Beyond Conventional Confirmatory Factor Analysis: Relaxing Model Constraints with Exploratory Structure Equation Model and Bayesian Estimation of Confirmatory Factor Analysis Modeling

BACKGROUND: Factor analysis represents an important analytical tool for social work researchers seeking to develop and examine evidence of the validity of our measurement tools. Confirmatory factor analysis (CFA) is particularly attractive to many researchers because of the requirement that theory and prior research be used to identify the factor structure of the measure that is being evaluated (Hurley et al., 1997). There is growing evidence from the extensive research on the development of personality measures, particular among those investigating the (Big) five-factor model (Marsh et al., 2009), that the requirement that indicators in CFA load on only one factor, the independent clusters model (ICM-CFA), is too restrictive and often lead to over-estimated factor correlations (Asparouhov & Muthén, 2009; Browne, 2001). Two advances in estimation of structural models, Exploratory Structural Equation Modeling (Asparouhov & Muthén, 2009) and Bayesian structural equation models (Asparouhov & Muthén, 2009; Rupp, Dey, & Zumbo, 2004) have given researchers the ability to specify less restrictive models that allow for a greater number cross-loadings. Exploratory and Bayesian structural equation modeling both allow for greater flexibility in the models that can be estimated, improve correspondence between exploratory and confirmatory factor analysis results, and more efficient model modification procedures within the context of CFA than are presently used (Asparouhov & Muthén, 2009; Muthén & Asparouhov, 2010).

PURPOSE: Using Mplus 6.0 this workshop will introduce participants to the estimation of CFA models with in both an Exploratory Structural Equation Modeling (ESEM) and Bayesian framework. It provides an overview of the means by which each approach extents researcher's ability to estimate models that are more accurate representations of the theoretical underpinnings of our research. Topics that will be covered: overview of Exploratory and Bayesian structural equation modeling estimation, new methods of model modification and evaluation (for example, the use of Posterior Predictive Probability to evaluate models). The workshop only assumes that participants have had some prior experience with CFA modeling. Three data sets will be used to illustrate the unique CFA modeling opportunities offered by ESEM and Bayesian based CFA modeling. Data from multiple waves of cross-sectional data use to develop and validate of an adult Rape Myth measure, data from the longitudinal study of Adolescent Future Interests Orientation and data from a cross-sectional study of middle and senior high school youth's multifaceted alienation will all be used to illustrate these modeling techniques.

LEARNING OBJECTIVES: At the end of the workshop participants will be familiar with the use of ESEM and Bayesian structural equation modeling techniques for the estimation of CFA models. They will learn new methods for the evaluation of CFA models that are only available using these two approaches.

IMPLICATIONS: ESEM and Bayesian models are valuable alternative to ICM-CFA models when those models don't fit the data well (and are not supported by theory). Both ESEM and Bayesian models will provide social work researchers considerable flexibility in addressing complex CFA structures that are often found in the development of measures of social phenomena.