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 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).     

Interrelationships among biological markers of aging, health, activity, acculturation, and cognitive performance in late adulthood

In this study a structural equation model of predictors of age differences in cognitive performance in late adulthood was developed. Biological markers of aging (vision, hearing, vibration sense, forced expiratory volume, and grip strength) were used as indicators of a latent variable called BioAge. A sample of 180 community-dwelling women aged 60 to 90 years was assessed. Results showed that BioAge explained all of the age-related variance in cognitive test performance. Physical health and physical activity had direct effects on BioAge. Measures of acculturation explained non-age-related variance in cognitive test performance. Some variables used as biomarkers also explained individual differences in measures of crystallized intelligence and perceptual speed. It is concluded that the association between biomarkers and cognition in old age is due to more than a common statistical association with age.     

Sources of motivation, interpersonal conflict management styles, and leadership effectiveness: a structural model

126 leaders and 624 employees were sampled to test the relationship between sources of motivation and conflict management styles of leaders and how these variables influence effectiveness of leadership. Five sources of motivation measured by the Motivation Sources Inventory were tested-intrinsic process, instrumental, self-concept external, self-concept internal, and goal internalization. These sources of work motivation were associated with Rahim's modes of interpersonal conflict management-dominating, avoiding, obliging, complying, and integrating-and to perceived leadership effectiveness. A structural equation model tested leaders' conflict management styles and leadership effectiveness based upon different sources of work motivation. The model explained variance for obliging (65%), dominating (79%), avoiding (76%), and compromising (68%), but explained little variance for integrating (7%). The model explained only 28% of the variance in leader effectiveness.     

Statistical guidelines for studies of the theory of reasoned action and the theory of planned behaviour

Abstract

We identify potential problems in the statistical analysis of social cognition model data, with special emphasis on the theories of reasoned action (TRA) and planned behaviour (TPB). Some statistical guidelines are presented for empirical studies of the TRA and the TPB based upon multiple linear regression and structural equation modelling (SEM). If the model is tested using multiple regression, the assumptions of this technique must be considered and variables transformed if necessary. Adjusted R² (not R²) should be used as a measure of explained variance and semipartial correlations are useful in assessing each component's unique contribution to explained variance. R² is not an indicator of model adequacy and residuals should be examined. Expectancy-value variables that are the product of expectancy and value measures represent the interaction term in a multiple regression and should not be used. SEM approaches make explicit the assumptions of unidimensionality of constructs in the TRA/TPB, assumptions that might usefully be challenged by competing models with multidimensional constructs. Finally, statistical power and sample size should be considered for both approaches. Inattention to any of these aspects of analysis threatens the validity of TRA/TPB research.     

Factors That Explain Academic Dishonesty Among University Students in Thailand

Academic dishonesty is a problem that continues to plague universities. Few studies have examined how mind-set and individualism contribute to academic dishonesty. Using structural equation modeling, a model was developed to explain academic dishonesty, which included mind-set, individualistic learning environment, individualism, and motivation to study. A total of 207 university students in Thailand participated. The final model explained 30% of the variance in academic dishonesty. All variables in this study had a negative relationship with academic dishonesty, indicating that improvements in mind-set, learning environment, and motivation could change perceptions of academic dishonesty.     

Some Esoteric Aspects of SEM That Its Practitioners Should Want to Know

The topic of this article is the interpretation of structural equation modeling (SEM) solutions. Its purpose is to augment structural modeling's metatheoretic resources while enhancing awareness of how problematic is the causal significance of SEM-parameter solutions. Part I focuses on the nonuniqueness and consequent dubious interpretability of loop pathweights in nonrecursive SEMs: Solutions for a nonrecursive SEM's open parameters are strongly indeterminate absent constraints that in most applications would be arbitrary. The generic indeterminacy is well known, but how severely this thwarts identification of a linear dynamic system's structural coefficients from synchronic (one-panel) data still seems inadequately appreciated. Part II introduces an efficient formalism for recognizing an important facet of lawful regularity—locus displacements—that is generally suppressed by the equations in which mathematical models are standardly written. (Preoccupation with SEM's matrix algebra and fit appraisal has masked the cognitive poverty with which SEM applications are prevailingly conceived.) Introduced here are some unfamiliar concepts that enable us to think about system structure more deeply than matrix equations can express. The Appendix attempts to incite some debate on how we can best conceptualize and exploit different levels (molar vs. molecular) of subject conception while appreciating that not all becauses are productive causes. It provides an overview of explanatory determinations comprising more than just production causality.     

Explained Variance and Intraclass Correlation in a Two-Level AR(1) Model

The total variance of a first-order autoregressive AR(1) time series is well known in time series literature. However, despite the increased use and interest in two-level AR(1) models, an equation for the total variance of these models does not exist. This paper presents an approximation of this total variance. It will be used to compute the unexplained and explained variance at each level of the model, the proportion of explained variance, and the intraclass correlation (ICC). The use of these variances and the ICC will be illustrated using an example concerning structured diary data about the positive affect of 96 married women.     

Quantifying the Strength of General Factors in Psychopathology: A Comparison of CFA with Maximum Likelihood Estimation,BSEM, and ESEM/EFA Bifactor Approaches

Whether or not importance should be placed on an all-encompassing general factor of psychopathology (or p factor) in classifying, researching, diagnosing, and treating psychiatric disorders depends (among other issues) on the extent to which comorbidity is symptom-general rather than staying largely within the confines of narrower transdiagnostic factors such as internalizing and externalizing. In this study, we compared three methods of estimating p factor strength. We compared omega hierarchical and explained common variance calculated from confirmatory factor analysis (CFA) bifactor models with maximum likelihood (ML) estimation, from exploratory structural equation modeling/exploratory factor analysis models with a bifactor rotation, and from Bayesian structural equation modeling (BSEM) bifactor models. Our simulation results suggested that BSEM with small variance priors on secondary loadings might be the preferred option. However, CFA with ML also performed well provided secondary loadings were modeled. We provide two empirical examples of applying the three methodologies using a normative sample of youth (z-proso, n = 1,286) and a university counseling sample (n = 359).     

Emotional load and social support as indicators of bullying at work

This study sought to ascertain whether elevated emotional load and a lack of social support could be indicative of bullying at work. Participants totalled 1442 employees from the manufacturing industry in South Africa. Data on emotional load, social support, and bullying were gathered using a self-report survey. Structural equation modelling methods were implemented to establish the variance explained in bullying by colleagues and bullying by supervisors, as outcomes, with emotional load and social support as predictor variables. Additionally, multi-group analyses were performed to investigate how the explained variances might differ based on gender and race. Results revealed that the models fitted the data well and that emotional load and a lack of social support explained a substantial amount of variance in bullying by superiors and bullying by colleagues. With regard to the multi-group analysis more variance was explained for females than for males, but the values were quite similar in all groups which give strength to the generalisability of the findings. The findings of this study therefore indicate that elevated emotional load and a lack of social support are indicators of bullying behaviour at work.     

Perceived teacher confirmation.

This article reports an initial attempt to operationalize perceived teacher confirmation in behavioral terms and to explore relationships among perceived teacher confirmation, cognitive learning, and affective learning. Results for 2 samples (N=446; N=303) indicate that the final 16‐item version of the Teacher Confirmation Scale (TCS) is valid and reliable. Confirmatory factor analysis revealed that teacher confirmation is best represented by a 3‐factor solution: (a) teachers' response to students' questions‐comments, (b) demonstrated interest in students and in their learning, and teaching style. Results also indicate that teacher confirmation plays a significant role in college students' cognitive and affective learning. For Sample 1, confirmation uniquely explained 18% of the variance in cognitive learning and 30% of the variance in affective learning, after controlling for demographic variables and relevance of assignments. For Sample 2, confirmation uniquely explained 17% of the variance in cognitive learning and 31% of the variance in affective learning, after controlling for the same variables. Structural equation modeling revealed strong, significant paths between confirmation and affective learning and between affective and cognitive learning. The study revealed a large, significant, indirect effect of teacher confirmation on cognitive learning, suggesting that affective learning serves as a mediating variable between teacher confirmation and cognitive learning. A multiple groups comparison demonstrated that the structural model was invariant for the 2 samples.     

Structural equation models and personality research

This article is a nontechnical introduction to the use of structural equation models in personality research Although such models can be fruitfully used to address a variety of important theoretical issues, the substantive focus in this article is on the use of such models for elucidating the construct validity of personality measures We include numerous more specific topics under our treatment of construct validity First of all, we show how structural equation models can be applied to the issues of convergent and discriminant validity Do our variables measure the constructs we want them to measure and not other constructs that we would prefer not to measure? Second, we show the utility of structural equation models for predictive validity Do our variables reliably predict other constructs with which they are theoretically linked? Finally, we examine the stability of personality constructs through structural equation models Through-out, our emphasis is on the particular advantages that structural equation models bring to these analytic tasks Ultimately, such models must be used in the service of theory, and when used appropriately, they can help us to refine both our measures and our theories of individual differences     

Testing Cognitive and Emotion-Focused Models of Worry in Black and White Samples

Several models have been proposed to conceptualize worry. Broadly, the models can be classified as cognitive (including the Avoidance Model, the Intolerance of Uncertainty Model, and the Metacognitive Model) and emotion-focused (including Emotion Dysregulation and Acceptance-Based models). Although these models have received strong empirical investigation in primarily non-Hispanic White samples, no known study has examined the applicability to racial and ethnic minority groups. The current study compared the proportion of variance explained by cognitive and emotion-focused models of worry in White and Black samples. Results indicated that cognitive and emotion-focused models significantly predicted worry in both Black and White samples. However, the overall amount of variance in worry explained by the models was less for Black samples. Specifically, controlling for gender, the cognitive models explained 53% of the variance in worry in the White sample compared with 19% in the Black sample. Similarly, the emotion-focused models explained 34% of the variance in worry in the White sample but only 13% in the Black sample. These findings suggest that well-established conceptual frameworks for worry failed to explain the bulk of the variance in worry in Black samples, leaving much unknown. Additional research is needed to identify key variables that may further explain worry in ethnic minority samples.     

Regression among factor scores

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.     

Personality and job stress: a comparison of direct effects on parenting

The impact of personality and job characteristics on parental rearing styles was compared in 353 employees. Hypotheses concerning the relationships between personality and job variables were formulated in accordance with findings in past research and the Belsky's model (1984). Structural equation nested models showed that Aggression-hostility, Sociability and job Demand were predictive of Rejection and Emotional Warmth parenting styles, providing support for some of the hypothesized relationships. The findings suggest a well-balanced association of personality variables with both parenting styles: Aggression-Hostility was positively related to Rejection and negatively to Emotional Warmth, whereas Sociability was positively related to Emotional Warmth and negatively related to Rejection. Personality dimensions explained a higher amount of variance in observed parenting styles. However, a model that considered both, personality and job dimensions as antecedent variables of parenting was the best representation of observed data, as both systems play a role in the prediction of parenting behavior.     

Subjective Wellbeing as an Affective-Cognitive Construct

The affective content of Subjective Wellbeing (SWB) was investigated in two separate studies. Study 1 involved a representative sample of 478 participants from across Australia aged between 18 and 72 years. This study tested the circumplex model of affect and then determined the minimum set of affects that explain variance in SWB. The model was supported, with most affects congregated around the valence axis. Overall, 64% of the variance in SWB was explained by six Core Affects, indicating that SWB is a highly affective construct. Study 2 tested the relative strength of Core Affect (content, happy and excited), in three separate models of SWB incorporating cognition (seven discrepancies) and all five factors of personality. Using a sample of 854 participants aged been 18–86 years, structural equation modeling was used to compare an affective-cognitive driven model of SWB, with a personality driven model of SWB and a discrepancy driven model of SWB. The results provide support for an affective-cognitive model which explained 90 percent of the variance in SWB. All models confirm that the relationship between SWB, Core Affect and Discrepancies is far stronger than the relationship between personality and SWB. It is proposed that Core Affect and Discrepancies comprise the essence of SWB. Moreover, Core Affect is the driving force behind individual set-point levels in SWB homeostasis.     

The robustness of estimates of total indirect effects in covariance structure models estimated by maximum

The large sample distribution of total indirect effects in covariance structure models in well known. Using Monte Carlo methods, this study examines the applicability of the large sample theory to maximum likelihood estimates oftotal indirect effects in sample sizes of 50, 100, 200, 400, and 800. Two models are studied. Model 1 is a recursive model with observable variables and Model 2 is a nonrecursive model with latent variables. For the large sample theory to apply, the results suggest that sample szes of 200 or more and 400 or more are required for models such as Model 1 and Model 2, respectively.For helpful comments on a previous draft of this paper, we are grateful to Gerhard Arminger, Clifford C. Clogg, and several anonymous reviewers.     

Test of Structural Relationships Within a Proposed Exercise and Self-Esteem Model

This study tested structural relationships within a model proposed to explain the manner in which self-esteem changes are associated with exercise experiences. As initially assessed by self-efficacies (EFFs) specific to physical tasks within a training program, we postulated that competence can generalize to feelings of global self-esteem (SE) through an intervening construct of perceived physical competence (PC). Three measures of EFF and two each of PC and SE were administered to 145 people in their mid- to late adulthood. Confirmatory factor analysis examined orthogonal and oblique versions of three measurement models and identified three distinct but correlated factors, each assessed by its hypothesized indicators. Alternative structural equation models were specified and tested using both normal and nonnormal estimation procedures. The proposed model provided the most parsimonious fit and explained 29% of the variance in SE. Confirmation of its structural relationships provides preliminary validity for model use in examining the manner in which exercise experiences influence levels of self-perception.     

Test of structural relationships within a proposed exercise and self-esteem model

This study tested structural relationships within a model proposed to explain the manner in which self-esteem changes are associated with exercise experiences. As initially assessed by self-efficacies (EFFs) specific to physical tasks within a training program, we postulated that competence can generalize to feelings of global self-esteem (SE) through an intervening construct of perceived physical competence (PC). Three measures of EFF and two each of PC and SE were administered to 145 people in their mid- to late adulthood. Confirmatory factor analysis examined orthogonal and oblique versions of three measurement models and identified three distinct but correlated factors, each assessed by its hypothesized indicators. Alternative structural equation models were specified and tested using both normal and nonnormal estimation procedures. The proposed model provided the most parsimonious fit and explained 29% of the variance in SE. Confirmation of its structural relationships provides preliminary validity for model use in examining the manner in which exercise experiences influence levels of self-perception.     

大学生成人依恋、应对方式与负性情绪的关系研究

本文使用结构方程模型方法,研究大学生成人依恋、应对方式与负性情绪的关系。结果发现:(1)应对方式是依恋焦虑与负性情绪之间的完全中介;(2)应对方式是依恋回避与负性情绪之间的部分中介;(3)依恋焦虑和依恋回避对应对方式的解释率为40%,而依恋回避和依恋焦虑以及应对方式对负性情绪的解释率则为56%。