Package {fanc}

Type:	Package
Title:	Penalized Likelihood Factor Analysis via Nonconvex Penalty
Version:	2.4.0
Date:	2026-07-26
Depends:	Matrix
Imports:	grDevices, graphics, stats, utils
Description:	Computes the penalized maximum likelihood estimates of factor loadings and unique variances for various tuning parameters. The pathwise coordinate descent along with EM algorithm is used. This package also includes a graphical tool which outputs path diagrams, heatmaps, goodness-of-fit indices and model selection criteria for each regularization parameter (Yamamoto, M., Hirose, K. and Nagata, H., 2017 <doi:10.1007/s41237-016-0007-3>). The user can change the regularization parameter interactively with a built-in self-contained HTML viewer (no additional packages required), which is helpful to find a suitable value of regularization parameter. As a penalty, we can choose either the minimax concave penalty (Hirose, K. and Yamamoto, M., 2015 <doi:10.1007/s11222-014-9458-0>; Hirose, K. and Yamamoto, M., 2014 <doi:10.1016/j.csda.2014.05.011>) or the product-based elastic net penalty (Hirose, K. and Terada, Y., 2023 <doi:10.1007/s11336-022-09868-4>).
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://doi.org/10.1007/s11222-014-9458-0, https://doi.org/10.1016/j.csda.2014.05.011, https://doi.org/10.1007/s41237-016-0007-3, https://doi.org/10.1007/s11336-022-09868-4, https://keihirose.com
NeedsCompilation:	yes
Packaged:	2026-07-26 06:40:46 UTC; hirosekei
Author:	Kei Hirose [aut, cre], Michio Yamamoto [aut], Haruhisa Nagata [aut]
Maintainer:	Kei Hirose <mail@keihirose.com>
Repository:	CRAN
Date/Publication:	2026-07-26 07:10:02 UTC

Penalized Likelihood Factor Analysis via Nonconvex Penalties

Description

Computes solution paths of penalized maximum likelihood estimates for factor analysis or probabilistic principal component analysis. The available penalties are MC+, the product-based elastic net (prenet), and the elastic net.

Usage

fanc(x, factors, n.obs, rho, gamma, cor.factor=FALSE, normalize=TRUE,
     normalize.penalty=FALSE, covmat, type="MC", model="FA", control=list())

## S3 method for class 'fanc'
print(x, digits=max(3, getOption("digits") - 3),
                     num.result=20, ...)

Arguments

Details

The control argument can contain the following components:

length.rho

Number of rho candidates.

length.gamma

Number of gamma candidates.

max.rho

Maximum rho. For prenet and enet, a scalar is repeated for every gamma. Alternatively, supply one value per gamma. Other lengths are invalid.

max.gamma

Maximum finite gamma.

min.gamma

Minimum gamma.

eta

Non-negative tuning parameter used to prevent improper solutions.

ncand.initial

Number of candidate initial loading matrices. The default is 10.

ncand.initial.prenet

Number of candidate initial values for the prenet penalty. The default is 100.

maxit.em

Maximum number of EM iterations.

maxit.cd

Maximum number of coordinate-descent iterations.

maxit.bfgs

Maximum number of BFGS iterations.

maxit.initial

Maximum number of iterations used when choosing initial values.

start

Starting-value strategy, either "warm" or "cold".

Delta

Ratio of the minimum rho to the maximum rho.

min.uniquevar

Minimum unique variance.

tol.em

Convergence tolerance for the EM algorithm.

tol.cd

Convergence tolerance for coordinate descent.

tol.bfgs

Convergence tolerance for BFGS.

min.rhozero

Logical; if TRUE, the minimum rho is zero.

zita

Hyper-parameter for factor correlations.

progress

Logical; if TRUE, fitting progress is displayed.

openmp

Logical; if TRUE, OpenMP parallel computation is requested.

num.threads

Number of OpenMP threads.

gamma.ebic

Gamma used in the extended BIC.

Value

An object of class "fanc". Important components include:

When only covmat is supplied and n.obs is omitted, the model-selection criteria and goodness-of-fit indices are NULL.

Author(s)

Kei Hirose
mail@keihirose.com

References

Hirose, K. and Yamamoto, M. (2015). Sparse estimation via nonconcave penalized likelihood in a factor analysis model, Statistics and Computing, 25, 633–648.

See Also

out, select, and plot.fanc.

Examples

set.seed(0)
loadings0 <- matrix(c(rep(0.8, 5), rep(0, 5),
                      rep(0, 5), rep(0.8, 5)), 10, 2)
common.factors0 <- matrix(rnorm(50 * 2), 50, 2)
unique.factors0 <- matrix(rnorm(50 * 10, sd=sqrt(0.36)), 50, 10)
x <- common.factors0 %*% t(loadings0) + unique.factors0

fit <- fanc(x, 2)
print(fit)
out(fit, rho=0.1, gamma=Inf)
select(fit, criterion="BIC", gamma=Inf)

## Not run: 
plot(fit)
plot(fit, file="fanc-viewer.html")

## End(Not run)

Extract a Result from a "fanc" Object

Description

Extracts the fitted model at specified values of rho and gamma from a "fanc" object.

Usage

out(x, rho, gamma, scores=FALSE, df.method="active")

Arguments

Value

Author(s)

Kei Hirose
mail@keihirose.com

References

Hirose, K. and Yamamoto, M. (2015). Sparse estimation via nonconcave penalized likelihood in a factor analysis model,
Statistics and Computing, 25, 633–648.

See Also

fanc and plot.fanc objects.

Plot a Solution Path from a "fanc" Object

Description

This function plots the solution paths or heatmaps from a "fanc" object. By default it opens a self-contained, interactive HTML viewer in the browser or RStudio viewer pane (no additional packages required). The viewer has sliders for rho and gamma, buttons that jump to the model selected by AIC, BIC, CAIC or EBIC, and an overview mode showing every rho along the path at once. All data and code are embedded in the page, so it runs without a server and can be saved and shared as a single file via the file argument.

Usage

## S3 method for class 'fanc'
plot(x, Window.Height=500, type=NULL, df.method="active",
                    viewer=c("auto", "html", "base"), file=NULL,
                    rho.index=1, gamma.index=1, ...)

Arguments

Value

For viewer="html" the path to the generated HTML file (invisibly); otherwise NULL (invisibly). Called for the side effect of drawing or opening the viewer.

Author(s)

Kei Hirose
mail@keihirose.com

References

Hirose, K. and Yamamoto, M. (2015). Sparse estimation via nonconcave penalized likelihood in a factor analysis model,
Statistics and Computing, 25, 633–648.

See Also

fanc and out objects.

Select a Model from a "fanc" Object

Description

Selects the value of rho that minimizes a model-selection criterion, optionally at a specified value of gamma.

Usage

select(x, criterion=c("BIC","AIC","CAIC","EBIC"), 
	gamma,  scores=FALSE, df.method="active")

Arguments

Value

Author(s)

Kei Hirose
mail@keihirose.com

References

Hirose, K. and Yamamoto, M. (2015). Sparse estimation via nonconcave penalized likelihood in a factor analysis model,
Statistics and Computing, 25, 633–648.

See Also

fanc and plot.fanc objects.