Unrestricted factor analysis: A powerful alternative to confirmatory factor analysis

The gold standard for modeling multiple indicator measurement data is confirmatory factor analysis (CFA), which has many statistical advantages over traditional exploratory factor analysis (EFA). In most CFA applications, items are assumed to be pure indicators of the construct they intend to measure. However, despite our best efforts, this is often not the case. Cross-loadings incorrectly set to zero can only be expressed through the correlations between the factors, leading to biased factor correlations and to biased structural (regression) parameter estimates. This article introduces a third approach, which has emerged in the psychometric literature, viz., unrestricted factor analysis (UFA). UFA borrows strengths from both traditional EFA and CFA. In simulation studies, we show that ignoring cross-loadings even as low as .2 can substantially bias factor correlations when CFA is used and that even the commonly used guideline RMSEA <= .05 may be too lenient to guard against non-negligible bias in factor correlations in CFA. Next, we present two empirical applications using Schwartz's value theory, and electronic service quality. In the first case, UFA leads to much better model fit and more plausible regression estimates. In the second case, the difference is less dramatic but nevertheless, UFA provides richer results. We provide recommendations on when to use UFA vs. CFA.