Sylvia Frühwirth-Schnatter, Darjus Hosszejni, Hedibert Freitas Lopes
arXiv 16 Jan 2023 · Statistics — Methodology · publishedEconometrics (2023) · 13 citations (OpenAlex)
arXiv:2301.06354 · PDF · DOI · OpenAlex · Extracted main text
Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address 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 sparse 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 Bayesian sparse factor analysis.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Anderson, T. W. and H. Rubin (1956) Statistical inference in factor analysis | 1.000 | 11 | 4 | 100% |
| 2 | Frühwirth-Schnatter, S., D. Hosszejni, and H. F. Lopes (2022) Sparse finite Bayesian factor analysis when the number of factors is unknown | 1.000 | 8 | 3 | 100% |
| 3 | Reiersl, O (1950) On the identifiability of parameters in Thurstone's multiple factor analysis | 1.000 | 5 | 3 | 100% |
| 4 | Tumura, Y. and M. Sato (1980) On the identification in factor analysis | 0.965 | 10 | 4 | 90% |
| 5 | Sato, M (1992) A study of an identification problem and substitute use of principal component analysis in factor analysis | 0.941 | 6 | 4 | 83% |
| 6 | Conti, G., S. Frühwirth-Schnatter, J. J. Heckman, and R. Piatek (2014) Bayesian exploratory factor analysis | 0.737 | 3 | 2 | 100% |
| 7 | Lopes, H. F. and M. West (2004) Bayesian model assessment in factor analysis self | 0.737 | 3 | 2 | 100% |
| 8 | Frühwirth-Schnatter, S. and H. Lopes (2018) Sparse Bayesian Factor Analysis when the Number of Factors is Unknown | 0.644 | 2 | 2 | 100% |
| 9 | Geweke, J. F. and G. Zhou (1996) Measuring the pricing error of the arbitrage pricing theory | 0.644 | 2 | 2 | 100% |
| 10 | Hosszejni, D. and S. Frühwirth-Schnatter (2022) Cover it up! Bipartite graphs uncover identifiability in sparse factor analysis self | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 43 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis | 1.000 | 8 | 3 |