fanc: fanc (penalized maximum likelihood factor analysis via...

In fanc: Penalized Likelihood Factor Analysis via Nonconvex Penalty

fanc (penalized maximum likelihood factor analysis via nonconvex penalties)

Description

This package computes the solution path of penalized maximum likelihood estimates via MC+ penalties.

Usage

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

Arguments

x	A data matrix.
factors	The number of factors.
cor.factor	An indicator of the factor correlation. If "TRUE", the factor correlation is considered. Default is "FALSE".
normalize	If "TRUE", each variable is normalized, otherwise it is left alone.
normalize.penalty	If "TRUE", the penalty term for each variable has a weight so that the loading matrix is normalized.
rho	The values of rho. It can be a scalar or a matrix.
gamma	The values of gamma. It must be a vector.
covmat	A covariance matrix, which is needed if the data matrix "x" is not available.
n.obs	The number of observations, which is needed to calculate the model selection criteria and goodness-of-fit indices when the data matrix "x" is not available.
type	Type of penalty. If "MC", the MC penalty is used. If "prenet", the prenet penalty is used. If "enet", the elastic penalty is used. Default is "MC".
model	Type of model. "FA", the factor analysis model is used. If "PPCA", the probabilistic principal component analysis is conducted. In the PPCA, the unique variances have the same value. Default is "FA".
control	A list of control parameters. See ‘Details’.

Details

The control argument is a list that can supply any of the following components:

length.rho

Candidates of tuning parameters which is used for grid search of reparametrization of MC+.

length.gamma

A length of tuning parameter which controls sparsenesses. For each rho, gamma=Inf yields soft threshold operator (i.e., lasso penalty) and gamma=+1 produces hard threshold operator.

max.rho

Maximum value of rho.

max.gamma

A maximum value of gamma (excludes Inf.).

min.gamma

A minimum value of gamma.

eta

A tuning parameter used for preventing the occurrence of improper solutions. eta must be non-negative.

ncand.initial

The number of candidates of initial values of factor loadings.

ncand.initial.prenet

The number of candidates of initial values for prenet penalty. Because the prenet penalty is unstable when rho is large, ncand.initial.prenet must be large. Default is 1000.

maxit.em

A maximum number of iterations for EM algortihm.

maxit.cd

A maximum number of iterations for coordinate descent algortihm.

maxit.bfgs

A maximum number of iterations for BFGS algorithm used in the update of factor correlation.

maxit.initial

A maximum number of iterations for choosing the initial values.

start

Type of start. If "cold", the initial value of factor loadings is randomly chosen for each tuning parameter, which can be slow.

Delta

A proportion of maximum value of rho to minimum value of rho, i.e., rho.min =Delta*rho.max.

min.uniquevar

A minimum value of unique variances.

tol.em

A positive scalar giving the tolerance at which the parameter in EM is considered close enough to zero to terminate the algorithm.

tol.cd

A positive scalar giving the tolerance at which the factor loadings in coordinate descent is considered close enough to zero to terminate the algorithm.

tol.bfgs

A positive scalar giving the tolerance at which the factor correlation in BFGS algorithm is considered close enough to zero to terminate the algorithm.

min.rhozero

If "TRUE", the minimum value of "rho" is zero.

zita

A value of hyper-parameter of factor correlation.

progress

If "TRUE", the progress for each tuning parameter is displayed.

openmp

If "TRUE", the parallel computation via OpenMP is excecuted.

num.threads

The number of threads of the openmp. Only used when openmp is "TRUE",

gamma.ebic

The value of gamma used in the extended BIC

Value

loadings	factor loadings
uniquenesses	unique variances
Phi	factor correlation
rho	rho
AIC	AIC
BIC	BIC
CAIC	CAIC
df	degrees of freedom (number of non-zero parameters for the lasso estimation)
criteria	values of AIC, BIC and CAIC
goodness.of.fit	values of GFI and AGFI
gamma	a value of gamma
Npflag	If the number of observation is larger than the number of variables, 1, otherwise 0.
factors	the number of factors
cor.factor	An indicator of the factor correlation
x	data matrix
convergence	indicator of convergence of EM algorithm, coordinate descent and BFGS. If all of these variables are 0, the algorithm has been converged

Author(s)

Kei Hirose
[e-mail]

References

Hirose, K. and Yamamoto, M. (2014). Sparse estimation via nonconcave penalized likelihood in a factor analysis model,
Statistics and Computing, in press

See Also

out and plot.fanc objects.

Examples

#generate data
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 data
fit <- fanc(x,2)
fit2 <- fanc(x,2,cor.factor=TRUE) #factor correlation is estimated

#print candidates of gamma and rho
print(fit)

#output for fixed tuning parameters
out(fit, rho=0.1, gamma=Inf)

#select a model via model selection criterion
select(fit, criterion="BIC", gamma=Inf)


#plot solution path
plot(fit)

fanc documentation built on Nov. 15, 2022, 1:05 a.m.