TY - JOUR

T1 - Simultaneous analysis of coupled data matrices subject to different amounts of noise

AU - Wilderjans, Tom F.

AU - Ceulemans, Eva

AU - Van Mechelen, Iven

AU - Van Den Berg, Robert A.

PY - 2011/5/1

Y1 - 2011/5/1

N2 - In many areas of science, research questions imply the analysis of a set of coupled data blocks, with, for instance, each block being an experimental unit by variable matrix, and the variables being the same in all matrices. To obtain an overall picture of the mechanisms that play a role in the different data matrices, the information in these matrices needs to be integrated. This may be achieved by applying a data-analytic strategy in which a global model is fitted to all data matrices simultaneously, as in some forms of simultaneous component analysis (SCA). Since such a strategy implies that all data entries, regardless the matrix they belong to, contribute equally to the analysis, it may obfuscate the overall picture of the mechanisms underlying the data when the different data matrices are subject to different amounts of noise. One way out is to downweight entries from noisy data matrices in favour of entries from less noisy matrices. Information regarding the amount of noise that is present in each matrix, however, is, in most cases, not available. To deal with these problems, in this paper a novel maximum-likelihood-based simultaneous component analysis method, referred to as MxLSCA, is proposed. Being a stochastic extension of SCA, in MxLSCA the amount of noise in each data matrix is estimated and entries from noisy data matrices are downweighted. Both in an extensive simulation study and in an application to data stemming from cross-cultural emotion psychology, it is shown that the novel MxLSCA strategy outperforms the SCA strategy with respect to disclosing the mechanisms underlying the coupled data.

AB - In many areas of science, research questions imply the analysis of a set of coupled data blocks, with, for instance, each block being an experimental unit by variable matrix, and the variables being the same in all matrices. To obtain an overall picture of the mechanisms that play a role in the different data matrices, the information in these matrices needs to be integrated. This may be achieved by applying a data-analytic strategy in which a global model is fitted to all data matrices simultaneously, as in some forms of simultaneous component analysis (SCA). Since such a strategy implies that all data entries, regardless the matrix they belong to, contribute equally to the analysis, it may obfuscate the overall picture of the mechanisms underlying the data when the different data matrices are subject to different amounts of noise. One way out is to downweight entries from noisy data matrices in favour of entries from less noisy matrices. Information regarding the amount of noise that is present in each matrix, however, is, in most cases, not available. To deal with these problems, in this paper a novel maximum-likelihood-based simultaneous component analysis method, referred to as MxLSCA, is proposed. Being a stochastic extension of SCA, in MxLSCA the amount of noise in each data matrix is estimated and entries from noisy data matrices are downweighted. Both in an extensive simulation study and in an application to data stemming from cross-cultural emotion psychology, it is shown that the novel MxLSCA strategy outperforms the SCA strategy with respect to disclosing the mechanisms underlying the coupled data.

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U2 - 10.1348/000711010X513263

DO - 10.1348/000711010X513263

M3 - Article

C2 - 21492133

AN - SCOPUS:79954573846

VL - 64

SP - 277

EP - 290

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

SN - 0007-1102

IS - 2

ER -