TPC Journal-Vol 11-Issue-3 - FULL ISSUE

The Professional Counselor | Volume 11, Issue 3 275 and psychometric researchers sometimes refer to the modification indices (also referred to as Lagrange multiplier statistics), which denote the expected decrease in the X2 value (i.e., degree of improvement in model fit) if the parameter is freely estimated (Dimitrov, 2012). In these instances, correlating the error terms between items or removing problematic items will improve model fit; however, when considering model respecification, psychometric researchers should proceed cautiously, if at all, as a strong theoretical justification is necessary to defend model respecification (Byrne, 2016; Lewis, 2017; Schreiber et al., 2006). Researchers should also be clear that model respecification causes the CFA to become an EFA because they are investigating the dimensionality of a different or modified model rather than confirming the structure of an existing, hypothesized model. Higher-Order CFA Higher-order CFA is an extension of CFA that allows researchers to test nested models and determine if a second-order latent variable (factor) explains the associations between the factors in a single-order CFA (Credé & Harms, 2015). Similar to single-order CFA (see Figure 3, Model 1) in which the test items cluster together to form the factors or subscales, higher-order CFA reveals if the factors are related to one another strongly enough to suggest the presence of a global factor (see Figure 3, Model 3). Suppose, for example, the test developer of a scale for measuring dimensions of the therapeutic alliance confirmed the three following subscales via single-order CFA (see Figure 3, Model 1): Empathy, Unconditional Positive Regard, and Congruence. Computing a higher-order CFA would reveal if a higher-order construct, which the research team might name Therapeutic Climate, is present in the data. In other words, higher-order CFA reveals if Empathy, Unconditional Positive Regard, and Congruence, collectively, comprise the second-order factor of Therapeutic Climate. Determining if a higher-order factor explains the co-variation (association) between single-order factors is a complex undertaking. Thus, researchers should consider a number of criteria when deciding if their data are appropriate for higher-order CFA (Credé & Harms, 2015). First, moderate-to-strong associations (co-variance) should exist between first-order factors. Second, the unidimensional factor solution (see Figure 3, Model 2) should display a poor model fit (see Table 1) with the data. Third, theoretical support should exist for the presence of a higher-order factor. Referring to the example in the previous paragraph, person-centered therapy provides a theory-based explanation for the presence of a second-order or global factor (Therapeutic Climate) based on the integration of the single-order factors (Empathy, Unconditional Positive Regard, and Congruence). In other words, the presence of a secondorder factor suggests that Therapeutic Climate explains the strong association between Empathy, Unconditional Positive Regard, and Congruence. Finally, the single-order factors should display strong factor loadings (approximately ≥ .70) on the higher-order factor. However, there is not an absolute consensus among psychometric researchers regarding the criteria for higher-order CFA and the criteria summarized in this section are not a dualistic decision rule for retaining or rejecting a higher-order model. Thus, researchers are tasked with presenting that their data meet a number of criteria to justify the presence of a higher-order factor. If the results of a higher-order CFA reveal an acceptable model fit (see Table 1), researchers should directly compare (e.g., chi-squared test of difference) the single-order and higherorder models to determine if one model demonstrates a superior fit with the data at a statistically significant level.