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## Sample size in factor analysis

Venue: | Psychol. Methods |

Citations: | 189 - 4 self |

### Citations

459 |
Power analysis and determination of sample size for covariance structure modeling
- MacCallum, Browne, et al.
- 1996
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Citation Context ... size thai is sufficient to achieve that objective might be somewhat different from one that is sufficient to achieve some other objective, such as a specified level of nower for a test of model fit (=-=MacCallum, Browne, & Sugawara, 1996-=-) or standard errors of factor loading -. that are adequately small by some definition. An interesting topic for future study would be the consistency of sample sizes required to meet these various ob... |

258 |
Factor Analysis as a Statistical Method
- Lawley, Maxwell
- 1971
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Citation Context ...he loadings will have smaller standard errors). Formulas for estimating standard errors of factor loadings have been developed for various types of unrelated loadings (Girshick, 1939; Jennrich, 1974; =-=Lawley & Maxwell, 1971-=-) and rotated loadings (Archer & Jennrich, 1973; Jennrich, 1973, 1974). Cudeck and O'Dell (1994) reviewed the literature on this subject and provided further developments for obtaining standard errors... |

204 |
A first course in factor analysis
- Comrey, Lee
- 1992
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Citation Context ...ence or support that is provided for any of them. R ather, most of them seem to represent general guidelines developed from substantial experience on the part of their supporters. Some authors (e.g., =-=Comrey & Lee, 1992-=-) placed the sample size question into the context of the need to make standard errors of correlation coefficients adequately small so that ensuing factor analyses of those correlations would yield st... |

144 |
The foundation of factor analysis
- Mulaik
- 1972
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Citation Context ...ative of closer correspondence between sample and population factors or, in other words, more accurate recovery of the population factors in the sample solution. Several authors (e.g., Gorsuch, 1983; =-=Mulaik, 1972-=-) have suggested a rule of thumb whereby good matching of factors is indicated by a congruence coefficient of .90 or greater. However, on the basis of results obtained by Korth and Tucker (1975), as w... |

107 |
The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis
- Anderson, Gerbing
- 1984
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Citation Context ...ne or more unique variances (Heywood cases). Such solutions were expected under some of the conditions in our design. Several studies of confirmatory factor analysis and structural equation modeling (=-=Anderson & Gerbing, 1984-=-; Boomsma, 1985; Gerbing & Anderson, 1987; Velicer & Fava, 1998) have found nonconvergence and improper solutions to be more frequent with small N and poorly defined latent variables. McDonald (1985, ... |

83 | The scientific use of factor analysis - Cattell - 1978 |

82 | Psychometric methods (2nd ed - Guilford - 1954 |

80 | Factor analysis and related methods - McDonald - 1985 |

76 | Modern factor analysis (3rd ed - Harman - 1976 |

73 |
Designing experiments and analyzing data
- Maxwell, Delaney
- 2004
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Citation Context ...esulis of the three-way ANOVA for K, including effec t-size estimates using to2 values. This measure provides an estimate of the proportion of variance accounted for in the population by each effect (=-=Maxwell & Delaney, 1990-=-). Note that all main effects and interactions were highly significant. The largest effect was the main effect of level of communality (o>2 = .41), and substantial effect-size estimates also were obta... |

63 |
Effects of variable and subject sampling on factor pattern recovery
- Velicer, Fava
- 1998
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Citation Context ...ability, recovery of population factors) has been noted previously in the literature on Monte Carlo studies (e.g., Cliff & Hamburger, 1967; Cliff & Pennell, 1967; Pennell, 1968; Velicer et al., 1982; =-=Velicer & Fava, 1998-=-), but the theoretical basis for this phenomenon, as presented above, has not been widely recognized. Gorsuch (1983, p. 331) noted in referring to an equation similar to our Equation 13, that unique f... |

37 |
Rotation for simple loadings
- Jennrich, Sampson
- 1966
(Show Context)
Citation Context ...lation solutions could be freely rotated. Each population correlation matrix was analyzed by maximum likelihood factor analysis, and the r-factor solution was rotated using direct quartimin rotation (=-=Jennrich & Sampson, 1966-=-). This oblique analytical rotation was used to simulate good practice in empirical studies. Although population factors were orthogonal in Tucker et al.'s (1969) design, the relationships among the f... |

33 | Psychometrics and psychology - Kline - 1979 |

32 | Evaluation of factor analytic research procedures by means of simulated correlation matrices - Tucker, Koopman, et al. - 1969 |

28 |
Nonconvergence, improper solutions, and starting values in LISRIX maximum-likelihood estimation
- Boomsma
- 1980
(Show Context)
Citation Context ...s (Heywood cases). Such solutions were expected under some of the conditions in our design. Several studies of confirmatory factor analysis and structural equation modeling (Anderson & Gerbing, 1984; =-=Boomsma, 1985-=-; Gerbing & Anderson, 1987; Velicer & Fava, 1998) have found nonconvergence and improper solutions to be more frequent with small N and poorly defined latent variables. McDonald (1985, pp. 78-81) sugg... |

27 | Representing sources of error in the common factor model: Implications for theory and practice - MacCallum, Tucker - 1991 |

27 |
Multivariate Statistical Methods (3rd ed
- Morrison
- 1990
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Citation Context ...n 1 expresses measured variables as linear combinations of common and unique factors. Following a well-known expression for variances and covariances of linear combinations of random variables (e.g., =-=Morrison, 1990-=-, p. 84), we can write an expression for the population covariance matrix of the measured variables, 2VV: 2 = (4) where £,., is the population covariance matrix for the common and unique factor scores... |

25 |
On the sampling theory of roots of determinantal equations
- Girshick
- 1939
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Citation Context ...d samples will decrease (i.e., the loadings will have smaller standard errors). Formulas for estimating standard errors of factor loadings have been developed for various types of unrelated loadings (=-=Girshick, 1939-=-; Jennrich, 1974; Lawley & Maxwell, 1971) and rotated loadings (Archer & Jennrich, 1973; Jennrich, 1973, 1974). Cudeck and O'Dell (1994) reviewed the literature on this subject and provided further de... |

21 | Selection in Covariance Structures Analysis and the `Problem' of Sample Size: A Clarification - Cudeck, Henley - 1991 |

20 |
Standard errors for obliquely rotated factor loadings
- Jennrich
- 1973
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Citation Context ...s for estimating standard errors of factor loadings have been developed for various types of unrelated loadings (Girshick, 1939; Jennrich, 1974; Lawley & Maxwell, 1971) and rotated loadings (Archer & =-=Jennrich, 1973-=-; Jennrich, 1973, 1974). Cudeck and O'Dell (1994) reviewed the literature on this subject and provided further developments for obtaining standard errors of rotated factor loadings. Application of the... |

17 |
A comparison of component and factor patterns: A Monte Carlo approach. Multivariate Behavioral Research
- Velicer, Peacock, et al.
- 1982
(Show Context)
Citation Context ...ctor solutions (replicability, recovery of population factors) has been noted previously in the literature on Monte Carlo studies (e.g., Cliff & Hamburger, 1967; Cliff & Pennell, 1967; Pennell, 1968; =-=Velicer et al., 1982-=-; Velicer & Fava, 1998), but the theoretical basis for this phenomenon, as presented above, has not been widely recognized. Gorsuch (1983, p. 331) noted in referring to an equation similar to our Equa... |

15 |
Improper solutions in the analysis of covariance structures: Their interpretability and a comparison of alternate respecifications
- Gerbing, Anderson
- 1987
(Show Context)
Citation Context ...s). Such solutions were expected under some of the conditions in our design. Several studies of confirmatory factor analysis and structural equation modeling (Anderson & Gerbing, 1984; Boomsma, 1985; =-=Gerbing & Anderson, 1987-=-; Velicer & Fava, 1998) have found nonconvergence and improper solutions to be more frequent with small N and poorly defined latent variables. McDonald (1985, pp. 78-81) suggested that Heywood cases a... |

15 |
Simplified formulas for standard errors in maximum likelihood factor analysis
- Jennrich
- 1975
(Show Context)
Citation Context ...ecrease (i.e., the loadings will have smaller standard errors). Formulas for estimating standard errors of factor loadings have been developed for various types of unrelated loadings (Girshick, 1939; =-=Jennrich, 1974-=-; Lawley & Maxwell, 1971) and rotated loadings (Archer & Jennrich, 1973; Jennrich, 1973, 1974). Cudeck and O'Dell (1994) reviewed the literature on this subject and provided further developments for o... |

14 |
A comparison of factor analytic techniques
- Browne
- 1968
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Citation Context ... approach verifies their argument. Our approach also provides a somewhat more complete picture of the influence of overdetermination on recovery of factors. Such effects had been observed previously (=-=Browne, 1968-=-; Tucker et al.. 1969; Velicer & Fava, 1987, 1998). We have replicated these effects and have also shown interactive effects of overdetermination with communality level and sample size. Limitations an... |

12 |
An evaluation of the effects of variable sampling on component, image, and factor analysis
- Velicer, Fava
- 1987
(Show Context)
Citation Context ...ndings had not been questioned, a clear theoretical explanation for them had not been available. In addition, some authors had previously associated improved recovery of factors with higher loadings (=-=Velicer & Fava, 1987-=-, 1998). Cliff and Pennell had showed experimentally that improvement was due to communality size rather than loading size per se, and our approach verifies their argument. Our approach also provides ... |

9 | The distribution of chance congruence coefficients from simulated data - Korth, Tucker - 1975 |

8 |
Standard Errors for Orthogonally Rotated Factor Loadings
- Archer, Jennrich
- 1973
(Show Context)
Citation Context .... Formulas for estimating standard errors of factor loadings have been developed for various types of unrelated loadings (Girshick, 1939; Jennrich, 1974; Lawley & Maxwell, 1971) and rotated loadings (=-=Archer & Jennrich, 1973-=-; Jennrich, 1973, 1974). Cudeck and O'Dell (1994) reviewed the literature on this subject and provided further developments for obtaining standard errors of rotated factor loadings. Application of the... |

7 | The influence of communality, factor strength and loading size on the sample characteristics of factor loadings - Cliff, Pennell - 1967 |

5 |
Handbook for the Sixteen Personality Factor
- Cattell, Eber, et al.
- 1980
(Show Context)
Citation Context ...1981) investigated this issue by using two large empirical data sets. One set consisted of measures for 491 participants on the 16 scales of Cattell's Sixteen Personality Factor Questionnaire (16 PF; =-=Cattell, Eber, & Tatsuoka, 1970-=-). The second set consisted of measures for 1,198 participants on the 90 items of the Eysenck Personality Questionnaire (EPQ; Eysenck & Eysenck, 1975). From each data set, Barrett and Kline drew subsa... |

3 | A look, by simulation, at the validity of some asymptotic distribution resuhs for rotated loadings - Archer, Jennrich - 1976 |

3 | The observation to variable ratio in factor analysis. Personality Study - unknown authors - 1981 |

2 | An empirical test of the utility of the observations-to-variables ratio in factor and components analysis - unknown authors - 1985 |

2 | Applications of a certain representation of the Wishart matrix - Wijsman - 1959 |

1 |
TARROT: A computer program for carrying out an orthogonal or oblique rotation to a part ia l ly specified target [Computer software
- Browne
- 1991
(Show Context)
Citation Context ...restrictive oblique rotation more appropriate. Next, population solutions were used as target matrices, and each sample solution was subjected to oblique target rotation. The computer program TARROT (=-=Browne, 1991-=-) was used to carry out the target rotations. For each of these rotated sample solutions, a measure was calculated to assess the correspondence between the sample solution and the corresponding popula... |

1 |
A general approach to standard errors for rotated factor loadings. Paper presented at the European Meeting of the Psychometric Society, Santiago de Compostelo
- Browne, Cudeck
- 1997
(Show Context)
Citation Context ...hod of rotation, number of factors, and the degree of correlation among the factors. Furthermore, a general method for obtaining standard errors for rotated loadings has only recently been developed (=-=Browne & Cudeck, 1997-=-). Some Monte Carlo studies have demonstrated effects of sample size on factor solutions. For instance, Browne (1968) investigated the quality of solutions produced by different factor analytic method... |

1 |
The study of samSAMPLE SIZE IN FACTOR ANALYSIS 99 pling errors in factor analysis by means of artificial experiments
- Cliff, Hamburger
- 1967
(Show Context)
Citation Context ...factors. The effect of communality size on quality of sample factor solutions (replicability, recovery of population factors) has been noted previously in the literature on Monte Carlo studies (e.g., =-=Cliff & Hamburger, 1967-=-; Cliff & Pennell, 1967; Pennell, 1968; Velicer et al., 1982; Velicer & Fava, 1998), but the theoretical basis for this phenomenon, as presented above, has not been widely recognized. Gorsuch (1983, p... |

1 | Applications of standard eiror estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations - Cudeck, O'Dell - 1994 |

1 |
Eysenck Personalit: Questionnaire manual
- Eysenck, Eysenck
- 1975
(Show Context)
Citation Context ...n Personality Factor Questionnaire (16 PF; Cattell, Eber, & Tatsuoka, 1970). The second set consisted of measures for 1,198 participants on the 90 items of the Eysenck Personality Questionnaire (EPQ; =-=Eysenck & Eysenck, 1975-=-). From each data set, Barrett and Kline drew subsamples of various sizes and carried out factor analyses. They compared the subsample solutions with solutions obtained from the corresponding full sam... |

1 | The influence of communality and Won the sampling distributions of factor loadings - unknown authors - 1968 |