The Unified Approach for Model Evaluation in Structural Equation Modeling

Practical fit indices have been widely used for model fit evaluation in Structural Equation Modeling. This dissertation discusses the properties of the fit indices including their influencing factors. These properties prevent researchers from deriving one-size-fit-all cutoffs for the fit indices. In addition, the past simulation studies on model fit evaluation have several limitations. The major limitation is that most studies have focused on test of exact fit rather than approximate fit which is not consistent with the goal of practical fit indices. This dissertation reviews alternative approaches to account for the limitations and proposes a unified method for model fit evaluation combining the advantages of the alternative approaches. The unified approach allows researchers to test approximate fit and take into account sampling error in model evaluation. Two simulation studies are conducted to investigate the performance of the unified approach comparing to the other model fit evaluation methods. Two types of models are included in this study: confirmatory factor analysis and growth curve models. The results show that the unified approach appropriately rejects severely misspecified models and retains trivially misspecified models across all types of misspecification. Furthermore, the rejection rates are negligibly influenced by model characteristics and sample size. The other model evaluation methods do not have all of the desired properties described above. The unified approach, however, does not always provide model decision when sample size is low or when the level of maximal trivial misspecification specified by users is close to the actual degree of misspecification. If sample size is high and the level of specified maximal trivial misspecification is either lower or higher than the actual degree of misspecification, the unified approach is able to decide between model retention and model rejection. The extensions of the unified approach for nonnormal distribution, missing data, or nested model comparison are provided

Ignoring Clustering in Confirmatory Factor Analysis: Some Consequences for Model Fit and Standardized Parameter Estimates

In many situations, researchers collect multilevel (clustered or nested) data yet analyze the data either ignoring the clustering (disaggregation) or averaging the micro-level units within each cluster and analyzing the aggregated data at the macro level (aggregation). In this study we investigate the effects of ignoring the nested nature of data in confirmatory factor analysis (CFA). The bias incurred by ignoring clustering is examined in terms of model fit and standardized parameter estimates, which are usually of interest to researchers who use CFA. We find that the disaggregation approach increases model misfit, especially when the intraclass correlation (ICC) is high, whereas the aggregation approach results in accurate detection of model misfit in the macro level. Standardized parameter estimates from the disaggregation and aggregation approaches are deviated toward the values of the macro-and micro-level standardized parameter estimates, respectively. The degree of deviation depends on ICC and cluster size, particularly for the aggregation method. The standard errors of standardized parameter estimates from the disaggregation approach depend on the macro-level item communalities. Those from the aggregation approach underestimate the standard errors in multilevel CFA (MCFA), especially when ICC is low. Thus, we conclude that MCFA or an alternative approach should be used if possible