Estimating, testing, and comparing specific effects in structural equation models: the phantom model approach

The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main model. The following favorable features characterize the method: (a) It enables the estimation, testing, and comparison of arbitrary specific effects for recursive and nonrecursive models with latent and manifest variables; (b) it enables the bootstrapping of confidence intervals; and (c) it can be applied with all standard SEM programs permitting latent variables, the specification of equality constraints, and the bootstrapping of total effects. These features along with the fact that no manipulation of matrices and formulas is required make the approach particularly suitable for applied researchers. The method is illustrated by means of 3 examples with real data sets.     

Structural equation modeling: reviewing the basics and moving forward

This tutorial begins with an overview of structural equation modeling (SEM) that includes the purpose and goals of the statistical analysis as well as terminology unique to this technique. I will focus on confirmatory factor analysis (CFA), a special type of SEM. After a general introduction, CFA is differentiated from exploratory factor analysis (EFA), and the advantages of CFA techniques are discussed. Following a brief overview, the process of modeling will be discussed and illustrated with an example using data from a HIV risk behavior evaluation of homeless adults (Stein & Nyamathi, 2000). Techniques for analysis of nonnormally distributed data as well as strategies for model modification are shown. The empirical example examines the structure of drug and alcohol use problem scales. Although these scales are not specific personality constructs, the concepts illustrated in this article directly correspond to those found when analyzing personality scales and inventories. Computer program syntax and output for the empirical example from a popular SEM program (EQS 6.1; Bentler, 2001) are included.     

Hopes and cautions in implementing Bayesian structural equation modeling

Muthén and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero in a conventional model can be respecified using small-variance priors and (b) implementing their approach in software that is widely accessible. We recognize potential benefits for applied researchers as discussed by Muthén and Asparouhov, and we also see a tradeoff in that effective use of the proposed approach introduces increased demands in terms of expertise of users to navigate new complexities in model specification, parameter estimation, and evaluation of results. We also raise cautions regarding the issues of model modification and model fit. Although we see significant potential value in the use of Bayesian SEM, we also believe that effective use will require an awareness of these complexities. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Irritability and parenting practices as mediational variables between temperament and affective,anxiety, and oppositional defiant problems

Irritability and parenting are potential targets for transdiagnostic studies to identify the common and core dysfunctional characteristics underlying several diagnostic pictures with the goal of addressing these issues in treatment. Our objective was to investigate the different paths from temperament to child psychopathology (affective, anxiety, and oppositional problems) through irritability and parenting using a prospective design from ages 3 to 7. A sample of 614 3-year-old preschoolers was followed at ages 4, 6, and 7. Parents answered questionnaires about temperament (age 3), irritability (age 4), parenting practices (age 6), and psychopathology (age 7). Statistical analyses were carried out through structural equation modeling (SEM) to test the mediation effect of irritability and parenting practices from temperament (negative affectivity and effortful control) through to affective, anxious, and oppositional problems. The proposed model fit the data well. SEM showed (a) an indirect effect from temperament to affective problems, via irritability and positive parenting; (b) a direct effect from negative affectivity to anxiety, plus an indirect effect from both temperament dimensions, via irritability and autonomy parenting practices; and (c) an indirect effect from temperament to oppositional problems, via irritability and punitive parenting. Irritability and parenting are transdiagnostic mediational variables that should be focused on in intervention programs for affective, anxiety, and oppositional problems.     

Confirmatory Factor Analysis (CFA), Exploratory Structural Equation Modeling (ESEM), and Set-ESEM: Optimal Balance Between Goodness of Fit and Parsimony

Abstract

CFAs of multidimensional constructs often fail to meet standards of good measurement (e.g., goodness-of-fit, measurement invariance, and well-differentiated factors). Exploratory structural equation modeling (ESEM) represents a compromise between exploratory factor analysis’ (EFA) flexibility, and CFA/SEM’s rigor and parsimony, but lacks parsimony (particularly in large models) and might confound constructs that need to be kept separate. In Set-ESEM, two or more a priori sets of constructs are modeled within a single model such that cross-loadings are permissible within the same set of factors (as in Full-ESEM) but are constrained to be zero for factors in different sets (as in CFA). The different sets can reflect the same set of constructs on multiple occasions, and/or different constructs measured within the same wave. Hence, Set-ESEM that represents a middle-ground between the flexibility of traditional-ESEM (hereafter referred to as Full-ESEM) and the rigor and parsimony of CFA/SEM. Thus, the purposes of this article are to provide an overview tutorial on Set-ESEM, juxtapose it with Full-ESEM, and to illustrate its application with simulated data and diverse “real” data applications with accessible, heuristic explanations of best practice.     

Testing the Factor Structure and Measurement Invariance Across Gender of the Big Five Inventory Through Exploratory Structural Equation Modeling

Confirmatory factor analyses (CFAs) typically fail to support the a priori 5-factor structure of Big Five self-report instruments, due in part to the overly restrictive CFA assumptions. We show that exploratory structural equation modeling (ESEM), an integration of CFA and exploratory factor analysis, overcomes these problems in relation to responses to the 44-item Big Five Inventory (BFI) administered to a large Italian community sample. ESEM fitted the data better and resulted in less correlated factors than CFA, although ESEM and CFA factor scores correlated at near unity with observed raw scores. Tests of gender invariance with a 13-model taxonomy of full measurement invariance showed that the factor structure of the BFI is gender-invariant and that women score higher on Neuroticism, Agreeableness, Extraversion, and Conscientiousness. Through ESEM one could address substantively important issues about BFI psychometric properties that could not be appropriately addressed through traditional approaches.     

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.     

Comparing standardized coefficients in structural equation modeling: a model reparameterization approach

We propose a two-stage method for comparing standardized coefficients in structural equation modeling (SEM). At stage 1, we transform the original model of interest into the standardized model by model reparameterization, so that the model parameters appearing in the standardized model are equivalent to the standardized parameters of the original model. At stage 2, we impose appropriate linear equality constraints on the standardized model and use a likelihood ratio test to make statistical inferences about the equality of standardized coefficients. Unlike other existing methods for comparing standardized coefficients, the proposed method does not require specific modeling features (e.g., specification of nonlinear constraints), which are available only in certain SEM software programs. Moreover, this method allows researchers to compare two or more standardized coefficients simultaneously in a standard and convenient way. Three real examples are given to illustrate the proposed method, using EQS, a popular SEM software program. Results show that the proposed method performs satisfactorily for testing the equality of standardized coefficients.     

A tutorial on hierarchically structured constructs

Many psychological constructs are conceived to be hierarchically structured and thus to operate at various levels of generality. Alternative confirmatory factor analytic (CFA) models can be used to study various aspects of this proposition: (a) The one-factor model focuses on the top of the hierarchy and contains only a general construct, (b) the first-order factor model focuses on the intermediate level of the hierarchy and contains only specific constructs, and both (c) the higher order factor model and (d) the nested-factor model consider the hierarchy in its entirety and contain both general and specific constructs (e.g., bifactor model). This tutorial considers these CFA models in depth, addressing their psychometric properties, interpretation of general and specific constructs, and implications for model-based score reliabilities. The authors illustrate their arguments with normative data obtained for the Wechsler Adult Intelligence Scale and conclude with recommendations on which CFA model is most appropriate for which research and diagnostic purposes.     

Concern for Appropriateness Scale and Behavioral Conformity

The validity of the Concern for Appropriateness Scale (CFA; Lennox & Wolfe, 1984) as a measure of tendencies to conform to group conformity pressures was investigated. Thirty-four high and 28 low scorers on the CFA were placed in a conformity situation designed to modify previously expressed values. Pressures to conform were exerted on four critical questions that had been identified by subjects as either personally important or unimportant. A repeated measures analysis of variance (ANOVA) revealed statistically significant effects for concern and personal importance, as well as the interaction of both. Subjects scoring low on the CFA showed, little conformity regardless of value importance, whereas those scoring high on the CFA conformed more overall, and much more on unimportant than important issues. Results confirm that the CFA assesses individual differences in susceptibility to peer pressure.     

Validating the Ohio Scales in a Juvenile Justice Sample of Youth with Behavioral Health Issues

Between 65 and 75 % of juvenile-justice involved (JJI) youth present with at least one behavioral health disorder. Many communities have developed diversion programs that provide behavioral health services to JJI youth, often in lieu of detention. A key component of successful diversion programming is accurate screening and assessment. The Ohio Scales, a validated instrument designed to track service effectiveness in clinical samples of youth, are now being used with juvenile justice populations. The purpose of this study is to validate the Ohio Scales in a JJI youth population (N = 2246). The population (ages 12–18) is derived from Ohio’s Behavioral Health Juvenile Justice Initiative, a diversion program for JJI youth with behavioral health issues. We conducted Confirmatory Factor Analyses (CFA) on all forms of the Ohio Scales (parent, youth and worker) to measure fit for one factor, four factor and four factor second order solutions. We also conducted an Exploratory Factor Analysis (EFA) on the Problem Severity factor in the youth form to determine the number of appropriate sub-factors. The EFA indicated that the Problem Severity factor should be broken into three hypothesized sub-factors: Externalizing, Internalizing and Delinquency. The CFA confirmed this solution. CFA results indicated the four factor second order solution fits superior to the other two solutions. Using the Ohio Scales Problem Severity measure as a three sub-factor measure may increase clinical applicability by allowing a clinician to specifically measure and target externalizing or internalizing issues during treatment.     

Temporal patterns of variable relationships in person-oriented research: longitudinal models of configural frequency analysis

This article reviews the premises of configural frequency analysis (CFA), including methods of choosing significance tests and base models, as well as protecting alpha, and discusses why CFA is a useful approach when conducting longitudinal person-oriented research. CFA operates at the manifest variable level. Longitudinal CFA seeks to identify those temporal patterns that stand out as more frequent (CFA types) or less frequent (CFA antitypes) than expected with reference to a base model. A base model that has been used frequently in CFA applications, prediction CFA, and a new base model, auto-association CFA, are discussed for analysis of cross-classifications of longitudinal data. The former base model takes the associations among predictors and among criteria into account. The latter takes the auto-associations among repeatedly observed variables into account. Application examples of each are given using data from a longitudinal study of domestic violence. It is demonstrated that CFA results are not redundant with results from log-linear modeling or multinomial regression and that, of these approaches, CFA shows particular utility when conducting person-oriented research.     

Anger toward God: social-cognitive predictors, prevalence, and links with adjustment to bereavement and cancer

A recent model of collective action distinguishes 2 distinct pathways: an emotional pathway whereby anger in response to injustice motivates action and an efficacy pathway where the belief that issues can be solved collectively increases the likelihood that group members take action (van Zomeren, Spears, Fischer, & Leach, 2004). Research supporting this model has, however, focused entirely on relatively normative actions such as participating in demonstrations. We argue that the relations between emotions, efficacy, and action differ for more extreme, nonnormative actions and propose (a) that nonnormative actions are often driven by a sense of low efficacy and (b) that contempt, which, unlike anger, entails psychological distancing and a lack of reconciliatory intentions, predicts nonnormative action. These ideas were tested in 3 survey studies examining student protests against tuition fees in Germany (N = 332), Indian Muslims' action support in relation to ingroup disadvantage (N = 156), and British Muslims' responses to British foreign policy (N = 466). Results were generally supportive of predictions and indicated that (a) anger was strongly related to normative action but overall unrelated or less strongly related to nonnormative action, (b) contempt was either unrelated or negatively related to normative action but significantly positively predicted nonnormative action, and (c) efficacy was positively related to normative action and negatively related to nonnormative action. The implications of these findings for understanding and dealing with extreme intergroup phenomena such as terrorism are discussed.     

Examination of the Sociocultural Attitudes Towards Appearance Questionnaire-3 in a mixed-gender young-adolescent sample

Thin-ideal (or media) internalization is an important eating disorder risk factor that has become a central target of many prevention programs. However, evidence for its valid assessment in young, mixed-gender, adolescent samples is limited, and the current study is the first to explore the psychometric properties of the 30-item Sociocultural Attitudes Towards Appearance Questionnaire-3 (SATAQ-3; J. Thompson, P. van den Berg, M. Roehrig, A. S. Guarda, & L. J. Heinberg, 2004) in a nonadult community sample. Two samples of Grade 8 students (M age = 13.68 years), totaling 680 girls (N = 332) and boys (N = 348) completed the SATAQ-3 and other measures, whereas a smaller sample (N = 123) of Grade 10 girls (M age = 15.01 years) served as a comparison group for supplementary analyses. Principal component analyses (PCA) with data from Sample 1 (N = 201) revealed 4 factors with eigenvalues > 1.0, similar to the original authors' structure but with some cross-loading occurring between the Pressures and Internalization-General scales. Confirmatory factor analyses (CFA) were conducted with data from Sample 2 (N = 479) on the factor solution found in the PCA. The model did not fit well, leading to further revisions based on removal of cross-loading items and CFA modification indices, resulting in a 19-item, 4-factor solution with acceptable fit. Examinations of validity and reliability were generally acceptable. The overall findings suggest that an abbreviated version of the SATAQ-3 might be more appropriate than the original version with young-adolescent, mixed-gender audiences. Further examinations of the psychometric properties of the SATAQ-3 with this demographic are indicated.     

The longitudinal study of personality disorders: history, design considerations, and initial findings

The Longitudinal Study of Personality Disorders (LSPD) began in 1990 and it is the first NIMH-funded prospective multiwave longitudinal study of all DSM-defined personality disorders (PDs). The LSPD, now in its 16th year, has focused on several major issues including: (a) the epidemiology of the PDs; (b) the stability of individual differences and mean levels of PD features over time; (c); patterns of individual growth in PD features over time; (d) the development of a neurobehavioral model that links personality and personality disorder; (e) specification of those neurobehavioral systems predicting change in borderline personality disorder; and (f) illumination of simultaneous growth processes in neurobehavioral systems and PD. The LSPD possesses a number of methodological enhancements designed to increase the validity of the longitudinal findings such as a prospective multiwave design, use of a validated structured interview and well-known self-report instrument for Axis II assessments, double measurement of all major constructs under study, use of blinded interviewers for all interview Axis II assessments, and use of a community sample. The history and context in which the LSPD was developed is reviewed, methodological issues related to the study of PDs are discussed, primary LSPD findings to date are summarized, and future directions of the LSPD are introduced.     

The Factor Structure and Measurement Invariance of the Daily Spiritual Experiences Scale

The current study has two main goals: (a) to identify a factor structure of the Daily Spiritual Experiences Scale (DSES) on a large archival data, collected from 1,325 adults in the United States (709 women, 616 men) by the U.S. General Social Survey in 2004 and (b) to examine the measurement invariance of the 16 DSES items between women and men in the same data to see whether any of the items are favoring or biased toward either women or men. The one-factor confirmatory factor analysis (CFA) model fit our data better than the two-factor CFA models because of high correlations between the two factors (r > .90). The fit of the one-factor CFA to our sample data was improved when we specified seven correlated residuals suggested by overlapping item content and large modification indices. The ensuing measurement invariance testing of the one-factor CFA model with seven correlated residuals supported full measurement invariance of factor loadings, thresholds, and residual variances, as well as factor variances between the women and the men. Yet the factor mean for the women was .841 units (Cohen’s d = .496) higher than it was for the men, indicating that higher levels of daily spiritual experiences for women reported in gender comparison studies in the United States are not likely to be an artifact of bias in the questionnaire.     

The Value of Exploratory Structural Equation Modeling in Identifying Factor Overlap in the Mental Health Continuum-Short Form (MHC-SF): A Study with a New Zealand Sample

This study is the first to investigate the factor structure of the Mental Health Continuum-Short Form (MHC-SF) in New Zealand. Towards this end, traditional Confirmatory Factor Analysis (CFA) and the new method of Exploratory Structural Equation Modeling (ESEM) were used. Both ESEM and CFA supported the tripartite model of mental well-being in comparison to the one- and two-factor models; however, ESEM provided better fit with the data. Moreover, interfactor correlations were considerably lower in ESEM than they were in CFA, indicating greater factor distinctiveness in ESEM. ESEM also revealed a number of important cross-loadings for items in the measurement model of the MHC-SF. The results supported full metric and full scalar invariance of the MHC-SF across gender. The attenuated correlations among well-being factors obtained by ESEM here provide an important insight about the ongoing controversy regarding the failure of empirical research to identify distinct eudaimonic and hedonic factors in well-being measures. An overreliance on CFA methods may have led the field to rely on inflated estimates of shared variance between eudaimonia and hedonia.     

Modelling elderly patients’ perception of the community pharmacist image when providing professional services*

Professional pharmaceutical services may impact on patient’s health behaviour as well as influence on patients’ perceptions of the pharmacist image. The Health Belief Model predicts health-related behaviours using patients’ beliefs. However, health beliefs (HBs) could transcend beyond predicting health behaviour and may have an impact on the patients’ perceptions of the pharmacist image. This study objective was to develop and test a model that relates patients’ HBs to patient’s perception of the image of the pharmacist, and to assess if the provision of pharmacy services (Intervention group-IG) influences this perception compared to usual care (Control group). A qualitative study was undertaken and a questionnaire was created for the development of the model. The content, dimensions, validity and reliability of the questionnaire were pre-tested qualitatively and in a pilot mail survey. The reliability and validity of the proposed model were tested using Confirmatory Factor Analysis (CFA). Structural Equation Modelling (SEM) was used to explain relationships between dimensions of the final model and to analyse differences between groups. As a result, a final model was developed. CFA concluded that the model was valid and reliable (Goodness of Fit indices: x²(80) = 125.726, p = .001, RMSEA = .04, SRMR = .04, GFI = .997, NFI = .93, CFI = .974). SEM indicated that ‘Perceived benefits’ were significantly associated with ‘Perceived Pharmacist Image’ in the whole sample. Differences were found in the IG with also ‘Self-efficacy’ significantly influencing ‘Perceived pharmacist image’. A model of patients’ HBs related to their image of the pharmacist was developed and tested. When pharmacists deliver professional services, these services modify some patients’ HBs that in turn influence public perception of the pharmacist.     

Structural Equation Modeling in the Communication Sciences, 1995–2000

Structural equation modeling (SEM) is a viable multivariate tool used by communication researchers for the past quarter century. Building off Cappella (1975) as well as McPhee and Babrow (1987), this study summarizes the use of this technique from 1995–2000 in 37 communication‐based academic journals. We identify and critically assess 3 unique methods for testing structural relationships via SEM in terms of the specification, estimation, and evaluation of their respective structural equation models. We provide general guidelines for the use of SEM and make recommendations concerning latent variable models, sample size, reporting parameter estimates, model fit statistics, cross‐sectional data, univariate normality, cross‐validation, nonrecursive modeling, and the decomposition of effects (direct, indirect, and total).