Type:	Package
Title:	Variance Identification in Sparse Factor Analysis
Version:	0.1.0
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.
License:	GPL (≥ 3)
Encoding:	UTF-8
BuildResaveData:	best
VignetteBuilder:	knitr
BugReports:	https://github.com/hdarjus/sparvaride/issues
URL:	https://hdarjus.github.io/sparvaride/
Depends:	R (≥ 4.1)
Imports:	Rcpp
LinkingTo:	RcppArmadillo, Rcpp
RoxygenNote:	7.2.3
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
Config/testthat/edition:	3
NeedsCompilation:	yes
Packaged:	2023-03-10 12:14:03 UTC; dhosszej
Author:	Darjus Hosszejni [aut, cre], Sylvia Frühwirth-Schnatter [ths]
Maintainer:	Darjus Hosszejni <darjus.hosszejni@wu.ac.at>
Repository:	CRAN
Date/Publication:	2023-03-13 13:30:05 UTC

Verify that the counting rule CR(r,1) holds

Description

This is an implementation of the algorithm described in Section 3 of Hosszejni and Fruehwirth-Schnatter (2022). 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.

Usage

counting_rule_holds(delta)

Arguments

Value

TRUE if CR(r,1) holds, FALSE otherwise

References

Hosszejni and Fruehwirth-Schnatter (2022). "Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis". arXiv:2211.00671

See Also

stats::factanal()

Examples

# Two example matrices
cr_holds <-
  matrix(c(1, 0, 0,
           1, 0, 1,
           0, 1, 0,
           0, 1, 1,
           0, 1, 1,
           1, 1, 1,
           1, 1, 1),
         7, 3, byrow = TRUE)

cr_does_not_hold <-
  matrix(c(1, 0, 0,
           0, 0, 1,
           0, 1, 0,
           0, 1, 0,
           0, 1, 0,
           1, 1, 1,
           1, 1, 1),
         7, 3, byrow = TRUE)

# Check if the counting rule holds
counting_rule_holds(cr_holds)
#> [1] TRUE
counting_rule_holds(cr_does_not_hold)
#> [1] FALSE