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Lane Wakefield and Gregg Bennett

Virtual fan communities (VFC) have become very popular among fans of sports teams. A VFC provides an online place for fans to meet and discuss the team, consume media, and develop friendships. Students will learn, in this case study, how to use partial least squares structural equation modeling (PLS-SEM) to assess fan attitudes toward the VFC and sponsors of the firm. Students will also learn how sport organizations can benefit from leadership with statistical know-how. The case is fictional, but it is based on an actual research study conducted in conjunction with a prominent virtual fan community in which ownership had an interest in fans’ attitudes toward their service.

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Tyreal Yizhou Qian, Jerred Junqi Wang, and James Jianhui Zhang

related factors in e-sports livestreaming. The data collected through an online survey were used for the current investigation. We introduced formative measures to operationalize the push and pull factors and employed partial least squares structural equation modeling (PLS-SEM) analysis to examine the

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Andreas Stenling, Andreas Ivarsson, Urban Johnson, and Magnus Lindwall

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

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Paul J. Carpenter, Tara K. Scanlan, Jeffery P. Simons, and Marci Lobel

This article presents the results of a structural equation modeling analysis of the Sport Commitment Model. This model proposes that commitment is determined by sport enjoyment, involvement alternatives, personal investments, social constraints, and involvement opportunities. Preliminary analyses demonstrated that the model was applicable to both younger (< 12 years old) and older (> 13 years old) athletes, to males and females, and to three different team sports. Structural equation modeling results demonstrated that the proposed model was a good fit of the data (CFI = .981), with the findings accounting for 68% of the commitment variance. As predicted, greater sport enjoyment, involvement opportunities, and the personal investments of time and effort led to greater commitment. Counter to our initial hypothesis, commitment was negatively related to social constraints. Measurement problems led to the involvement alternatives component being excluded from tests of the model presented here, but not from the theoretical model.

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Nicholas D. Myers, Melissa A. Chase, Scott W. Pierce, and Eric Martin

The purpose of this article was to provide a substantive-methodological synergy of potential importance to future research in sport and exercise psychology. The substantive focus was to improve the measurement of coaching efficacy by developing a revised version of the coaching efficacy scale (CES) for head coaches (N = 557) of youth sport teams (CES II-YST). The methodological focus was exploratory structural equation modeling (ESEM), a methodology that integrates the advantages of exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) within the general structural equation model (SEM). The synergy was a demonstration of how ESEM (as compared with CFA) may be used, guided by content knowledge, to develop (or confirm) a measurement model for the CES II-YST. A single-group ESEM provided evidence for close model-data fit, while a single-group CFA fit significantly worse than the single-group ESEM and provided evidence for only approximate model-data fit. A multiple-group ESEM provided evidence for partial factorial invariance by coach’s gender.

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Alex C. Garn

Multidimensional measurement is a common theme in motivation research because many constructs are conceptualized as having an overarching general factor (e.g., situational interest) and specific dimensions (e.g., attention demand, challenge, exploration intention, instant enjoyment, novelty). This review addresses current issues associated with the multidimensional measurement of situational interest in elementary physical education (PE) and illustrates the application and benefits of bifactor exploratory structural equation modeling (ESEM). I perform secondary analysis on a large, previously published data set used to provide validation support for the Situational Interest Scale for Elementary PE. Findings clearly demonstrate the advantages of capturing the multidimensional nature of situational interest using bifactor ESEM. Specifically, a more accurate measurement model of situational interest is reproduced using bifactor ESEM compared with other techniques such as first-order and second-order confirmatory factor analysis. There is empirical support for an overall general factor of situational interest when using the Situational Interest Scale for Elementary PE, however, examining the five dimensions of situational interest as unique factors after accounting for the general factor does not appear warranted.

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David E. Vance, Karlene K. Ball, Daniel L. Roenker, Virginia G. Wadley, Jerri D. Edwards, and Gayla M. Cissell

Falls can impair health and reduce quality of life among older adults. Although many factors are related to falling, few analyses examine causal models of this behavior. In this study, factors associated with falling were explored simultaneously using structural-equation modeling. A variety of cognitive, physical-performance, and health measures were administered to 694 older adult drivers from the state of Maryland. The observed and latent variables of age, cognitive ability, physical functioning, health, and falling behavior were used to create a causal model. The model revealed that being older was associated with declines in cognition, and such cognitive declines predicted increased falling. Similarly, poorer health was related to poorer physical functioning, which, in turn, also predicted increased falling. This model indicates that in addition to existing fall-prevention interventions aimed at improving physical functioning, interventions to improve cognition and health might also be effective. It is speculated that fear of falling, which often results in reduced mobility among older adults, might account for the lack of a direct relationship between age and falling. This hypothesis should be examined in further research.

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Kathryn E. Wilson, Bhibha M. Das, Ellen M. Evans, and Rodney K. Dishman


A positive association between physical activity and mental health is well established, particularly for lower symptoms of depression and anxiety among active adults. However, it is unclear whether the association is influenced by personality, which might moderate or otherwise explain the association. In addition, past studies have not confirmed the association using an objective measure of physical activity.


Our objective was to examine whether Extraversion and Neuroticism influence the association between mental health and physical activity measured by convergent self-reports and an accelerometer.


Structural equation modeling was used to test competing models of the relationships between personality, physical activity, and mental health in a sample of female undergraduates.


In bivariate analysis, mental health was negatively related to Neuroticism and positively related to Extraversion, self-reported physical activity (which was related only to Extraversion, positively), and objective physical activity (which was related only to Neuroticism, negatively). In structural equation modeling, a 3-way interaction indicated that objective physical activity and mental health were unrelated in extraverts, but related positively in neurotic-introverts and negatively in stable-introverts.


Higher levels of physical activity were associated with better mental health only in neurotic-introverts, who are at higher risk for mental health problems.

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Ricardo Ribeiro Agostinete, Santiago Maillane-Vanegas, Kyle R. Lynch, Bruna Turi-Lynch, Manuel J. Coelho-e-Silva, Eduardo Zapaterra Campos, Suziane Ungari Cayres, and Romulo Araújo Fernandes

and BMD in adolescent swimmers, using structural equation models. The initial hypothesis of this study identifies that the training load affects the bone density independent of LST. Methods Sample The ethical research committee of São Paulo State University (Presidente Prudente, São Paulo, Brazil

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Inés Tomás, Herbert W. Marsh, Vicente González-Romá, Víctor Valls, and Benjamin Nagengast

Test of measurement invariance across translated versions of questionnaires is a critical prerequisite to comparing scores on the different versions. In this study, we used exploratory structural equation modeling (ESEM) as an alternative approach to evaluate the measurement invariance of the Spanish version of the Physical Self-Description Questionnaire (PSDQ). The two versions were administered to large samples of Australian and Spanish adolescents. First, we compared the CFA and ESEM approaches and showed that ESEM fitted the data much better and resulted in substantially more differentiated factors. We then tested measurement invariance with a 13-model ESEM taxonomy. Results justified using the Spanish version of the PSDQ to carry out cross-cultural comparisons in sport and exercise psychology research. Overall, the study can stimulate research on physical self-concept across countries and foster better cross-cultural comparisons.