Choosing an appropriate number of factors in factor analysis with incomplete data

When we conduct factor analysis, the number of factors is often unknown in advance. Among many decision rules for an appropriate number of factors, it is easy to find approaches that make use of the estimated covariance matrix. When data include missing values, the estimated covariance matrix using either complete cases or available cases may not accurately represent the true covariance matrix, and decision based on the estimated covariance matrix may be misleading. We discuss how to apply model selection techniques using AIC or BIC to choose an appropriate number of factors when data include missing values. In the simulation study, it is shown that the suggested methods select the correct number of factors for simulated data with known number of factors.

[1]  H. Kaiser.  The Application of Electronic Computers to Factor Analysis , 1960 .

[2]  Maia Berkane.  Latent Variable Modeling and Applications to Causality , 1997 .

[3]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[4]  P. Green,et al.  Analyzing multivariate data , 1978 .

[5]  H. Akaike.  Factor analysis and AIC , 1987 .

[6]  Mortaza Jamshidian,et al.  An EM Algorithm for ML Factor Analysis with Missing Data , 1997 .

[7]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[8]  D. Rubin,et al.  Parameter expansion to accelerate EM: The PX-EM algorithm , 1998 .

[9]  D. Rubin,et al.  Parameter expansion to accelerate EM : The PX-EM algorithm , 1997 .

[10]  K. Bollen.  A New Incremental Fit Index for General Structural Equation Models , 1989 .

[11]  J. S. Long,et al.  Testing Structural Equation Models , 1993 .

[12]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[13]  R. Cattell.  The Scree Test For The Number Of Factors. , 1966, Multivariate behavioral research.

[14]  K. Jöreskog,et al.  Analysis of linear structural relationships by maximum likelihood and least squares methods , 1983 .

[15]  R. Stine,et al.  Bootstrapping Goodness-of-Fit Measures in Structural Equation Models , 1992 .

[16]  S. Mulaik,et al.  EVALUATION OF GOODNESS-OF-FIT INDICES FOR STRUCTURAL EQUATION MODELS , 1989 .

[17]  Jandyra Maria Guimarães Fachel.  The C-type distribution as an underlying model for categorical data and its use in factorial analysis , 1986 .

[18]  P. Bentler,et al.  Comparative fit indexes in structural models. , 1990, Psychological bulletin.

[19]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[20]  P. Bentler,et al.  Significance Tests and Goodness of Fit in the Analysis of Covariance Structures , 1980 .

[21]  Thomas R Belin,et al.  Imputation for incomplete high‐dimensional multivariate normal data using a common factor model , 2004, Statistics in medicine.