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.

     

A comparative evaluation of factor- and component-based structural equation modelling approaches under (in)correct construct representations

Structural equation modelling (SEM) has evolved into two domains, factor-based and component-based, dependent on whether constructs are statistically represented as common factors or components. The two SEM domains are conceptually distinct, each assuming their own population models with either of the statistical construct proxies, and statistical SEM approaches should be used for estimating models whose construct representations correspond to what they assume. However, SEM approaches have often been evaluated and compared only under population factor models, providing misleading conclusions about their relative performance. This is partly because population component models and their relationships have not been clearly formulated. Also, it is of fundamental importance to examine how robust SEM approaches can be to potential misrepresentation of constructs because researchers may often lack clear theories to determine whether a factor or component is more representative of a given construct. Addressing these issues, this study begins by clarifying several population component models and their relationships and then provides a comprehensive evaluation of four SEM approaches – the maximum likelihood approach and factor score regression for factor-based SEM as well as generalized structured component analysis (GSCA) and partial least squares path modelling (PLSPM) for component-based SEM – under various experimental conditions. We confirm that the factor-based SEM approaches should be preferred for estimating factor models, whereas the component-based SEM approaches should be chosen for component models. Importantly, the component-based approaches are generally more robust to construct misrepresentation than the factor-based ones. Of the component-based approaches, GSCA should be chosen over PLSPM, regardless of whether or not constructs are misrepresented.     

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.