A checklist for testing measurement invariance

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Brand loyalty: Exploring self-brand connection and brand experience (2018, methodology): “Owing to the BIC value being smaller and indicating the best model fit (Posada and Buckley, 2004; Van de Schoot et al., 2012), brand experience was included in the model as a second-order reflective construct with the four underlying dimensions (as proposed by Brakus et al., 2009).”
Does accountability pressure through school inspections promote school improvement? (2015, methodology): “In our model, partial invariance was achieved (ΔCFI < 0.01; Byrne, 2010), which allows comparing the relationship of the constructs between all groups in the structural equation model (Van de Schoot et al., 2012; Weiber & Mühlhaus, 2010).”
The Parental Reflective Functioning Questionnaire in Mothers and Fathers of School-Aged Children (2017, methodology): “First, the model was tested independently for both parents to establish configural invariance (van de Schoot et al. 2012).”