result in a significant improvement to fit to the observed data. Data are from a sample of 274 people with spinal cord injury. Issues commonly encountered in preparing data for SEM analyses (e.g., missing data, nonnormality) are reviewed, as is the debate surrounding some aspects of SEM (e.g., acceptable sample size). Conclusion: SEM can be a powerful procedure for empirically representing complex and sophisticated theoretical models of interest to rehabilitation psychologists. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Factors affecting depression among people with chronic musculoskeletal pain: A structural equation model.

Objective: To adapt and test P. M. Lewinsohn, H. M. Hoberman, L. Teri, and M. Hautzinger's (1985) integrative model of depression for individuals with chronic musculoskeletal pain. Design: Structural equation modeling. Participants: Individuals with chronic pain (N = 171), recruited from 6 outpatient rehabilitation facilities in Canada. Outcome Measures: Two measures of the latent variable, depression (the Center for Epidemiologic Studies-Depression Scale and the Zung Self-Rating Depression Scale), along with multiple measures of each of 5 latent predictors (pain, interferences, stress, coping, and social and family support) and 2 measured predictors (preinjury psychopathology and catastrophizing). Results: The normed fit index, comparative fit index, and parsimony ratio indicated an adequate fit for the model, suggesting that stress, perceived severity of pain, activity interferences, and catastrophizing contributed to increased depression (vulnerabilities), whereas pain coping skills and social and family support contributed to decreased depression (immunities). Conclusions: Empirical support was found for the proposed model of depression for people with chronic musculoskeletal pain, and the model appears to provide useful information for clinical rehabilitation interventions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

When constraints interact: A caution about reference variables, identification constraints and scale dependencies in structural equation modeling.

In traditional approaches to structural equations modeling, variances of latent endogenous variables cannot be specified or constrained directly and, consequently, are not identified, unless certain precautions are taken. The usual method for achieving identification has been to fix one factor loading for each endogenous latent variable at unity. An alternative approach is to fix variances using newer constrained estimation algorithms. This article examines the philosophy behind such constraints and shows how their appropriate use is neither as straightforward nor as noncontroversial as portrayed in textbooks and computer manuals. The constraints on latent variable variances can interact with other model constraints to interfere with the testing of certain kinds of hypotheses and can yield incorrect standardized solutions with some popular software. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Structural equation modeling of multitrait-multimethod data: Different models for different types of methods.

The question as to which structural equation model should be selected when multitrait-multimethod (MTMM) data are analyzed is of interest to many researchers. In the past, attempts to find a well-fitting model have often been data-driven and highly arbitrary. In the present article, the authors argue that the measurement design (type of methods used) should guide the choice of the statistical model to analyze the data. In this respect, the authors distinguish between (a) interchangeable methods, (b) structurally different methods, and (c) the combination of both kinds of methods. The authors present an appropriate model for each type of method. All models allow separating measurement error from trait influences and trait-specific method effects. With respect to interchangeable methods, a multilevel confirmatory factor model is presented. For structurally different methods, the correlated trait-correlated (method-1) model is recommended. Finally, the authors demonstrate how to appropriately analyze data from MTMM designs that simultaneously use interchangeable and structurally different methods. All models are applied to empirical data to illustrate their proper use. Some implications and guidelines for modeling MTMM data are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The mediating effects of job satisfaction and propensity to leave on role stress-job performance relationships: Combining meta-analysis and structural equation modeling.

This article combines meta-analysis with structural equation modeling to compare alternative models of the relationships among work stress, psychological mediators, and job performance. Specifically, the authors examined the mediating effects of job satisfaction and propensity to leave and their effect on the relationships between role ambiguity, role conflict, and job performance. The meta-analysis included both published and unpublished studies conducted over a period of 25 years, resulting in 113 independent samples with more than 22,000 individuals. As hypothesized, the structural model that best fit the meta-analytic estimates was the partial mediation model, in which stress is related to job performance both directly and indirectly through job satisfaction and propensity to leave and in which all path coefficients were reliably different from zero. The results are discussed in terms of theoretical contributions and implications for future stress-performance research. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Construct validity of the multidimensional structure of bullying and victimization: An application of exploratory structural equation modeling.

Existing research posits multiple dimensions of bullying and victimization but has not identified well-differentiated facets of these constructs that meet standards of good measurement: goodness of fit, measurement invariance, lack of differential item functioning, and well-differentiated factors that are not so highly correlated as to detract from their discriminant validity and substantive usefulness in school settings. Here we demonstrate exploratory structural equation modeling, an integration of confirmatory factor analysis and exploratory factor analysis. On the basis of responses to the 6-factor Adolescent Peer Relations Instrument (verbal, social, physical facets of bullying and victimization), we tested invariance of factor loadings, factor variances–covariances, item uniquenesses, item intercepts (a lack of differential item functioning), and latent means across gender, year in school, and time. Using a combination of relations with student characteristics and a multitrait–multimethod analysis, we showed that the 6 bully/victim factors have discriminant validity over time and in relation to gender, year in school, and relevant psychosocial correlates (e.g., depression, 11 components of academic and nonacademic self-concept, locus of control, attitudes toward bullies and victims). However, bullies and victims are similar in many ways, and longitudinal panel models of the positive correlations between bully and victim factors suggest reciprocal effects such that each is a cause and an effect of the other. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Fitting data to model: Structural equation modeling diagnosis using two scatter plots.

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts the residual-based M-distance with the quantile of a chi distribution. It allows the researcher to visually identify clusters of potential outliers. The article further studies the effect of the potential outliers on the overall model evaluation when they are removed according to the order of the clusters exhibited in the plot. Suggestions are provided on determining the outlier status of outstanding cases in real data analysis. Recommendations are also made on the choice of robust methods and maximum likelihood following outlier removal. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Principles and practice in reporting structural equation analyses.

Principles for reporting analyses using structural equation modeling are reviewed, with the goal of supplying readers with complete and accurate information. It is recommended that every report give a detailed justification of the model used, along with plausible alternatives and an account of identifiability. Nonnormality and missing data problems should also be addressed. A complete set of parameters and their standard errors is desirable, and it will often be convenient to supply the correlation matrix and discrepancies, as well as goodness-of-fit indices, so that readers can exercise independent critical judgment. A survey of fairly representative studies compares recent practice with the principles of reporting recommended here. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Structural equation modeling with interchangeable dyads.

Structural equation modeling (SEM) can be adapted in a relatively straightforward fashion to analyze data from interchangeable dyads (i.e., dyads in which the 2 members cannot be differentiated). The authors describe a general strategy for SEM model estimation, comparison, and fit assessment that can be used with either dyad-level or pairwise (double-entered) dyadic data. They present applications illustrating this approach with the actor-partner interdependence model, confirmatory factor analysis, and latent growth curve analysis. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A model for integrating fixed-, random-, and mixed-effects meta-analyses into structural equation modeling.

Meta-analysis and structural equation modeling (SEM) are two important statistical methods in the behavioral, social, and medical sciences. They are generally treated as two unrelated topics in the literature. The present article proposes a model to integrate fixed-, random-, and mixed-effects meta-analyses into the SEM framework. By applying an appropriate transformation on the data, studies in a meta-analysis can be analyzed as subjects in a structural equation model. This article also highlights some practical benefits of using the SEM approach to conduct a meta-analysis. Specifically, the SEM-based meta-analysis can be used to handle missing covariates, to quantify the heterogeneity of effect sizes, and to address the heterogeneity of effect sizes with mixture models. Examples are used to illustrate the equivalence between the conventional meta-analysis and the SEM-based meta-analysis. Future directions on and issues related to the SEM-based meta-analysis are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Attitudes "cause" behaviors: A structural equation analysis.

Confirmatory maximum likelihood estimation of linear structural equation models with latent variables was employed to evaluate the causal predominance of attitudes over behaviors. Two wave, 2 variable (2W2V) crosslagged structural models were developed using attitude and behavior panel data from 158 college students on studying, exercise, and dating. Additional causal factors that have been shown to have predictive utility in the context of attitude and behavior models were added to the 2W2V models to determine the impact of the specification of other relevant factors on the cross-lag parameter estimates. Although attitudes consistently had a significant direct effort on subsequent behavior in the 2W2V models, this pattern did not hold in the expanded models. Results suggest that the specification of added factors clarifies the direct as well as indirect impact of attitudes on behavior for varying content domains and enables a more complete assessment of the generality of the nature of attitude–behavior relations. (32 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)