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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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“These results are consistent with findings by Velicer and Fava (1998) and others.”
BackgroundResultInfluentialScale Development Research: A Content Analysis and Recommendations for Best Practices
Worthington, R. L., & Whittaker, T. A. (2006) · The Counseling Psychologist · doi:10.1177/0011000006288127 · Cited by 4,087
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“These characteristics of a model have also been shown to influence other important aspects of model output that are not under consideration in this study, such as the performance and stability of fit indices (see Jackson, 2001; Kim, 2005; Velicer & Fava, 1998).”
BackgroundCostello, A. B., & Osborne, J. (2005) · University of Massachusetts Amherst · doi:10.7275/jyj1-4868 · Cited by 10,297
“8 or greater (Velicer and Fava, 1998) – but this is very unlikely to occur in real data.”
BackgroundExploratory Factor Analysis: A Guide to Best Practice
Watkins, M. W. (2018) · Journal of Black Psychology · doi:10.1177/0095798418771807 · Cited by 2,218
“…specialists have conducted simulation studies and concluded that parallel analysis and MAP are the most accurate empirical estimates of the number of factors to retain and that scree is a useful subjective adjunct to the empirical estimates (Velicer, Eaton, & Fava, 2000; Velicer & Fava, 1998).”
BackgroundInfluentialKyriazos, T. A. (2018) · Psychology · doi:10.4236/psych.2018.98126 · Cited by 1,882
“Second regarding CFA and SEM 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.”
BackgroundMethodInfluentialLower bounds on sample size in structural equation modeling
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“…sample size are 200 to 500 participants (depending on communalities and other factors; Comrey & Lee, 1992; MacCallum, Widaman, Zhang, & Hong, 1999) and between a 5-to-20 and participant-to-variable ratio (Costello & Osborne, 2005; Hair, Black, Babin, Anderson, & Tatham, 2006; Velicer & Fava, 1998).”
Revisiting sample size and number of parameter estimates: some support for the N:q hypothesis
Jackson, D. L. (2003) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem1001_6 · Cited by 1,254
“As noted previously, the reliability of the variables (strength of association between the variable and factor) has been found to influence CSM solutions (e.g., Anderson & Gerbing, 1984; Bandalos, 1997; Velicer & Fava, 1998).”
BackgroundMethodResultDelineating the Structure of Normal and Abnormal Personality: An Integrative Hierarchical Approach.
Markon, K. E., Krueger, R. F., & Watson, D. (2005) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.88.1.139 · Cited by 1,249
Exploratory Factor Analysis With Small Sample Sizes
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“A number of studies have discussed the effects of sample size and p/f on the proportion of sample solutions exhibiting a Heywood case (or improper solutions; e.g., Gerbing & Anderson, 1987; Marsh et al., 1998; Velicer & Fava, 1998).”
BackgroundInfluentialSample Size in Factor Analysis: The Role of Model Error
MacCallum, R. C., Widaman, K. F., Preacher, K. J., & Hong, S. (2001) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3604_06 · Cited by 1,143
“This study extends recent work by MacCallum et al. (1999) and Velicer and Fava (1998), as well as earlier MULTIVARIATE BEHAVIORAL RESEARCH 635 studies of this issue, which made use of the context where no model error was present.”
MethodResultInfluentialThe Jefferson Scale of Physician Empathy: Development and Preliminary Psychometric Data
Hojat, M., Mangione, S., Nasca, T. J., Cohen, M. J. M., Gonnella, J. S., Erdmann, J. B., Veloski, J. J., & Magee, M. (2001) · Educational and Psychological Measurement · doi:10.1177/00131640121971158 · Cited by 1,052
“According to Velicer and Fava (1998), a minimum number of three items per factor is required for a stable factor.”
BackgroundRussell, D. W. (2002) · Personality and Social Psychology Bulletin · doi:10.1177/014616702237645 · Cited by 954
“Technically speaking, principal components analysis does not represent a factor analysis, given that the method does not involve the assumption that you are extracting common factors underlying a set of measures (see discussion by Fabrigar, Wegener, MacCallum, & Strahan, 1999; Velicer & Fava, 1998).”
Velicer, W. F., Eaton, C. A., & Fava, J. L. (2000) · Springer eBooks · doi:10.1007/978-1-4615-4397-8_3 · Cited by 886
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“…most of our items ultimately had moderate communalities (MacCallum, Widaman, Zhang, & Hong, 1999) and that all of our factors were overdetermined (Velicer & Fava, 1998), this sample size is consistent with recommended estimates that allow a stable interpretation of the results (Fabrigar,…”
An item selection procedure to maximise scale reliability and validity
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“Results of other studies suggest that sample size is less influential on the stability of factor loadings as the communalities of the variables increase (see, for example, Pennell, 1968; and Velicer & Fava, 1998).”
BackgroundSample Size Planning for Statistical Power and Accuracy in Parameter Estimation
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“MacCallum et al. (1999, 2001), Hogarty et al. (2005), Nasser & Wisenbaker (2001), and Velicer & Fava (1998) each review the existing literature and show that, in general, such rules of thumb regarding necessary sample size are oversimplified and should not be trusted.”
BackgroundEvaluating the Use of Exploratory Factor Analysis in Developmental Disability Psychological Research
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“Following others, we argue that only factors or scales containing at least three variables are viable (e.g., Glorfeld, 1995; Velicer & Fava, 1998; Zwick & Velicer, 1986).”
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“To assess the degree of factor recovery, two indices were computed: K, the average coefficient of congruence across the m factors (Tucker, 1951); and g, the root mean squared deviation between sample and population loadings (Velicer and Fava, 1998).”
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“Third, the current study only retained factors with at least three items, per the suggestions of prior research (Little, Lindenberger, & Nesselroade, 1999; Raubenheimer, 2004; Velicer & Fava, 1998).”
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“the standardized mean difference) between the g of PAF and the g of MLFA, with g defined as the root mean-squared difference between the sample and population loading matrices [52]: g = √√√ trace [( − ̂)′( − ̂)]”
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“…that an adequate sample size for factor analysis depends on the communalities of measured variables and the number of variables with substantial loadings per factor, rather than on the number of variables per se (Guadagnoli & Velicer, 1988 ; MacCallum et al., 1999 ; Velicer & Fava, 1998 ).”
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“We excluded countries where we had less than 150 responses, given the recommendation that there should be at least 10 cases for each item in the instrument being used (Hinkin, 2005; Nunnally, 1978; Velicer & Fava, 1998).”
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“The absolute sample size exceeds most suggestions found in the literature (n>100 Hatcher 1994; Malhotra and Grover, 1998; n=100-200 Velicer and Fava 1998) and is similar to other e-business studies over the last ten years, for example, Autry et al (2010, n=195), Cullen and Taylor (2009, n=153),…”
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“166], and Velicer and Fava [[79], p.”
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“Item 5 was omitted due to a low item ( .40) loading result (Velicer and Fava 1998).”
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“A second set of criteria involves component saturation (when components contain multiple moderate to large loadings) and component identification (when components load at least three variables; Velicer & Fava, 1998; Zwick & Velicer, 1986).”
BackgroundPsychological Antecedents of Risk-Taking Behavior in Construction
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“Guadagnoli and Velicer argued that components indicated by four or more variables loading higher than .60 can be interpreted regardless of sample size (Velicer & Fava, 1998, reduced this criterion to three or more large loadings).”
BackgroundMethodInfluentialDevelopment of a scale to measure adults' perceptions of health: Preliminary findings
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“…of the data such as the magnitude of the communalities, magnitudes of the loadings, the number of factors, and the number of variables per factors (e.g., de Winter, Dodou, & Wieringa, 2009; Gagn e & Hancock, 2006; MacCallum et al., 1999; Mundfrom, Shaw, & Ke, 2005; Velicer & Fava, 1998).”
BackgroundPrinciples of Exploratory Factor Analysis.
Goldberg, L. R., & Velicer, W. F. (2006) · Cited by 145
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Critical Consciousness and Vocational Development Among Latina/o High School Youth
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“A factor with fewer than 3 items is generally weak and unstable (Little, Lindenberger, & Nesselroade, 1999; Velicer & Fava, 1998), thus we developed an additional Critical Behavior item.”
BackgroundGuerci, M., & Pedrini, M. (2013) · The International Journal of Human Resource Management · doi:10.1080/09585192.2013.860388 · Cited by 154
“Although the sample size of 89 is below the generally accepted minimum sample for factor analysis (100 observations) (Tabachnick and Fidell 2007), we felt that, on the basis of methodological studies indicating that the subject-to-variable (STV) ratio is a second reliable criteria for assessing the right sample size,…”
MethodGutiérrez, X. (2013) · Studies in Second Language Acquisition · doi:10.1017/s0272263113000041 · Cited by 149
“Furthermore, Pennell ( 1968 ), Velicer, Peacock, and Jackson ( 1982 ), Velicer and Fava ( 1998 ), and MacCallum et al. ( 1999 ) found that the necessary sample size depends mainly on the level of communality of the variables and, to a lesser extent, on the level of overdetermination of the factors.”
BackgroundThe Development of a Virtue Ethics Scale
Shanahan, K. J., & Hyman, M. R. (2003) · Journal of Business Ethics · doi:10.1023/a:1021914218659 · Cited by 131
Selecting the “Best” Factor Structure and Moving Measurement Validation Forward: An Illustration
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“The existence of too few items per factor becomes not only an issue of model identification and replication (Bollen, 1989; Little, Lindenberger, & Nesselroade, 1999; Velicer & Fava, 1998), but also a matter of construct underrepresentation (Kaplan & Saccuzzo, 2008).”
BackgroundBrown, T. A., White, K. S., Forsyth, J. P., & Barlow, D. H. (2004) · Behavior Therapy · doi:10.1016/s0005-7894(04)80005-4 · Cited by 129
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“It is generally recommended that variable and subject sampling are optimized for factor/principal components analysis–based methods and/or that there be more than 100 subjects involved in validation (Terwee et al., 2007; Velicer & Fava, 1998).”
MethodExploratory factor analysis in transportation research: Current practices and recommendations
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“guidelines (Guadagnoli and Velicer 1988; Steger 2006; Velicer and Fava 1998).”
BackgroundSocial Relationships and PTSD Symptomatology in Combat Veterans
Wilcox, S. (2010) · Psychological Trauma Theory Research Practice and Policy · doi:10.1037/a0019062 · Cited by 115
Chu, J. P., Floyd, R. M., Diep, H., Pardo, S. T., Goldblum, P. B., & Bongar, B. M. (2013) · Psychological Assessment · doi:10.1037/a0031264 · Cited by 117
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“An item with communality of less than 0.40 was removed from the analysis (Velicer & Fava, 1998) and the PCA was computed again.”
MethodInfluentialInternal disinhibition predicts weight regain following weight loss and weight loss maintenance
Niemeier, H. M., Phelan, S., Fava, J. L., & Wing, R. R. (2007) · Obesity · doi:10.1038/oby.2007.295 · Cited by 114
Self-citationAchenbach, T. M., Bernstein, A., & Dumenci, L. (2005) · Journal of Personality Assessment · doi:10.1207/s15327752jpa8401_10 · Cited by 110
“The reproducibility of factors was assessed according to the criteria originally proposed by Guadagnoli and Velicer (1988) and later validated by Velicer and Fava (1998): a minimum sample size of 150 and either (a) a minimum of four items with standardized loadings ≥ .60 on the target factor or (b)…”
MethodWho are my family members? Bridging and binding social capital in family configurations
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“Several factors in the initial analyses are associated with two rather than three terms, a threshold that some consider as a minimum for reliable factors (Velicer & Fava, 1998).”
BackgroundNasser, F. (2004) · Journal of Statistics Education · doi:10.1080/10691898.2004.11910717 · Cited by 111
Exploratory factor analysis with small sample sizes: A comparison of three approaches
Jung, S. (2013) · Behavioural Processes · doi:10.1016/j.beproc.2012.11.016 · Cited by 109
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VALIDATING GRAMMATICALITY JUDGMENT TESTS
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“MacCallum, Widaman, Zhang, and Hong (1999) and Velicer and Fava (1998) provide a thorough review of studies investigating the role of sample size in factor analysis.”
BackgroundAn assessment of dental students' empathy levels in Malaysia
Babar, M. G., Omar, H., Lim, L. P., Khan, S. A., Mitha, S., Ahmad, S. F., & Hasan, S. S. (2013) · International Journal of Medical Education · doi:10.5116/ijme.5259.4513 · Cited by 107
KIEFFER, M. J., BIANCAROSA, G., & MANCILLA-MARTINEZ, J. (2013) · Applied Psycholinguistics · doi:10.1017/s0142716411000920 · Cited by 105
“…awareness However, as demonstrated by the reviews of research in quantitative methods conducted by MacCallum, Widaman, Zhang, and Hong (1999) and by Velicer and Fava (1998), such simple rules of thumb are invalid, because they do not account for the fact that adequate sample size will always…”
MethodThe relation between firm size and R&D productivity in different technological regimes
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The Scale of Ethnic Experience: Development and Psychometric Properties
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“Retention criteria (Guadagnoli & Velicer, 1988; Velicer & Fava, 1998) proposed in the literature have suggested the acceptability of small number of items (as few as 3) when sample sizes are relatively large, and item loadings are very high (.80).”
BackgroundAssociations of Environmental Factors With Quality of Life in Older Adults
Gobbens, R. J. J., & van Assen, M. A. L. M. (2017) · The Gerontologist · doi:10.1093/geront/gnx051 · Cited by 101
“…strategy, which is to only retain a factor having at least three items (i) with sufficiently high factor loadings (at least 0.3, preferably much higher if the number of items loading on the factor is small), and that (ii) load higher on this factor than on other factors (Velicer & Fava, 1998).”
BackgroundInfluentialGroden, J., Diller, A., Bausman, M., Velicer, W., Norman, G., & Cautela, J. (2001) · Journal of Autism and Developmental Disorders · doi:10.1023/a:1010755300436 · Cited by 124
Self-citationPark, S., Kang, M., & Kim, E. (2014) · Computers in Human Behavior · doi:10.1016/j.chb.2014.06.005 · Cited by 98
“This is because measuring a latent variable through two observed variables may lead to parameter estimate bias (Velicer & Fava, 1998).”
BackgroundExploring the '5Cs' of Positive Youth Development in sport.
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Different sides of the same coin? Intercorrelations of cognitive biases in schizophrenia
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“Others have recommended samples sizes in the range of 100 200 persons (e.g., Guadagnoli & Velicer, 1988; Velicer & Fava, 1998).”
BackgroundSome things you should know about structural equation modeling but never thought to ask
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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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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