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Simultaneous analysis of coupled data matrices subject to different amounts of noise
Author(s) -
Wilderjans Tom F.,
Ceulemans Eva,
Van Mechelen Iven,
van den Berg Robert A.
Publication year - 2011
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711010x513263
Subject(s) - noise (video) , computer science , matrix (chemical analysis) , data matrix , set (abstract data type) , extension (predicate logic) , data set , variable (mathematics) , data mining , block (permutation group theory) , data analysis , algorithm , mathematics , artificial intelligence , combinatorics , clade , mathematical analysis , biochemistry , chemistry , materials science , image (mathematics) , composite material , gene , programming language , phylogenetic tree
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.