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.