Structural Equation Modeling With AMOS by Byrne Barbara M
Author:Byrne, Barbara M.
Language: eng
Format: epub
Publisher: Taylor and Francis
Figure 7.1 Initially hypothesized model of 20-item MBI structure for elementary and secondary teachers.
Establishing baseline models: The general notion
Because the estimation of baseline models involves no between-group constraints, the data can be analyzed separately for each group. However, in testing for invariance, equality constraints are imposed on particular parameters and, thus, the data for all groups must be analyzed simultaneously to obtain efficient estimates (Bentler, 2005; Jöreskog & Sörbom, 1996a); the pattern of fixed and free parameters nonetheless remains consistent with the baseline model specification for each group.4 However, it is important to note that because measuring instruments are often group specific in the way they operate, it is possible that these baseline models may not be completely identical across groups (see Bentler, 2005; Byrne, Shavelson, & Muthén, 1989). For example, it may be that the best-fitting model for one group includes an error covariance (see, e.g., Bentler, 2005) or a cross-loading (see, e.g., Byrne, 1988b, 2004; Reise, Widaman, & Pugh, 1993), whereas these parameters may not be specified for the other group. Presented with such findings, Byrne et al. (1989) showed that by implementing a condition of partial measurement invariance, multigroup analyses can still continue. As such, some but not all measurement parameters are constrained equal across groups in the testing for structural equivalence or latent factor mean differences. It is important to note, however, that over the intervening years, the concept of partial measurement equivalence has sparked a modest debate in the technical literature (see Millsap & Kwok, 2004; Widaman & Reise, 1997). Nonetheless, its application remains a popular strategy in testing for multigroup equivalence and is especially so in the area of cross-cultural research. The perspective taken in this book is consistent with our original postulation that a priori knowledge of major model specification differences is critical to the application of invariance-testing procedures.
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