The Professional Counselor | Volume 11, Issue 3 277 Multiple-Group Confirmatory Factor Analysis Multiple-group confirmatory factor analysis (MCFA) is an extension of CFA for testing the factorial invariance (psychometric equivalence) of a scale across subgroups of a sample or population (C.-C. Chen et al., 2020; Dimitrov, 2010). In other words, MCFA has utility for testing the extent to which a particular construct has the same meaning across different groups of a larger sample or population. Suppose, for example, the developer of the Therapeutic Climate scale (see example in the previous section) validated scores on their scale with undergraduate college students. Invariance testing has potential to provide further support for the internal structure validity of the scale by testing whether Empathy, Unconditional Positive Regard, and Congruence have the same meaning across different subgroups of undergraduate college students (e.g., between different gender identities, ethnic identities, age groups, and other subgroups of the larger sample). Levels of Invariance. Factorial invariance can be tested in a number of different ways and includes the following primary levels or aspects: (a) configural invariance, (b) measurement (metric, scalar, and strict) invariance, and (c) structural invariance (Dimitrov, 2010, 2012). Configural invariance (also referred to as pattern invariance) serves as the baseline mode (typically the best fitting model with the data), which is used as the point of comparison when testing for metric, scalar, and structural invariance. In layperson’s terms, configural invariance is a test of whether the scales are approximately similar across groups. Measurement invariance includes testing for metric and scalar invariance. Metric invariance is a test of whether each test item makes an approximately equal contribution (i.e., approximately equal factor loadings) to the latent variable (composite scale score). In layperson’s terms, metric invariance evaluates if the scale reasonably captures the same construct. Scalar invariance adds a layer of rigor to metric invariance by testing if the differences between the average scores on the items are attributed to differences in the latent variable means. In layperson’s terms, scalar invariance indicates that if the scores change over time, they change in the same way. Strict invariance is the most stringent level of measurement invariance testing and tests if the sum total of the items’ unique variance (item variation that is not in common with the factor) is comparable to the error variance across groups. In layperson’s terms, the presence of strict invariance demonstrates that score differences between groups are exclusively due to differences in the common latent variables. Strict invariance, however, is typically not examined in social sciences research because the latent factors are not composed of residuals. Thus, residuals are negligible when evaluating mean differences in latent scores (Putnick & Bornstein, 2016). Finally, structural invariance is a test of whether the latent factor variances are equivalent to the factor covariances (Dimitrov, 2010, 2012). Structural invariance tests the null hypothesis that there are no statistically significant differences between the unconstrained and constrained models (i.e., determines if the unconstrained model is equivalent to the constrained model). Establishing structural invariance indicates that when the structural pathways are allowed to vary across the two groups, they naturally produce equal results, which supports the notion that the structure of the model is invariant across both groups. In layperson’s terms, the presence of structural invariance indicates that the pathways (directionality) between variables behave in the same way across both groups. It is necessary to establish configural and metric invariance prior to testing for structural invariance. Sample Size and Criteria for Evaluating Invariance. Researchers should check their sample size before computing invariance testing, as small samples (approximately < 200) can overestimate model fit
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