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  • 1
    ISSN: 1860-0980
    Keywords: simultaneous components analysis ; alternating least squares ; principal components analysis ; longitudinal data ; cross-sectional data ; stationary component weights
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract Millsap and Meredith (1988) have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions. The algorithm they provide has some disadvantages. The present paper offers two alternating least squares algorithms for their method, suitable for small and large data sets, respectively. Lower and upper bounds are given for the loss function to be minimized in the Millsap and Meredith method. These can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Psychometrika 59 (1994), S. 81-90 
    ISSN: 1860-0980
    Keywords: simple structure ; oblique rotation ; principal components analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract Procedures for oblique rotation of factors or principal components typically focus on rotating the pattern matrix such that it becomes optimally simple. An important oblique rotation method that does so is Harris and Kaiser's (1964) independent cluster (HKIC) rotation. In principal components analysis, a case can be made for interpreting the components on the basis of the component weights rather than on the basis of the pattern, so it seems desirable to rotate the components such that the weights rather than the pattern become optimally simple. In the present paper, it is shown that HKIC rotates the components such that both the pattern and the weights matrix become optimally simple. In addition, it is shown that the pattern resulting from HKIC rotation is columnwise proportional to the associated weights matrix, which implies that the interpretation of the components does not depend on whether it is based on the pattern or on the component weights matrix. It is also shown that the latter result only holds for HKIC rotation and slight modifications of it.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Psychometrika 61 (1996), S. 601-628 
    ISSN: 1860-0980
    Keywords: principal components analysis ; common factor analysis ; alternating least squares algorithms ; identification ; uniqueness ; partitioning of fit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.
    Type of Medium: Electronic Resource
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