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

278 The Professional Counselor | Volume 11, Issue 3 (Dimitrov, 2010). Similar to single-order CFA, no absolute sample size guidelines exist in the literature for invariance testing. Generally, a minimum sample of at least 200 participants per group is recommended for invariance testing (although < 200 to 300+ is advantageous). Referring back to the Therapeutic Climate scale example (see the previous section), investigators would need a minimum sample of 400 if they were seeking to test the invariance of the scale by generational status (200 first generation + 200 non-first generation = 400). The minimum sample size would increase as more levels are added. For example, a minimum sample of 600 would be recommended if investigators quantified generational status on three levels (200 first generation + 200 second generation + 200 third generation and beyond = 600). Factorial invariance is investigated through a computation of the change in model fit at each level of invariance testing (F. F. Chen, 2007). Historically, the Satorra and Bentler chi-square difference test was the sole criteria for testing factorial invariance, with a non-significant p-value indicating factorial invariance (Putnick & Bornstein, 2016). The chi-square difference test is still commonly reported by contemporary psychometric researchers; however, it is rarely used as the sole criteria for determining invariance, as the test is sensitive to large samples. The combined recommendations of F. F. Chen (2007) and Putnick and Bornstein (2016) include the following thresholds for investigating invariance: ≤ ∆ 0.010 in CFI, ≤ ∆ 0.015 in RMSEA, and ≤ ∆ 0.030 in SRMR for metric invariance or ≤ ∆ 0.015 in SRMR for scalar invariance. In a simulation study, Kang et al. (2016) found that McDonald’s NCI (MNCI) outperformed the CFI in terms of stability. Kang et al. (2016) recommend < ∆ 0.007 in MNCI for the 5th percentile and ≤ ∆ 0.007 in MNCI for the 1st percentile as cutoff values for measurement quality. Strong measurement invariance is achieved when both metric and scalar invariance are met, and weak invariance is accomplished when only metric invariance is present (Dimitrov, 2010). Exemplar Review of a Psychometric Study The following section will include a review of an exemplar psychometric study based on the recommendations for EFA (see Figure 2) and CFA (see Table 1) that are provided in this manuscript. In 2020, I collaborated with Ryan Flinn on the development and validation of scores on the Mental Distress Response Scale (MDRS) for appraising how college students are likely to respond when encountering a peer in mental distress (Kalkbrenner & Flinn, 2020). A total of 13 items were entered into an EFA. Following the steps for EFA (see Figure 1), the sample size (N = 569) exceeded the guidelines for sample size that I published in my 2021 article (Kalkbrenner, 2021b), including an STV of 10:1 or 200 participants, whichever produces a larger sample. Flinn and I (2020) ensured that our 2020 study’s data were consistent with a normal distribution (skewness & kurtosis values ≤ ±1) and computed preliminary assumption checking, including inter-item correlation matrix, KMO (.73), and Bartlett’s test of sphericity (p < .001). An ML factor extraction method was employed, as the data were largely consistent (skewness & kurtosis values ≤ ±1) with a normal distribution. We used the three most rigorous factor retention criteria—percentage of variance accounted for, scree test, and parallel analysis—to extract a twofactor solution. An oblique factor rotation method (direct oblimin) was employed, as the two factors were correlated. We referred to the recommended factor retention criteria, including h2 values .30 to .99, factor loadings ≥ .40, and cross-loading ≥ .30, to eliminate one item with low commonalities and two cross-loading items. Using a research team, we named the first factor Diminish/Avoid, as each item that marked this factor reflected a dismissive or evasive response to encountering a peer in mental distress. The second factor was named Approach/Encourage because each item that marked this factor included a response to a peer in mental distress that was active and likely to help connect their peer to mental health support services.