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

Sylvia Frühwirth-Schnatter, Darjus Hosszejni () and Hedibert Freitas Lopes ()
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Sylvia Frühwirth-Schnatter: Department of Finance, Accounting, and Statistics, WU Vienna University of Economics and Business, 1020 Vienna, Austria
Darjus Hosszejni: Department of Finance, Accounting, and Statistics, WU Vienna University of Economics and Business, 1020 Vienna, Austria

Econometrics, 2023, vol. 11, issue 4, 1-30

Abstract: 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.

Keywords: identifiability; sparsity; rank deficiency; rotational invariance; variance identification (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: When it counts -- Econometric identification of the basic factor model based on GLT structures (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jecnmx:v:11:y:2023:i:4:p:26-:d:1283993

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