Abstract
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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Notes
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.
References
Bandalos, D. L. (2002). The effects of item parceling on goodness-of-fit and parameter estimate bias in structural equation modeling. Structural Equation Modeling, 9(1), 78–102. https://doi.org/10.1207/S15328007SEM0901_5.
Bandalos, D. L. (2008). Is parceling really necessary? A comparison of results from item parceling and categorical variable methodology. Structural Equation Modeling, 15(2), 211–240. https://doi.org/10.1080/10705510801922340.
Bandalos, D. L., & Finney, S. J. (2001). Item parceling issues in structural equation modeling. In G. A. Marcoulides & R. E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 269–296). Mahwah: LEA.
Borsboom, D. (2005). Measuring the mind: Conceptual issues in contemporary psychometrics. Cambridge: Cambridge University.
Gentle, J. E. (2017). Matrix algebra (2nd ed.). Cham: Springer.
Guttman, L. (1955). The determinacy of factor score matrices with implications for five other basic problems of common-factor theory. British Journal of Statistical Psychology, 8(2), 65–81. https://doi.org/10.1111/j.2044-8317.1955.tb00321.x.
Haig, B. D., & Evers, C. W. (2016). Realist inquiry in social science. London: Sage.
Hall, R. J., Snell, A. F., & Foust, M. S. (1999). Item parceling strategies in SEM: Investigating the subtle effects of unmodeled secondary constructs. Organizational Research Methods, 2(3), 233–256. https://doi.org/10.1177/109442819923002.
Hoyle, R. H. (Ed.). (2014). Handbook of structural equation modeling. New York: Guilford Press.
Landis, R. S., Beal, D. J., & Tesluk, P. E. (2000). A comparison of approaches to forming composite measures in structural equation models. Organizational Research Methods, 3(2), 186–207. https://doi.org/10.1177/109442810032003.
Lastovicka, J. L., & Thamodaran, K. (1991). Common factor score estimates in multiple regression problems. Journal of Marketing Research, 28(1), 105–112. https://doi.org/10.1177/002224379102800109.
Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling, 9(2), 151–173. https://doi.org/10.1207/S15328007SEM0902_1.
Maraun, M. D. (1996). Metaphor taken as math: Indeterminacy in the factor analysis model. Multivariate Behavioral Research, 31(4), 517–538. https://doi.org/10.1207/s15327906mbr3104_6.
Marsh, H. W., Lüdtke, O., Nagengast, B., Morin, A. J., & Von Davier, M. (2013). Why item parcels are (almost) never appropriate: Two wrongs do not make a right—Camouflaging misspecification with item parcels in CFA models. Psychological Methods, 18(3), 257–284. https://doi.org/10.1037/a0032773.
Marsh, H. W., Hau, K.-T., Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33(2), 181–220. https://doi.org/10.1207/s15327906mbr3302_1.
Mulaik, S. A. (2010). Foundations of factor analysis (2nd ed.). Boca Raton: Chapman & Hall.
Plummer, B. (2000). To parcel or not to parcel: The effects of item parceling in confirmatory factor analysis. Providence: Dissertation, The University of Rhode Island.
Psillos, S. (1999). Scientific realism: How science tracks truth. Abingdon: Routledge.
Revelle, W. (2018). psych: Procedures for personality and psychological research. Evanston: Northwestern University. https://CRAN.R-project.org/package=psych Version = 1.8.12. Accessed 27 Jan 2019.
Rhemtulla, M. (2016). Population performance of SEM parceling strategies under measurement and structural model misspecification. Psychological Methods, 21(3), 348–368. https://doi.org/10.1037/met0000072.
Rigdon, E. E., Becker, J. M., & Sarstedt, M. (2019). Factor indeterminacy as metrological uncertainty: Implications for advancing psychological measurement. Multivariate Behavioral Research, 54(3), 429–443. https://doi.org/10.1080/00273171.2018.1535420.
Sass, D. A., & Smith, D. L. (2006). The effects of parceling unidimensional scales on structural parameter estimates in structural equation modeling. Structural Equation Modeling, 13(4), 566–586. https://doi.org/10.1207/s15328007sem1304_4.
Schönemann, P. H., & Haagen, K. (1987). On the use of factor scores for prediction. Biometrical Journal, 29(7), 835–847. https://doi.org/10.1002/bimj.4710290712.
Schönemann, P. H., & Steiger, J. H. (1978). On the validity of indeterminate factor scores. Bulletin of the Psychonomic Society, 12(4), 287–290. https://doi.org/10.3758/BF03329685.
Schönemann, P. H., & Wang, M.-M. (1972). Some new results on factor indeterminacy. Psychometrika, 37(1), 61–91. https://doi.org/10.1007/BF02291413.
Skrondal, A., & Laake, P. (2001). Regression among factor scores. Psychometrika, 66(4), 563–575. https://doi.org/10.1007/BF02296196.
Steiger, J. H. (1979). The relationship between external variables and common factors. Psychometrika, 44(1), 93–97. https://doi.org/10.1007/BF02293788.
Williams, L. J., & O’Boyle, E. H, Jr. (2008). Measurement models for linking latent variables and indicators: A review of human resource management research using parcels. Human Resource Management Review, 18, 233–242. https://doi.org/10.1016/j.hrmr.2008.07.002.
Wilson, E. B. (1928). The abilities of man: Their nature and measurement. Science, 67(1731), 244–248.
Yang, C., Nay, S., & Hoyle, R. H. (2010). Three approaches to using lengthy ordinal scales in structural equation models: Parceling, latent scoring, and shortening scales. Applied Psychological Measurement, 34(2), 122–142. https://doi.org/10.1177/0146621609338592.
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Rigdon, E.E., Becker, JM. & 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
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DOI: https://doi.org/10.1007/s11336-019-09677-2