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The present contribution provides a tutorial for the estimation of the social relations model (SRM) by means of structural equation modeling (SEM). In the overarching SEM-framework, the SRM without roles (with interchangeable dyads) is derived as a more restrictive form of the SRM with roles (with noninterchangeable dyads). Starting with the simplest type of the SRM for one latent construct assessed by one manifest round-robin indicator, we show how the model can be extended to multiple constructs each measured by multiple indicators. We illustrate a multiple constructs multiple indicators SEM SRM both with and without roles with simulated data and explain the parameter interpretations. We present how testing the substantial model assumptions can be disentangled from testing the interchangeability of dyads. Additionally, we point out modeling strategies that adhere to cases in which only some members of a group can be differentiated with regards to their roles (i.e., only some group members are noninterchangeable). In the online supplemental materials , we provide concrete examples of specific modeling problems and their implementation into statistical software (Mplus, lavaan, and OpenMx). Advantages, caveats, possible extensions, and limitations in comparison with alternative modeling options are discussed. The present contribution provides a tutorial for the estimation of the social relations model (SRM) by means of structural equation modeling (SEM). In the overarching SEM-framework, the SRM without roles (with interchangeable dyads) is derived as a more restrictive form of the SRM with roles (with noninterchangeable dyads). Starting with the simplest type of the SRM for one latent construct assessed by one manifest round-robin indicator, we show how the model can be extended to multiple constructs each measured by multiple indicators. We illustrate a multiple constructs multiple indicators SEM SRM both with and without roles with simulated data and explain the parameter interpretations. We present how testing the substantial model assumptions can be disentangled from testing the interchangeability of dyads. Additionally, we point out modeling strategies that adhere to cases in which only some members of a group can be differentiated with regards to their roles (i.e., only some group members are noninterchangeable). In the online supplemental materials , we provide concrete examples of specific modeling problems and their implementation into statistical software (Mplus, lavaan, and OpenMx). Advantages, caveats, possible extensions, and limitations in comparison to alternative modeling options are discussed. [ABSTRACT FROM AUTHOR]

AbstractThe social relations model (SRM) is the standard approach for analyzing dyadic data stemming from round-robin designs. The model can be used to estimate correlation-coefficients that reflect the overall reciprocity or accuracy of judgements for individual and dyads on the sample- or population level. Within the social relations structural equation modeling framework and on the statistical grounding of stochastic measurement and classical test theory, we show how the multiple indicator SRM can be modified to capture inter-individual and inter-dyadic differences in reciprocal engagement or inter-individual differences in reciprocal accuracy. All models are illustrated on an open-access round-robin data set containing measures of mimicry, liking, and meta-liking (the belief to be liked). Results suggest that people who engage more strongly in reciprocal mimicry are liked more after an interaction with someone and that overestimating one’s own popularity is strongly associated with being liked less. Further applications, advantages and limitations of the models are discussed. [ABSTRACT FROM AUTHOR]

We didactically derive a correlated traits correlated (methods – 1) [CTC(M – 1)] multitrait‐multimethod (MTMM) model for dyadic round‐robin data augmented by self‐reports. The model is an extension of the CTC(M – 1) model for cross‐classified data and can handle dependencies between raters and targets by including reciprocity covariance parameters that are inherent in augmented round‐robin designs. It can be specified as a traditional structural equation model. We present the variance decomposition as well as consistency and reliability coefficients. Moreover, we explain how to evaluate fit of a CTC(M – 1) model for augmented round‐robin data. In a simulation study, we explore the properties of the full information maximum likelihood estimation of the model. Model (mis)fit can be quite accurately detected with the test of not close fit and dynamic root mean square errors of approximation. Even with few small round‐robin groups, relative parameter estimation bias and coverage rates are satisfactory, but several larger round‐robin groups are needed to minimize relative parameter estimation inaccuracy. Further, neglecting the reciprocity covariance‐structure of the augmented round‐robin data does not severely bias the remaining parameter estimates. All analyses (including data, R scripts, and results) and the simulation study are provided in the Supporting Information. Implications and limitations are discussed. [ABSTRACT FROM AUTHOR]

This study contributes to understanding students' emotional responses to academic stressors by integrating grit into the well-established Job Demands-Resources Model and by examining the relationship between academic demands, grit (consistency of interests, perseverance of effort), burnout, engagement, academic achievement, depression, and life satisfaction in Chinese students. We conducted a self-report study with N = 1527 Chinese high school students (Mage = 16.38 years, SD = 1.04). The results of structural equation modeling showed that after controlling for gender, socio-economic status, and school types, demands positively related to burnout and negatively related to engagement. Both facets of grit negatively related to exhaustion, whereas only perseverance of effort positively related to engagement. Burnout positively related to depression and negatively related to life satisfaction, whereas engagement positively related to life satisfaction. However, neither burnout nor engagement was related to academic achievement. Our findings indicate that grit may be protective against school burnout. [ABSTRACT FROM AUTHOR]

The current study builds on research concerning self-other agreement, specifically the Trait-Reputation-Identity (TRI) Model, and combines this theoretical approach and recent advances from multitrait-multimethod research, specifically the CTC(M-1) and the latent difference model. This combination was applied to avoid statistical problems associated with latent trait models of the type previously used in TRI Model research. A further aim was to fully exploit the TRI Model's potential by simultaneously modeling more than one trait in one psychometric model. This makes it possible to explore whether raters use similar information to assess different traits or whether this information is observer-specific, as well as whether the traits themselves can shape an individual's Reputation. All analyses were based on a data set capturing the Dark Triad. As the Dark Triad has only rarely been examined from different rater perspectives before, the study also provides new insights into this network of maladaptive traits. A sample of 290 students, their best friends, and one parent were asked to fill out the NPI, Mach IV, and SRP-III. The results suggest that accuracy is high only for narcissism. Moreover, a dark halo could be observed among each of the other-raters for Machiavellianism and psychopathy; target's standings on these two traits were also underestimated by the other-raters. The study's combined use of the TRI Model and modern structural equation methods highlights the usefulness of the TRI Model and adds to the debate about the specific nature of Dark Triad traits. [ABSTRACT FROM AUTHOR]

Personal values and attitudes can help to explain food choice. This study confirmed a hierarchical organization of the value-attitude-behavior chain: Food-related values influence attitudes, and these, in turn, impact behavior. Contrary to previous findings, values are only partially mediated by attitudes: Some food-related values are fully mediated, whereas others are partially mediated, and still others have exclusively direct effects on purchase behavior. Questionnaire data from a roughly representative sample of 851 adults living in Switzerland was complemented with actual food purchase behavior measured by a loyalty card of a Swiss retailer over the period of one year. Four theoretically derived structural equation models were compared across eight different food product categories (organic, fair trade, low-budget, fresh convenience, ready-to-eat, light, functional foods, fruits and vegetables). The results question central assumptions of the theory of planned behavior and emphasize the role of food-related values in food consumption. Implications for marketing and future product developments of food companies are discussed. [ABSTRACT FROM AUTHOR]

The analysis of convergent and discriminant validity is an integral part of the construct validation process. Models for analyzing the convergent and discriminant validity have typically been developed for cross-sectional data. There exist, however, only a few approaches for longitudinal data that can be applied for analyzing the construct validity of fluctuating states. In this article, the authors show how models of latent state—trait theory can be combined with models of multitrait—multimethod analysis to develop a model that allows for analyzing convergent and discriminant validity in time: the multimethod latent state—trait model. The model allows for identifying different sources of variance (trait consistency, trait-method specificity, occasion-specific consistency, occasion-specific method specificity, and unreliability). It is applied to the repeated measurement of depression and anxiety in children, which was assessed by self and teacher reports (N = 375). The application shows that the proposed models fit the data well and allow a deeper understanding of method effects in clinical assessment. [ABSTRACT FROM AUTHOR]

In a recent article, A. Maydeu-Olivares and D. L. Coffman (2006) presented a random intercept factor approach for modeling idiosyncratic response styles in questionnaire data and compared this approach with competing confirmatory factor analysis models. Among the competing models was the CT-C(M-1) model (M. Eid, 2000). In an application to the Life Orientation Test (M. F. Scheier & C. S. Carver, 1985), Maydeu-Olivares and Coffman found that results obtained from the CT-C(M-1) model were difficult to interpret. In particular, Maydeu-Olivares and Coffman challenged the asymmetry of the CT-C(M-1) model. In the present article, the authors show that the difficulties faced by Maydeu-Olivares and Coffman rest upon an improper interpretation of the meaning of the latent factors. The authors' aim is to clarify the meaning of the latent variables in the CT-C(M-1) model. The authors explain how to properly interpret the results from this model and introduce an alternative restricted model that is conceptually similar to the CT-C(M-1) model and nested within it. The fit of this model is invariant across different reference methods. Finally, the authors provide guidelines as to which model should be used in which research context. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]