Equivalence of Measurement Models: How to Conduct Multiple Group Confirmatory Factor Analysis with a Detailed Example Using the Daily Spiritual Experience Scale

Multiple group confirmatory factor analysis (CFA) involves simultaneous CFAs in two or more groups using separate variance-covariance matrices (or raw data) for each group. The equivalence or invariance of measurement can be tested by placing equality constraints on model parameters (i.e., requiring parts of the model to be equivalent across groups). This approach allows us to say whether a measure can be used in groups beyond those it was created for or to test how well a measure works across different populations. It may also help identify modifications needed for specific populations or instances when a measure is not appropriate for use in a different population from the one it was created for. This workshop will focus on using multiple group CFA to examine the appropriateness of CFA models across groups or populations. CFA focuses on relationships between observed variables and latent variables and allows one to examine equivalence (or invariance) of CFA models across groups, populations, or time. By testing invariance we can identify items that have different meanings for different populations. Multiple group CFA can also be used to identify different relationships across groups among observed variables and latent variables (i.e., different factor structures). The steps involved in conducting a multiple group CFA will be presented and two different approaches will be discussed. Several considerations for conducting a multiple group CFA will be addressed, such as marker variable selection, chi-square difference test, use of large sample sizes, and partial measurement invariance. A detailed example of a multiple group CFA on the Daily Spiritual Experience Scale (DSES) (Underwood & Teresi, 2002) will be presented. Data from two studies, one of kinship care providers and the other foster care providers, are used to illustrate the process. Although both groups consist of mostly women from a large city, the groups differed in terms of education, marital status and employment. Further, whereas both groups were predominantly African-American, one group had a smaller proportion of non-African-American participants than the other group. The one factor DSES model fit well in both groups. However, when looked at in a multi-group analysis it was found that constraining the factor loadings to be equal degraded the fit. Demographic differences between the groups provide plausible explanations for the differences found and will be discussed. In addition to the information described above, the authors will present several examples of multiple group CFAs from the social work literature and handouts for the detailed DSES example will be provided. This is one of the more complex uses of CFA, and this workshop is intended to introduce the topic; additional resources and examples from the literature will be provided at the end of the workshop for more information. Participants are welcome to ask questions throughout and discussion will be encouraged.