https://doi.org/10.1177/1073191117711020 Assessment 1–17 © The Author(s) 2017 Reprints and permissions: sagepub.com/journalsPermissions.nav DOI: 10.1177/1073191117711020 journals.sagepub.com/home/asm Article Measurement invariance refers to the case that the same latent construct is measured by the same observed vari- ables, in a similar way across different measurement condi- tions. These conditions include subgroups of a population (e.g., national cultures, ethnic groups, gender, etc.), occa- sions of data collection (i.e., repeatedly measured data), or test-taking situations (e.g., paper/pencil vs. web-based tests; Meade & Wright, 2012). The establishment of measure- ment invariance ensures that cross-condition differences in observed variables reflect true changes among latent con- structs, rather than alterations in the psychometric proper- ties of the measures. Lately, measurement invariance has gained recognition as an important prerequisite for making meaningful comparisons in clinical assessments (Floyd & Widaman, 1995; Meredith & Teresi, 2006; Pentz & Chou, 1994). Multiple-group confirmatory factor analysis (CFA; Jöreskog, 1971; McGaw & Jöreskog, 1971) has widely been used to test measurement invariance by assessing the equivalence of factor models across groups, or factorial invariance (Meredith, 1993). Researchers have defined many levels of factorial invariance, primarily in terms of cross-group equality of model parameters such as factor loadings, intercepts, residual variances, and so on (e.g., Byrne, Shavelson, & Muthén, 1989; Horn & McArdle, 1992; Meredith, 1993; Millsap, 2011; Steenkamp & Baumgartner, 1998; Widaman & Reise, 1997; see also Vandenberg & Lance, 2000, for a review).When testing for a certain level of factorial invariance (such as the equiva- lence of factor loadings), full invariance is said to be achieved if all factor loadings can be constrained to be equivalent across groups; otherwise, when only a subset of those factor loadings is the same across groups, partial invariance is said to have occurred. As is often the case, full invariance is difficult to achieve in real-world research. For example, approximately half of the 75 reviewed empirical studies in Schmitt and Kuljanin (2008) included provisions for some level of partial invariance. Due to the frequent occurrence of partial invariance in empirical research, methodologists suggest using a model capable of accom- modating it in subsequent cross-group comparisons (e.g., Byrne et al., 1989; Cheung & Rensvold, 2002; Schmitt & Kuljanin, 2008; Vandenberg & Lance, 2000). Whether it is appropriate to use measures or tests with partial invariance is now an important issue in both empiri- cal and methodological research. Methodological study has shed some light on this issue. One line of inquiry concerns the impact of certain noninvariances on cross-group com- parisons using composite scores in which composites, 711020ASM XX X 10.1177/1073191117711020AssessmentShi et al. research-article 2017 1 University of Oklahoma, Norman, OK, USA 2 University of South Carolina, Columbia, SC, USA Corresponding Author: Dexin Shi, Department of Psychology, University of South Carolina, 1512 Pendleton Street, Barnwell College, Columbia, SC 29208, USA. Email: shid@mailbox.sc.edu The Impact of Partial Factorial Invariance on Cross-Group Comparisons Dexin Shi 1,2 , Hairong Song 1 , and Melanie D. Lewis 1 Abstract This study explored the impact of partial factorial invariance on cross-group comparisons of latent variables, including latent means, latent variances, structural relations (or correlations) with other constructs, and regression coefficients as predicting external variables. The results indicate that the estimates of factor mean differences are sensitive to violations of invariance on both factor loadings and intercepts. Noninvariant factor loadings were also found to influence the cross-group comparisons of factor variances and regression coefficients (slopes, in the raw metric) with external variables. However, cross-group comparisons of standardized slopes and interfactor correlations were not subject to noninvariance. Under conditions of partial invariance, we further compared the performance of four different model specification strategies. In general, fitting partially invariant models with all noninvariant parameters that were freely estimated yielded more accurate estimates of the parameters of interest. The implications of the major findings of this work, as well as recommendations and guidelines for future empirical researchers, are discussed below. Keywords partial factorial invariance, multiple group comparisons, CFA