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Second-Order Disjoint Factor Analysis.

Carlo Cavicchia1, Maurizio Vichi2

  • 1Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, The Netherlands. cavicchia@ese.eur.nl.

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|August 17, 2021
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Summary
This summary is machine-generated.

This study introduces second-order disjoint factor analysis, a novel exploratory method for uncovering hierarchical structures in data. The approach ensures reliable measurement of latent constructs, demonstrated through simulations and an application to well-being factors.

Keywords:
factor analysishierarchical modelslatent variable modelsreflective modelssecond-order

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Factor Analysis

Background:

  • Hierarchical models are crucial for measuring latent concepts within nested manifest variables.
  • Existing methods may not fully capture unknown or complex hierarchical structures.
  • The need for exploratory, simultaneous estimation of nested factor structures.

Purpose of the Study:

  • To propose a new latent factor model, second-order disjoint factor analysis (SODFA).
  • To model and analyze unknown two-order hierarchical structures of manifest variables.
  • To provide an exploratory alternative to second-order confirmatory factor analysis.

Main Methods:

  • Development of the second-order disjoint factor analysis model.
  • Simultaneous estimation using the maximum likelihood method.
  • Constraining factor loadings to be nonnegative for internal consistency and reliability.
  • Implementation of a cyclic block coordinate descent algorithm for likelihood maximization.

Main Results:

  • A simulation study demonstrated the model's ability to yield reliable factors.
  • Application to well-being data successfully identified underlying latent factors.
  • The methodology proved effective in characterizing hierarchical data structures.

Conclusions:

  • Second-order disjoint factor analysis offers a robust method for exploring hierarchical latent variables.
  • The model ensures internal consistency and reliability of measured constructs.
  • This approach advances the analysis of complex, nested data structures in various scientific domains.