Software package sparvaride-matlab

Matlab implementation of the main algorithm of the R package sparvaride plus two utilitites for the generalized lower triangular (GLT) framework in our working paper by Sylvia Frühwirth-Schnatter, Darjus Hosszejni, and Hedibert Freitas Lopes.

The R package sparvaride implements the variance identification algorithm for sparse factor analysis described in the paper "Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis" by Darjus Hosszejni and Sylvia Frühwirth-Schnatter. The paper is available at arXiv.

Functionality

There are three functions and two further Matlab files in this repository.

• to_glt rotates the input into GLT representation
  • a Matlab-default numeric tolerance is applied
  • this function is for continuous factor loadings matrices
  • the transpose of the factor loadings matrix is the input
  • further info in Section 3.3 of our working paper
• is_identified_indicator verifies the counting rule for the sparsity pattern of a factor loadings matrix
  • there is no numeric error involved in this algorithm
  • the sparsity pattern of the transpose of the factor loadings matrix is the input
  • further info in our working paper, which is about what this algorithm is and why it works
• is_identified is the sequence of to_glt and is_identified_indicator on the sparsity pattern of the resulting GLT structure

How to use

You need to have Matlab on your computer first; I tested it with Matlab R2021b. Then, you have to download the .m files of this repository onto your computer and put them into your Matlab's working directory. See tests.m in this repository for code examples. Execute run_tests.m to run the unit tests.

Citation

Please cite our working papers if you use the code.

Relevant paper for citing the is_identified function:

Darjus Hosszejni and Sylvia Frühwirth-Schnatter (2022). "Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis." doi:10.48550/arXiv.2211.00671

A BibTeX entry for LaTeX users is

@unpublished{,
  title = {Cover It Up! {Bipartite} Graphs Uncover Identifiability in Sparse Factor Analysis},
  author = {Darjus Hosszejni and Sylvia Fr\"uhwirth-Schnatter},
  year = {2022},
  note = {arXiv: 2211.00671},
  doi = {10.48550/arXiv.2211.00671},
}

Relevant paper for citing the to_glt function:

Sylvia Frühwirth-Schnatter, Darjus Hosszejni, and Hedibert Freitas Lopes (2023). "When It Counts - Econometric Identification of the Basic Factor Model Based on GLT Structures." doi:10.48550/arXiv.2301.06354

A BibTex entry for LaTeX users is

@unpublished{,
  title = {When It Counts - {Econometric} Identification of the Basic Factor Model Based on {GLT} Structures},
  author = {Sylvia Fr\"uhwirth-Schnatter and Darjus Hosszejni and Hedibert Freitas Lopes},
  year = {2023},
  note = {arXiv: 2301.06354},
  doi = {10.48550/arXiv.2301.06354},
}

Issues

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