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The ultrametric correlation matrix for modelling hierarchical latent concepts. (English) Zbl 1459.62097

Summary: Many relevant multidimensional phenomena are defined by nested latent concepts, which can be represented by a tree-structure supposing a hierarchical relationship among manifest variables. The root of the tree is a general concept which includes more specific ones. The aim of the paper is to reconstruct an observed data correlation matrix of manifest variables through an ultrametric correlation matrix which is able to pinpoint the hierarchical nature of the phenomenon under study. With this scope, we introduce a novel model which detects consistent latent concepts and their relationships starting from the observed correlation matrix.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62P15 Applications of statistics to psychology
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