When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures

Sylvia Frühwirth-Schnatter, Darjus Hosszejni*, Hedibert Freitas Lopes

*Corresponding author for this work

Publication: Scientific journalJournal articlepeer-review


Despite the popularity of factor models with simple loading matrices, little attention has been given to formally address the identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in simple factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class, the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in sparse Bayesian factor analysis.

Original languageEnglish
Article number26
Issue number4
Publication statusPublished - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 by the authors.


  • identifiability
  • rank deficiency
  • rotational invariance
  • sparsity
  • variance identification

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