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Nicholas D. Myers, Deborah L. Feltz, Félix Guillén and Lori Dithurbide

The purpose of this multistudy report was to develop, and then to provide initial validity evidence for measures derived from, the Referee Self-Efficacy Scale. Data were collected from referees (N = 1609) in the United States (n = 978) and Spain (n = 631). In Study 1 (n = 512), a single-group exploratory structural equation model provided evidence for four factors: game knowledge, decision making, pressure, and communication. In Study 2 (n = 1153), multiple-group confirmatory factor analytic models provided evidence for partial factorial invariance by country, level of competition, team gender, and sport refereed. In Study 3 (n = 456), potential sources of referee self-efficacy information combined to account for a moderate or large amount of variance in each dimension of referee self-efficacy with years of referee experience, highest level refereed, physical/mental preparation, and environmental comfort, each exerting at least two statistically significant direct effects.

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Alex J. Benson and Mark Eys

advantage of ESEM with targeted rotation is that it allows one to specify a factor structure based on a priori knowledge while enabling researchers to identify misspecified elements through inspection of the standardized factor loadings and corresponding standard error estimates ( Browne, 2001 ; Marsh

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Mark Eys, Mark R. Beauchamp, Michael Godfrey, Kim Dawson, Todd M. Loughead and Robert J. Schinke

) identify items with clear cross loadings and/or low factor loadings and (b) reduce the number of items prior to utilizing ESEM to aid in interpretation. The second and main approach was then to use ESEM with targeted rotation with the remaining items. This latter approach is appropriate, because it allows

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Daniel Milton, Paul R. Appleton, Anna Bryant and Joan L. Duda

. Models were tested based on the robust weighted least square estimator. For the ESEM, target rotation was used, where all cross-loadings were specified to be close to zero, and the main loadings were freely estimated ( Morin et al., 2016 ). Invariance Millsap and Yun-Tein’s ( 2004 ) recommendations for

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Valérian Cece, Noémie Lienhart, Virginie Nicaise, Emma Guillet-Descas and Guillaume Martinent

target factor. ESEM was specified using target rotation; each item loads on both target factor and nontarget factors (targeted the 0). The bifactor model was specified as orthogonal; each item loads on both a specific factor and a general factor. Finally, Bi-ESEM was estimated using target rotation in