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Second-Order Disjoint Factor Analysis.

Authors
  • Cavicchia, Carlo1
  • Vichi, Maurizio2
  • 1 Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, The Netherlands. [email protected] , (Netherlands)
  • 2 Department of Statistical Sciences, University of Rome La Sapienza, Rome, Italy. , (Italy)
Type
Published Article
Journal
Psychometrika
Publication Date
Mar 01, 2022
Volume
87
Issue
1
Pages
289–309
Identifiers
DOI: 10.1007/s11336-021-09799-6
PMID: 34403112
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

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. © 2021. The Author(s).

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