fanc: Penalized Likelihood Factor Analysis via Nonconvex Penalties

In fanc: Penalized Likelihood Factor Analysis via Nonconvex Penalty

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

x	A numeric data matrix.
factors	The number of factors.
n.obs	The number of observations. This is required to calculate model-selection criteria and goodness-of-fit indices when only covmat is supplied. If it is omitted, model fitting is performed but these indices are unavailable.
rho	Values of rho. This may be a scalar or a matrix with one column for each gamma value.
gamma	Values of gamma.
cor.factor	Logical; if TRUE, factor correlations are estimated. The default is FALSE.
normalize	Logical; if TRUE, each variable is normalized. The default is TRUE.
normalize.penalty	Logical; if TRUE, variable-specific penalty weights are calculated. The default is FALSE.
covmat	A covariance matrix, used when the data matrix x is unavailable.
type	Penalty type: "MC", "prenet", or "enet". The default is "MC".
model	Model type: "FA" for factor analysis or "PPCA" for probabilistic principal component analysis. The default is "FA".
control	A list of control parameters. See ‘Details’.
digits	Number of digits used by the print method.
num.result	Retained for compatibility with earlier versions; it currently does not change the printed output.
...	Reserved for compatibility; currently unused.

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:

loadings	Factor-loading matrices for every rho and gamma.
uniquenesses	Unique variances for every rho and gamma.
Phi	Factor-correlation matrices.
rho	Matrix of rho values.
gamma	Vector of gamma values.
df, dfnonzero	Degrees of freedom.
AIC, BIC, CAIC, EBIC	Model-selection criteria based on reparametrized degrees of freedom.
AIC_dfnonzero, BIC_dfnonzero, CAIC_dfnonzero, EBIC_dfnonzero	Model-selection criteria based on active parameters.
GFI, AGFI, CFI, RMSEA, SRMR	Goodness-of-fit indices.
AGFI_dfnonzero, CFI_dfnonzero, RMSEA_dfnonzero	Goodness-of-fit indices based on active parameters.
factors	Number of factors.
cor.factor	Whether factor correlations were estimated.
x	The original data matrix, or NULL when only covmat was supplied.
convergence	Convergence indicators for the fitting algorithms.
type, model	Penalty and model types.

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
[e-mail]

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)

fanc documentation built on July 26, 2026, 9:06 a.m.