Measurement invariance conventions and reporting: The state of the art and future directions for psychological research

“A uthor M anuscript A uthor M anuscript A uthor M anuscript A uthor M anuscript indices and criteria should be used to judge “practical” differences in model fit between groups (e.g., Chen, 2007; Cheung & Rensvold, 2002).”

“Overall, the Δχ2 was reported for 62.6% of tests, the change in CFI was reported for 73.2% of tests, and the change in another alternative fit index (e.g., ΔRMSEA, ΔTLI, ΔSRMR) was reported for 56.1% of tests.”

“Perhaps tests of many groups rarely appear in the literature because fewer researchers study many groups, measurement invariance is not achieved (e.g., the file drawer problem; Rosenthal, 1979), or model complexity causes researchers to shy away from tests with many groups.”

“Vandenberg and Lance (2000) soon after outlined 8 steps for testing measurement invariance, with the first 5 steps consisting of the main tests of measurement invariance.”

“Steenkamp and Baumgartner (1998) suggested that ideally more than half of items on a factor should be invariant.”

“) Although a required component for full factorial invariance (Meredith, 1993), testing for residual invariance is not a prerequisite for testing mean differences because the residuals are not part of the latent factor, so invariance”

“This criterion was used to obtain a wide range of fit indices and to be able to perform the invariance analysis comparing Groups 1 and 2 (see Putnick & Bornstein, 2016).”

“Following the guidelines proposed by Putnick and Bornstein [43], we evaluated model fit using the root mean square error of approximation (RMSEA) and the comparative fit index (CFI).”

“Once the most robust factor structure for the FCV-19S was established, measurement invariance analyses were performed to assess the psychometric equivalence (same struc - ture and meaning) of the construct across groups (Putnick & Bornstein, 2016 ).”

“A non-significant chi-square difference (Δχ2), and satisfactory fit indices (i.e., adding constraints of equality across gender does not worsen the fit) indicates gender invariance (Chen, 2007; Putnick & Bornstein, 2016).”

“Evidence of invariance was determined based on changes in fit indices: ΔCFI ≤ 0.010 and ΔRMSEA ≤ 0.015 [64, 65].”

“We can therefore conclude that the differences observed between countries are due to variations in prevalence rates, not discrepancies in participants’ interpretation of the instrument (Putnick & Bornstein, 2016; Vandenberg & Lance, 2000).”

“All analyses were conducted in SPSS 28.0 (IBM Corp.) and cross-verified for consistency with recommended practices in factor analysis and measurement invariance research [50].”

“…number of factors and respective items for each factor are the same across groups; metric invariance indicates that participants across groups understand and respond to items in the same way; scalar invariance would mean that latent scores can be compared across groups (Putnick & Bornstein, 2016).”

“Measurement invariance testing confirmed scalar invariance across time ( Δ CFI ≤ 0.008) and age groups ( Δ CFI ≤ 0.009) (Putnick and Bornstein, 2016). version of the Competitive State Anxiety Inventory-2 (CSAI-2) (Martens et al., 1990), adapted and normed for Chinese athletes by Zhu (1994).”