Teacher's Corner: Testing Measurement Invariance of Second-Order Factor Models

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Testing the dimensionality of place attachment and its relationships with place satisfaction and pro-environmental behaviours: A structural equation modelling approach (2013, background): “Chen et al. (2005) argue that a second-order factor model separates variance due to specific factors from measurement error, leading to a theoretically error-free estimate of the specific factors.”
Reciprocity in Relationship Marketing: A Cross-Cultural Examination of the Effects of Equivalence and Immediacy on Relationship Quality and Satisfaction with Performance (2015, methodology): “Although there was an increase in the chisquare value, following the logic of Chen, Sousa, and West (2005), it can be concluded that first-order metric invariance is exhibited given the lack of substantial change in fit.”
Testing multidimensional models of youth civic engagement: Model comparisons, measurement invariance, and age differences (2017, methodology): “Finally, in higher-order and bifactor models, invariance of the first-order disturbances (i.e., variances of specific or lower-order factors) must be tested (Chen et al., 2005).”
Using ΔGoodness-of-Fit Indexes in Assessing Mean Structure Invariance (2009, background): “As discussed in Chen, Sousa, and West (2005), goodness-of-fit indexes were originally designed to assess model fit in terms of the covariance structure.”