Understanding Composite-Based Structural Equation Modeling Methods From the Perspective of Regression Component Analysis

Regression component analysis (RCA) replaces the factors in a factor analysis model with weighted composites of the model’s observed variables. The weight matrix may be calculated from the factor model’s parameter estimates. Thus, RCA parameter estimates can be obtained using factor model software, but RCA composites have determinate scores, rather than the indeterminate scores of factors. Analytically, RCA equates to modeling with “regression method” factor scores, except that, while those scores will be inconsistent with the original factor model, they are strictly consistent with the RCA model. When the original factor model is strictly correct in the population and the composites in RCA are standardized, RCA parameter estimates replicate those from regression-weighted forms of partial least squares (PLS) path modeling and generalized structured component analysis (GSCA)—affirming that those methods also equate to modeling with regression method factor scores under the same conditions. Parallel measurement allows RCA to replicate both correlation weight and regression weight versions of PLS and GSCA. These results suggest that RCA and regression-weighted forms of PLS and GSCA are all consistent approaches for modeling data that conforms to a factor model. All analytical methods are described using one consistent symbol palette. Complete R syntax is provided.