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Existing research posits multiple dimensions of bullying and victimization but has not identified well-differentiated facets of these constructs that meet standards of good measurement: goodness of fit, measurement invariance, lack of differential item functioning, and well-differentiated factors that are not so highly correlated as to detract from their discriminant validity and substantive usefulness in school settings. Here we demonstrate exploratory structural equation modeling, an integration of confirmatory factor analysis and exploratory factor analysis. On the basis of responses to the 6-factor Adolescent Peer Relations Instrument (verbal, social, physical facets of bullying and victimization), we tested invariance of factor loadings, factor variances–covariances, item uniquenesses, item intercepts (a lack of differential item functioning), and latent means across gender, year in school, and time. Using a combination of …