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Second-order disjoint factor analysis. (English) Zbl 1486.62302

Summary: Hierarchical models are often considered to measure latent concepts defining nested sets of manifest variables. Therefore, by supposing a hierarchical relationship among manifest variables, the general latent concept can be represented by a tree structure where each internal node represents a specific order of abstraction for the latent concept measured. In this paper, we propose a new latent factor model called second-order disjoint factor analysis in order to model an unknown hierarchical structure of the manifest variables with two orders. This is a second-order factor analysis, which – respect to the second-order confirmatory factor analysis – is exploratory, nested and estimated simultaneously by maximum likelihood method. Each subset of manifest variables is modeled to be internally consistent and reliable, that is, manifest variables related to a factor measure “consistently” a unique theoretical construct. This feature implies that manifest variables are positively correlated with the related factor and, therefore, the associated factor loadings are constrained to be nonnegative. A cyclic block coordinate descent algorithm is proposed to maximize the likelihood. We present a simulation study that investigates the ability to get reliable factors. Furthermore, the new model is applied to identify the underlying factors of well-being showing the characteristics of the new methodology. A final discussion completes the paper.

MSC:

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