How to perform multiblock component analysis in practice

To explore structural differences and similarities in multivariate multiblock data (e.g., a number of variables have been measured for different groups of subjects, where the data for each group constitute a different data block), researchers have a variety of multiblock component analysis and factor analysis strategies at their disposal. In this article, we focus on three types of multiblock component methods—namely, principal component analysis on each data block separately, simultaneous component analysis, and the recently proposed clusterwise simultaneous component analysis, which is a generic and flexible approach that has no counterpart in the factor analysis tradition. We describe the steps to take when applying those methods in practice. Whereas plenty of software is available for fitting factor analysis solutions, up to now no easy-to-use software has existed for fitting these multiblock component analysis methods. Therefore, this article presents the MultiBlock Component Analysis program, which also includes procedures for missing data imputation and model selection.

[1]  D. Jackson,et al.  Component Analysis versus Common Factor Analysis: Some Further Observations. , 1990, Multivariate behavioral research.

[2]  H. Kaiser,et al.  Oblique factor analytic solutions by orthogonal transformations , 1964 .

[3]  D. Sörbom.  A GENERAL METHOD FOR STUDYING DIFFERENCES IN FACTOR MEANS AND FACTOR STRUCTURE BETWEEN GROUPS , 1974 .

[4]  J. Fleiss,et al.  Intraclass correlations: uses in assessing rater reliability. , 1979, Psychological bulletin.

[5]  Beat Neuenschwander,et al.  Ontogeny and Individual Variation: Analysis of Patterned Covariance Matrices with Common Principal Components , 1996 .

[6]  Peter C. M. Molenaar,et al.  Using structural equation modeling to fit models incorporating principal components , 1999 .

[7]  L. Tucker.  A METHOD FOR SYNTHESIS OF FACTOR ANALYSIS STUDIES , 1951 .

[8]  Jozefien De Leersnyder,et al.  Where Do My Emotions Belong? A Study of Immigrants’ Emotional Acculturation , 2011, Personality & social psychology bulletin.

[9]  Rex B. Kline,et al.  Principles and Practice of Structural Equation Modeling , 1998 .

[10]  Russell V. Lenth,et al.  Statistical Analysis With Missing Data (2nd ed.) (Book) , 2004 .

[11]  P. Deb.  Finite Mixture Models , 2008 .

[12]  H. Kaiser.  The varimax criterion for analytic rotation in factor analysis , 1958 .

[13]  H. Kiers,et al.  Three-mode principal components analysis: choosing the numbers of components and sensitivity to local optima. , 2000, The British journal of mathematical and statistical psychology.

[14]  P. Costa,et al.  Personality trait structure as a human universal. , 1997, The American psychologist.

[15]  L. F. Barrett.  Discrete Emotions or Dimensions? The Role of Valence Focus and Arousal Focus , 1998 .

[16]  B. Muthén,et al.  Multilevel Covariance Structure Analysis , 1994 .

[17]  H. Kiers,et al.  Selecting among three-mode principal component models of different types and complexities: a numerical convex hull based method. , 2006, The British journal of mathematical and statistical psychology.

[18]  G. W. Milligan,et al.  The Effect of Cluster Size, Dimensionality, and the Number of Clusters on Recovery of True Cluster Structure , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  P. Kroonenberg.  Applied Multiway Data Analysis , 2008 .

[20]  W. J. Krzanowski,et al.  Recent Advances in Descriptive Multivariate Analysis. , 1996 .

[21]  Claudio Barbaranelli,et al.  Measuring emotional instability, prosocial behavior and aggression in pre-adolescents: A cross-national study , 1997 .

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

[23]  W F Velicer,et al.  Component Analysis versus Common Factor Analysis: Some issues in Selecting an Appropriate Procedure. , 1990, Multivariate behavioral research.

[24]  Iven Van Mechelen,et al.  UvA-DARE ( Digital Academic Repository ) A structured overview of simultaneous component based data integration , 2009 .

[25]  Henk A. L. Kiers,et al.  Hierarchical relations between methods for simultaneous component analysis and a technique for rotation to a simple simultaneous structure , 1994 .

[26]  Jae-On Kim,et al.  The Treatment of Missing Data in Multivariate Analysis , 1977 .

[27]  T. Berge.  Least squares optimization in multivariate analysis , 2005 .

[28]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[29]  Marieke E. Timmerman,et al.  Four simultaneous component models for the analysis of multivariate time series from more than one subject to model intraindividual and interindividual differences , 2003 .

[30]  Jelte M. Wicherts,et al.  Testing Measurement Invariance in the Target Rotated Multigroup Exploratory Factor Model , 2009 .

[31]  B. Fredrickson,et al.  Psychological resilience and positive emotional granularity: examining the benefits of positive emotions on coping and health. , 2004, Journal of personality.

[32]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[33]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[34]  K. G. J8reskoC,et al.  Simultaneous Factor Analysis in Several Populations , 2007 .

[35]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[36]  Marieke E Timmerman,et al.  Multilevel component analysis. , 2006, The British journal of mathematical and statistical psychology.

[37]  F. Floyd,et al.  Factor analysis in the development and refinement of clinical assessment instruments. , 1995 .

[38]  R. Kline.  Principles and practice of structural equation modeling, 2nd ed. , 2005 .

[39]  A. Basilevsky,et al.  Factor Analysis as a Statistical Method. , 1964 .

[40]  J. Hox,et al.  Sufficient Sample Sizes for Multilevel Modeling , 2005 .

[41]  Eva Ceulemans,et al.  A clusterwise simultaneous component method for capturing within-cluster differences in component variances and correlations. , 2013, The British journal of mathematical and statistical psychology.

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

[43]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.

[44]  David J. Francis,et al.  An Investigation of the Structural Validity of Loevinger's Model and Measure of Ego Development , 1994 .

[45]  Henk A. L. Kiers,et al.  The Harris-Kaiser independent cluster rotation as a method for rotation to simple component weights , 1994 .

[46]  B. Muthén,et al.  Exploratory Structural Equation Modeling , 2009 .

[47]  Stephen A. Stumpf.  A Note on Handling Missing Data , 1978 .

[48]  P M Bentler,et al.  Use of structural equation modeling to test the construct validity of the SF-36 Health Survey in ten countries: results from the IQOLA Project. International Quality of Life Assessment. , 1998, Journal of clinical epidemiology.

[49]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[50]  T. Haavelmo.  The Statistical Implications of a System of Simultaneous Equations , 1943 .

[51]  R. Bro,et al.  Centering and scaling in component analysis , 2003 .

[52]  H. Kiers.  Weighted least squares fitting using ordinary least squares algorithms , 1997 .

[53]  Eva Ceulemans,et al.  Clusterwise simultaneous component analysis for analyzing structural differences in multivariate multiblock data. , 2012, Psychological methods.

[54]  Lai-Min Paul Lee,et al.  Confirmatory Factor Analyses of the Wechsler Intelligence Scale for Children-Revised and the Hong Kong-Wechsler Intelligence Scale for Children , 1988 .