Is More Ever Too Much? The Number of Indicators per Factor in Confirmatory Factor Analysis
Abstract
We evaluated whether "more is ever too much" for the number of indicators (p) per factor (p/f) in confirmatory factor analysis by varying sample size (N = 50-1000) and p/f (2-12 items per factor) in 35,000 Monte Carlo solutions. For all N's, solution behavior steadily improved (more proper solutions, more accurate parameter estimates, greater reliability) with increasing p/f. There was a compensatory relation between N and p/f: large p/f compensated for small N and large N compensated for small p/f, but large-N and large-p/f was best. A bias in the behavior of the χ(2) was also demonstrated where apparent goodness of fit declined with increasing p/f ratios even though approximating models were "true". Fit was similar for proper and improper solutions, as were parameter estimates form improper solutions not involving offending estimates. We also used the 12-p/f data to construct 2, 3, 4, or 6 parcels of items (e.g., two parcels of 6 items per factor, three parcels of 4 items per factor, etc.), but the 12-indicator (nonparceled) solutions were somewhat better behaved. At least for conditions in our simulation study, traditional "rules" implying fewer indicators should be used for smaller N may be inappropriate and researchers should consider using more indicators per factor that is evident in current practice.
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If the sample size is small, more observed indicators per factor could alleviate its impact.
“Generally, if the sample size is small more observed indicators per factor could alleviate its impact (Marsh et al., 1998; Marsh & Hau, 1999).”
From Applied Psychometrics: Sample Size and Sample Power Considerations in Factor Analysis (EFA, CFA) and SEM in General (2018) · cites this paper as Marsh et al., 1998
Cites
Factor-analytic methods of scale development in personality and clinical psychology
Comrey, A. L. (1988) · Journal of Consulting and Clinical Psychology · doi:10.1037/0022-006x.56.5.754 · Cited by 1,154 · see citing works
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Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003) · Department of Psychology - University of Koblenz-Landau · doi:10.23668/psycharchives.12784 · Cited by 8,975 · see citing works
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Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013) · Educational and Psychological Measurement · doi:10.1177/0013164413495237 · Cited by 3,931 · see citing works
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Reinartz, W., Haenlein, M., & Henseler, J. (2009) · International Journal of Research in Marketing · doi:10.1016/j.ijresmar.2009.08.001 · Cited by 2,906 · see citing works
The reliability of a two-item scale: Pearson, Cronbach, or spearman-brown?
Eisinga, R., Grotenhuis, M. T., & Pelzer, B. (2013) · International Journal of Public Health · doi:10.1007/s00038-012-0416-3 · Cited by 2,695 · see citing works
Skinner, E. A., Edge, K., Altman, J., & Sherwood, H. (2003) · Psychological Bulletin · doi:10.1037/0033-2909.129.2.216 · Cited by 2,639 · see citing works
Reporting practices in confirmatory factor analysis: an overview and some recommendations
Jackson, D. L., Gillaspy, J. A., & Purc-Stephenson, R. (2009) · Psychological Methods · doi:10.1037/a0014694 · Cited by 2,242 · see citing works
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Greco, L. A., Baer, R. A., & Smith, G. T. (2011) · Psychological Assessment · doi:10.1037/a0022819 · Cited by 685 · see citing works
Using parcels to convert path analysis models into latent variable models
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Jackson, D. L. (2001) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem0802_3 · Cited by 321 · see citing works
Hou, J., Wong, S. Y.-S., Lo, H. H.-M., Mak, W. W.-S., & Ma, H. S.-W. (2014) · Assessment · doi:10.1177/1073191113485121 · Cited by 215 · see citing works
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Brown, G. T. L., Peterson, E. R., & Yao, E. S. (2016) · British Journal of Educational Psychology · doi:10.1111/bjep.12126 · Cited by 198 · see citing works
Soenens, B., Luyckx, K., Vansteenkiste, M., Duriez, B., & Goossens, L. (2008) · Merrill-Palmer Quarterly · doi:10.1353/mpq.0.0005 · Cited by 140 · see citing works
Briggs‐Gowan, M. J., & Carter, A. S. (2007) · Infant Mental Health Journal · doi:10.1002/imhj.20154 · Cited by 123 · see citing works
Olsen, S. O., Tudoran, A. A., Honkanen, P., & Verplanken, B. (2016) · Psychology & Marketing · doi:10.1002/mar.20853 · Cited by 113 · see citing works
Burns, R. A., Crisp, D. A., & Burns, R. B. (2020) · British Journal of Educational Psychology · doi:10.1111/bjep.12265 · Cited by 109 · see citing works
Boone, L., Vansteenkiste, M., Soenens, B., Van der Kaap-Deeder, J., & Verstuyf, J. (2014) · Journal of Counseling Psychology · doi:10.1037/a0036418 · Cited by 100 · see citing works
Gunn, R. L., & Smith, G. T. (2010) · Psychology of Addictive Behaviors · doi:10.1037/a0020334 · Cited by 100 · see citing works
Chen, B., Vansteenkiste, M., Beyers, W., Soenens, B., & Van Petegem, S. (2013) · Journal of Cross-Cultural Psychology · doi:10.1177/0022022113480038 · Cited by 83 · see citing works
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Scott, A. J., Rowse, G., & Webb, T. L. (2017) · PLOS ONE · doi:10.1371/journal.pone.0186233 · Cited by 30 · see citing works
Chen, J., & Kouhsari, M. (2025) · Computers & Education · doi:10.1016/j.compedu.2024.105232 · Cited by 13 · see citing works
Profe, W. B., Wild, L. G., & Tredoux, C. (2021) · Journal of Social and Personal Relationships · doi:10.1177/02654075211000433 · Cited by 7 · see citing works
- Authors
- Marsh, H. W., Hau, K.-T., Balla, J. R., & Grayson, D.
- Affiliations
- The University of Sydney (AU)
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 1998-04
- Volume
- 33
- Issue
- 2
- Pages
- 181-220
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- OpenAlex
- W2158805524
- Cited by
- 1,307
- References
- 1
- Citations by year
- 2026: 56 · 2025: 64 · 2024: 78 · 2023: 85 · 2022: 90 · 2021: 96 · 2020: 72 · 2019: 65 · 2018: 57 · 2017: 52 · 2016: 51 · 2015: 51 · 2014: 58 · 2013: 64 · 2012: 47
- FWCI
- 22.09
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Multivariate Behavioral Research (publishedVersion)
- PubMed (publishedVersion)
- Research Bank (Australian Catholic University) (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Keywords
- confirmatory factor analysis, sample size, goodness of fit, chi-square test, improper solutions, parameter estimation accuracy, reliability statistics, parceling, Monte Carlo simulation
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