Entropy Fit Indices: New Fit Measures for Assessing the Structure and Dimensionality of Multiple Latent Variables

Abstract

The accurate identification of the content and number of latent factors underlying multivariate data is an important endeavor in many areas of Psychology and related fields. Recently, a new dimensionality assessment technique based on network psychometrics was proposed (Exploratory Graph Analysis, EGA), but a measure to check the fit of the dimensionality structure to the data estimated via EGA is still lacking. Although traditional factor-analytic fit measures are widespread, recent research has identified limitations for their effectiveness in categorical variables. Here, we propose three new fit measures (termed entropy fit indices) that combines information theory, quantum information theory and structural analysis: Entropy Fit Index (EFI), EFI with Von Neumman Entropy (EFI.vn) and Total EFI.vn (TEFI.vn). The first can be estimated in complete datasets using Shannon entropy, while EFI.vn and TEFI.vn can be estimated in correlation matrices using quantum information metrics. We show, through several simulations, that TEFI.vn, EFI.vn and EFI are as accurate or more accurate than traditional fit measures when identifying the number of simulated latent factors. However, in conditions where more factors are extracted than the number of factors simulated, only TEFI.vn presents a very high accuracy. In addition, we provide an applied example that demonstrates how the new fit measures can be used with a real-world dataset, using exploratory graph analysis.

KEYWORDS:

• Fit measures
• dimensionality analysis
• information theory
• network psychometrics
• exploratory graph analysis

Article information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: Financial support from Velux Stiftung to World Health Organization (WHO) has supported WHO staff contribution to conduct analysis and prepare this article. Luis Eduardo Garrido is supported by Grant 2018-2019-1D2-085 from the Fondo Nacional de Innovación y Desarrollo Científico y Tecnológico (FONDOCYT) of the Dominican Republic.

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The authors would like to thank the reviewers, associated editors and the Editor-in-Chief for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions is not intended and should not be inferred.

Notes

1 It is important to note that in the TEFI.vn code used in the current paper, entropy is estimated as the negative of the trace of the product of the density matrix by the log of elements of the density matrix, instead of using the matrix logarithm or the eigenvalues of the density matrix (as implemented to calculate EFI.vn). Therefore, in the current implementation, TEFI.vn is based on an entropy-like quantity. We should explore this difference in future papers.