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.
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An anonymous reviewer suggested this substantially generalized proof, the analogy to regression, and the application of that analogy to identifying circumstances where parceling does not worsen factor indeterminacy. We very much thank the reviewer for these remarkable insights.
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Rigdon, E.E., Becker, J. & Sarstedt, M. Parceling Cannot Reduce Factor Indeterminacy in Factor Analysis: A Research Note. Psychometrika 84, 772–780 (2019). https://doi.org/10.1007/s11336-019-09677-2
- factor analysis
- factor indeterminacy