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.

Parceling Cannot Reduce Factor Indeterminacy in Factor Analysis: A Research Note.

Parceling-using composites of observed variables as indicators for a common factor-strengthens loadings, but reduces the number of indicators. Factor indeterminacy is reduced when there are many observed variables per factor, and when loadings and factor correlations are strong. It is proven that parceling cannot reduce factor indeterminacy. In special cases where the ratio of loading to residual variance is the same for all items included in each parcel, factor indeterminacy is unaffected by parceling. Otherwise, parceling worsens factor indeterminacy. While factor indeterminacy does not affect the parameter estimates, standard errors, or fit indices associated with a factor model, it does create uncertainty, which endangers valid inference.

Factor Indeterminacy as Metrological Uncertainty: Implications for Advancing Psychological Measurement.

Researchers have long been aware of the mathematics of factor indeterminacy. Yet, while occasionally discussed, the phenomenon is mostly ignored. In metrology, the measurement discipline of the physical sciences, uncertainty - distinct from both random error (but encompassing it) and systematic error - is a crucial characteristic of any measurement. This research argues that factor indeterminacy is uncertainty. Factor indeterminacy fundamentally threatens the validity of psychometric measurement, because it blurs the linkage between a common factor and the conceptual variable that the factor represents. Acknowledging and quantifying factor indeterminacy is important for progress in reducing this component of uncertainty in measurement, and thus improving psychological measurement over time. Based on our elaborations, we offer a range of recommendations toward achieving this goal.