Description
Variance Identification in Sparse Factor Analysis
Description
This is an implementation of the algorithm described in Section 3 of Hosszejni and Frühwirth-Schnatter (2022) <doi:10.48550/arXiv.2211.00671>. The algorithm is used to verify that the counting rule CR(r,1) holds for the sparsity pattern of the transpose of a factor loading matrix. As detailed in Section 2 of the same paper, if CR(r,1) holds, then the idiosyncratic variances are generically identified. If CR(r,1) does not hold, then we do not know whether the idiosyncratic variances are identified or not.
README.md
Package sparvaride
The package 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.
The package is still under development and the API is subject to change.
Installation
You can install the development version of sparvaride from GitHub with:
# install.packages("devtools")
devtools::install_github("hdarjus/sparvaride")
The counting_rule_holds Function
We can check whether the 3579 counting rule holds for a given binary matrix delta using the counting_rule_holds function in the sparvaride package.
library(sparvaride)
We define two matrices as above in R:
delta1 <-
matrix(c(1, 0, 0,
0, 1, 0,
0, 0, 1,
1, 1, 1,
1, 0, 1,
1, 0, 1,
1, 0, 1),
nrow = 7, ncol = 3,
byrow = TRUE)
delta2 <-
matrix(c(1, 0, 0,
0, 1, 0,
0, 0, 1,
1, 1, 1,
1, 0, 1,
1, 1, 1,
1, 0, 1),
nrow = 7, ncol = 3,
byrow = TRUE)
Then, we call the counting_rule_holds function on these matrices:
counting_rule_holds(delta1)
#> [1] FALSE
counting_rule_holds(delta2)
#> [1] TRUE
Citation
For citing our work, please check the citation function in R:
citation("sparvaride")
#>
#> To cite sparvaride in publications use:
#>
#> Hosszejni D, Frühwirth-Schnatter S (2022). "Cover It Up! Bipartite
#> Graphs Uncover Identifiability in Sparse Factor Analysis."
#> doi:10.48550/arXiv.2211.00671
#> <https://doi.org/10.48550/arXiv.2211.00671>, 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 @Unpublished{,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 Frühwirth-Schnatter},
#> year = {2022},
#> note = {arXiv: 2211.00671},
#> doi = {10.48550/arXiv.2211.00671},
#> }