Exploratory factor analysis for small samples

Traditionally, two distinct approaches have been employed for exploratory factor analysis: maximum likelihood factor analysis and principal component analysis. A third alternative, called regularized exploratory factor analysis, was introduced recently in the psychometric literature. Small sample size is an important issue that has received considerable discussion in the factor analysis literature. However, little is known about the differential performance of these three approaches to exploratory factor analysis in a small sample size scenario. A simulation study and an empirical example demonstrate that regularized exploratory factor analysis may be recommended over the two traditional approaches, particularly when sample sizes are small (below 50) and the sample covariance matrix is near singular.

[1]  Y. Kano,et al.  A new estimator of the uniqueness in factor analysis , 1986 .

[2]  Jacob Cohen Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[3]  Carl T. Finkbeiner,et al.  Approximate uniqueness estimates for singular correlation matrices , 1982 .

[4]  Hongtu Zhu,et al.  Latent volumetric structure of the human brain: Exploratory factor analysis and structural equation modeling of gray matter volumes in healthy children and adults , 2008, Human brain mapping.

[5]  Franklin A. Graybill,et al.  Introduction to The theory , 1974 .

[6]  B P O'Connor,et al.  SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test , 2000, Behavior research methods, instruments, & computers : a journal of the Psychonomic Society, Inc.

[7]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[8]  T. Micceri The unicorn, the normal curve, and other improbable creatures. , 1989 .

[9]  R. MacCallum,et al.  Sample size in factor analysis. , 1999 .

[10]  Scott E. Maxwell,et al.  Designing Experiments and Analyzing Data , 1992 .

[11]  Gösta Hägglund Factor analysis by instrumental variables methods , 1982 .

[12]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[13]  J. S. Tanaka "How Big Is Big Enough?": Sample Size and Goodness of Fit in Structural Equation Models with Latent Variables. , 1987 .

[14]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.

[15]  D. Flora,et al.  An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. , 2004, Psychological methods.

[16]  P. Lachenbruch Statistical Power Analysis for the Behavioral Sciences (2nd ed.) , 1989 .

[17]  R. MacCallum,et al.  Applications of structural equation modeling in psychological research. , 2000, Annual review of psychology.

[18]  R. Wijsman Applications of a Certain Representation of the Wishart Matrix , 1959 .

[19]  Louis Legendre,et al.  The Importance of Being Digital , 1963 .

[20]  S. Geer,et al.  Regularization in statistics , 2006 .

[21]  A Conceptual and Empirical Approach to Creativityin Industrial Organizations , 2008 .

[22]  Ke-Hai Yuan,et al.  Structural equation modeling with near singular covariance matrices , 2008, Comput. Stat. Data Anal..

[23]  C. Spearman General intelligence Objectively Determined and Measured , 1904 .

[24]  Godfrey D. Pearlson,et al.  Exploratory factor analysis of MRI brain structure measures in schizophrenia , 1996, Schizophrenia Research.

[25]  P. Wieringa,et al.  Exploratory Factor Analysis With Small Sample Sizes , 2009, Multivariate behavioral research.

[26]  S. West,et al.  The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. , 1996 .

[27]  Allen I. Fleishman A method for simulating non-normal distributions , 1978 .

[28]  Duane T. Wegener,et al.  Evaluating the use of exploratory factor analysis in psychological research. , 1999 .

[29]  B. Everitt,et al.  Multivariate Exploratory Data Analysis: A Perspective on Exploratory Factor Analysis. , 1988 .

[30]  Donald Robertson,et al.  Maximum likelihood factor analysis with rank-deficient sample covariance matrices , 2007 .

[31]  Charlotte H. Mason,et al.  Collinearity, power, and interpretation of multiple regression analysis. , 1991 .

[32]  Scott E. Maxwell,et al.  Designing Experiments and Analyzing Data , 1991 .