Computational Statistics & Data Analysis vol:53 issue:4 pages:1086-1098
Research questions in several research domains imply the simultaneous analysis of different blocks of information that pertain to the same research objects. In personality psychology, for example, to study the relation between individual differences in behavior and cognitive-affective units that can account for these differences, two types of information pertaining to the same set of persons need to be analyzed simultaneously: (1) information about the situation-specific behavior profile of these persons, and (2) information about the cognitive-affective units these persons exhibit. When dealing with such coupled data blocks (i.e., different N-way N-mode data blocks that have one or more modes in common) it often happens that one data block is much larger in size than the other(s). In this case, the question arises whether the data entries or the data blocks should be considered as the units of information, in order to disclose the true structure underlying the coupled data blocks. To answer this question, two weighting schemes are compared that are obtained by applying weights in the overall objective function that is to be optimized in the data analysis, with each weight indicating the extent to which the corresponding data block influences the integrated analysis. In a simulation study it is showed that weighting the different data blocks such that each data entry influences the analysis to the same extent (i.e., data entries as units of information) outperforms a weighting scheme in which each data block has an equal influence on the analysis (i.e., data blocks as units of information). This superior performance is demonstrated for two global models for coupled data consisting of a three-way three-mode data block and a two-way two-mode data block that have one mode in common: (1) a multiway multiblock component model for coupled real-valued data, and (2) a simultaneous clustering model for coupled binary data.