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Affects of variable and subject sampling on factor pattern recovery.
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“the guidelines of Velicer and Fava (1998) about the size of the factor loadings and the number of variables as a function of the sample size are pertinent in CFA/SEM too.”
From Applied Psychometrics: Sample Size and Sample Power Considerations in Factor Analysis (EFA, CFA) and SEM in General (2018) · cites this paper as Velicer and Fava (1998)
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“…used in several of the EFA studies are questionable, because (a) they used varimax rotation when factors were known to be correlated and (b) the sample sizes were somewhat small for EFA, as per the recommendations of Velicer and Fava (1998) to guarantee stable estimates of pattern coefficients.”
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“Additionally, 4 new items were generated in this study to examine conference as a point of attachment, which is in agreement with previous scholars’ recommendations of having 3 to 5 items representing a factor (Velicer & Fava, 1998).”
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“Indeed, a large sample size in factor analysis has been found to favorably influence the percentage of proper solutions, and the accuracy and sampling variability of parameter estimates (Velicer & Fava, 1998).”
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“8% of the cumulative variance), but one item (question 14) cross-loaded, and removing it would result in a component with only 2 items, which is generally inappropriate for a subscale (Little et al., 1999; Velicer and Fava, 1998).”
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“All except one (g40) of the extracted communalities were above .30 (M = .578, SD = .116; Velicer & Fava, 1998).”
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“Prior research has shown them to be meaningful conditions for differentiating the performance of factor analysis procedures (e.g., Velicer and Fava, 1998; MacCallum et al., 1999; Timmerman and Lorenzo-Seva, 2011).”
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“8), which maximizes the sample-to-population fit for the extracted factors (Velicer and Fava, 1998).”
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“…very simple structure and Velicer’s minimal average partial test), we submitted these variables to factor analysis (for which a 10:1 subject-to-ratio is recommended - e.g., Velicer & Fava, 1998, p. 232 -, whereas our design involved a higher ratio of 13.2:1, suggesting an adequate sample size)47.”
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“During several attempts of rotation, a total of five items were eliminated because they did not contribute to a simple factor structure (cross-loaded in different factors), or failed to have a primary factor loading of .4 or above (Field, 2009; Velicer & Fava, 1998).”
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“Findings of studies such as (Hogarty et al., 2005; MacCallum et al., 2001; Mundfrom et al., 2005; Velicer and Fava, 1998) revealed that the sample size for quantitative analysis is chosen based upon the ratio of variables under investigation and the expected factors.”
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“The sample size was determined by considering 10 cases for each of the 21 items in order to develop a factorial analysis (Velicer and Fava 1998).”
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“…the second issue, simulation studies found that a low number of indicators per factor can lead to unstable solutions or underidentification and can prevent a correct factor recovery (Costello & Osborne, 2005; de Winter & Dodou, 2012; MacCallum, Widaman, Zhang, & Hong, 1999; Velicer & Fava, 1998).”
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“Velicer and Fava (1998) also noted that three variables per factor in a sample are a bare minimum requirement for recovering a population factor pattern.”
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“In neither factor, notable cross-loadings emerged (Costello and Osborne 2005; Velicer and Fava 1998).”
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“First, the data met the recommended minimum sample size of 100 (MacCallum, Widaman, Zhang, & Hong, 1999) and have a ratio of at least 10 cases for each item in the instrument (Velicer & Fava, 1998).”
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“There is considerable debate around the requisite sample size for conducting a factor analysis and whether the criteria of the total sample size or the subjects-to-variables ratio should be used (MacCallum et al ., 1999; Velicer and Fava, 1998).”
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“The importance of large communalities in diminishing the effects of small datasets for performing FA has been already pointed out in a series of studies (e.g. Pennell, 1968; Velicer, Peacock and Jackson, 1982; Velicer and Fava, 1998 ).”
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“However, empirical studies have repeatedly shown that these rules of thumb are false; the adequacy of a factor solution cannot be predicted from a participant-to-variable ratio (Guadagnoli & Velicer, 1988; MacCallum, Widaman, Zhang, & Hong, 1999; Velicer & Fava, 1998).”
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“Final exploratory models were determined viable when resulting factors included (a) at least three items (Velicer & Fava, 1998), (b) item factor pattern coefficients (loadings) were ≥ .40 (promax rotation κ = 4) (Stevens, 2009), (c) achieved simple structure (items saliently loaded on only one…”
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“The development of 4-item scales also exceeds the recommendation of a minimum of three items for scales (Little, Lindenberger, & Nesselroade, 1999; Spector, 1992; Velicer & Fava, 1998).”
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“33 The items went through cognitive and pilot testing to ensure their comprehensibility.”
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“Each subgroup consisted of at least 98 participants, which is an adequate sample size for the model to converge (Velicer & Fava, 1998).”
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“According to Velicer and Fava, a minimum of 3 items are required for a stable factor structure (Velicer and Fava, 1998).”
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“In addition, structural models would run more logical and consistent when a large sample is included (Boomsma, 1982; Gagné & Hancock, 2006; Velicer & Fava, 1998).”
BackgroundVveinhardt, J., & Gulbovaitė, E. (2018) · Oeconomia Copernicana · doi:10.24136/oc.2018.028 · Cited by 16
“As one can see, it seems that these conditions would not comply with the subscale of professional values, but according to other authors (Velicer & Fava, 1998), the Oeconomia Copernicana, 9(3), 545–571 556 minimum factor loading cannot be lower than 0.4, as the lower one shows that there is an…”
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“According to Velicer and Fava [18], a minimum of three items per factor is required for a stable factor.”
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“For example, as more items are obtained for each factor, the tendency for the factor to be replicated is higher [81], [82].”
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“The sample we chose to build the scale from is statistically sufficient [29, 30]; however, the topic we chose is so varied, vast, and complex that it certainly deserves a larger sample as well as a different approach to the research.”
ResultMeier, L., & Oros, L. B. (2018) · Psykhe (Santiago) · doi:10.7764/psykhe.27.2.1169 · Cited by 16
Li, L., Niu, Z., Griffiths, M. D., & Mei, S. (2022) · International Journal of Mental Health and Addiction · doi:10.1007/s11469-022-00857-3 · Cited by 21
“Every factor should retain at least three items (Maccallum et al., 1999; Velicer & Fava, 1998).”
Empathy level towards patients among thai dental students: a cross-sectional study
Detsomboonrat, P., Theppanich, S., Banyen, S., Hongviphat, S., Khamnil, Y., Lapauthaya, K., Somboonsavatdee, A., & Min, S. N. (2023) · BMC Oral Health · doi:10.1186/s12903-023-02891-6 · Cited by 15
“Among the five factors of the eigenvalues > 1, only the first three factors met the criteria in which at least three items per factor are necessary for a stable factor [21].”
BackgroundEstablishing the Brief Assessment of Cognition - Short form
Lam, M., Wang, M., Huang, W., Eng, G. K., Rapisarda, A., Kraus, M., Kang, S., Keefe, R. S. E., & Lee, J. (2017) · Journal of Psychiatric Research · doi:10.1016/j.jpsychires.2017.05.006 · Cited by 14
“Three item solutions were chosen from prior work that suggests a minimum three items were necessary for stable factors (Anderson and Rubin, 1956; McDonald and Krane, 1979, 1977; Rindskopf, 1984; Velicer and Fava, 1998).”
MethodRobot's Impression of Appearance and Their Trustworthy and Emotion Richness
Matsui, T., & Yamada, S. (2018) · IEEE RO-MAN · doi:10.1109/roman.2018.8525796 · Cited by 15
“In general, one factor needs at least three variables[38].”
BackgroundPsychometry and estimation of cutoff points of Jefferson Scale of empathy in dental students
Diaz, V., Reyes‐Reyes, A., Calzadilla, A., Martínez, P. T., González, E., Bilbao, J., Martínez, F. D. G., Estrada-Méndez, N., Mesa, N. F., Sepúlveda, W., et al. (2020) · Journal of Dental Education · doi:10.1002/jdd.12444 · Cited by 15
University chemistry students' learning approaches and willingness to change major
Lastusaari, M., & Murtonen, M. (2013) · Chemistry Education Research and Practice · doi:10.1039/c3rp00045a · Cited by 15
Boehlen, F. H., Herzog, W., Schellberg, D., Maatouk, I., Saum, K.-U., Brenner, H., & Wild, B. (2016) · Aging & Mental Health · doi:10.1080/13607863.2016.1220918 · Cited by 15
“In accordance with Velicer and Fava (1998), we decided to work with a minimum factor loading of >0.4, representing moderate to strong communality.”
MethodInfluentialDeveloping a Genetically Informative Measure of Alcohol Consumption Using Past-12-Month Indices
Arpana Agrawal, A., Lynskey, M. T., Heath, A. C., & Chassin, L. (2011) · Journal of Studies on Alcohol and Drugs · doi:10.15288/jsad.2011.72.444 · Cited by 15
“Because four alcohol consumption indices were used, exploratory factor analyses were not performed (i.e., too few variables for more than one factor to be extracted; Velicer and Fava, 1998).”
MethodCivic Engagement and Personality: Associations with the Big Five and the Dark Triad
Rico‐Bordera, P., Piqueras, J. A., Soto‐Sanz, V., Rodríguez‐Jiménez, T., Marzo, J. C., Galán, M., & Pineda, D. (2023) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph20032126 · Cited by 14
“To determine the sample size (convenience sampling), we allocated several observations 6 to 10 times greater than the variables [48].”
Mallin, M. L., Hancock, T. D., Pullins, E. B., & Johnson, C. (2025) · Industrial Marketing Management · doi:10.1016/j.indmarman.2025.01.013 · Cited by 17
PEOPLE'S EVALUATION TOWARDS MEDIA FAÇADE AS NEW URBAN LANDMARKS AT NIGHT
Moghaddam, E. V., & Ibrahim, R. (2016) · International Journal of Architectural Research Archnet-IJAR · doi:10.26687/archnet-ijar.v10i1.871 · Cited by 14
Sanz, A. F., Serrano, J. R., Meza, H. T., & Moreno, J. M. (2021) · Neurología (English Edition) · doi:10.1016/j.nrleng.2019.03.019 · Cited by 14
COVID-19 Impact Battery: Development and Validation
Schmidt, N. B., Allan, N. P., Koscinski, B., Mathes, B. M., Eackles, K., Accorso, C., Saulnier, K. G., Allan, D. M., Potter, K., Garey, L., et al. (2021) · Journal of Psychopathology and Behavioral Assessment · doi:10.1007/s10862-021-09919-7 · Cited by 14
“Acceptable factors were defined as factors with three or more items (Velicer & Fava, 1998).”
Background
Metadata
- Authors
- Velicer, W. F., & Fava, J. L.
- Affiliations
- University of Rhode Island (US)
- Venue
- Psychological Methods
- Published
- 1998-06
- Volume
- 3
- Issue
- 2
- Pages
- 231-251
- ISSN
- 1082-989X (ISSN-L)
- 1939-1463
- OpenAlex
- W2014533626
- Cited by
- 998
- References
- 97
- Citations by year
- 2026: 34 · 2025: 47 · 2024: 53 · 2023: 46 · 2022: 48 · 2021: 55 · 2020: 70 · 2019: 49 · 2018: 64 · 2017: 65 · 2016: 56 · 2015: 51 · 2014: 62 · 2013: 55 · 2012: 48
- FWCI
- 11.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychological Methods (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- variable sampling, sample size, factor analysis
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