Package 'fanc'

Title: Penalized Likelihood Factor Analysis via Nonconvex Penalty
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 new graphical tool which outputs path diagram, goodness-of-fit indices and model selection criteria for each regularization parameter. The user can change the regularization parameter by manipulating scrollbars, which is helpful to find a suitable value of regularization parameter.
Authors: Kei Hirose [aut, cre] , Michio Yamamoto [aut], Haruhisa Nagata [aut]
Maintainer: Kei Hirose <[email protected]>
License: GPL (>= 2)
Version: 2.3.11
Built: 2024-11-10 06:39:56 UTC
Source: CRAN

Help Index

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
[email protected]

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)

output from a "fanc" object for fixed value of gamma.

Description

This functions give us the loadings from a "fanc" object for fixed value of gamma.

Usage

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

Arguments

x

Fitted "fanc" model object.

gamma

The value of gamma.

rho

The value of rho.

scores

Logical flag for outputting the factor scores. Defalut is FALSE.

df.method

Two types of degrees of freedom are supported. If "reparametrization", the degrees of freedom of the MC+ are reparametrized based on the degrees of freedom of the lasso. If "active", the degrees of freedom of are the number of nonzero parameters.

Value

loadings

factor loadings
uniquenesses

unique variances
Phi

factor correlation
scores

factor scores
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
rho

a value of rho
gamma

a value of gamma

Author(s)

Kei Hirose
[email protected]

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

fanc and plot.fanc objects.

plot the solution path from a "fanc" object.

Description

This functions plots the solution paths from a "fanc" object for fixed value of gamma.

Usage

## S3 method for class 'fanc'
plot(x, Window.Height=500, type=NULL, df.method="active", ...)

Arguments

x

Fitted "fanc" model object.

Window.Height

A window height. The default is 500.

type

Two plot types are supported. If "path", the path diagram is depicted. If "heatmap", the heatmap is depicted.

df.method

Two types of degrees of freedom are supported. If "reparametrization", the degrees of freedom of the MC+ are reparametrized based on the degrees of freedom of the lasso. If "active", the degrees of freedom of are the number of nonzero parameters.

...

Other graphical parameters to plot

Value

NULL

Author(s)

Kei Hirose
[email protected]

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

fanc and out objects.

select from a "fanc" object for fixed value of gamma.

Description

This functions give us the loadings from a "fanc" object for fixed value of gamma.

Usage

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

Arguments

x

Fitted "fanc" model object.

criterion

The criterion by which to select the tuning parameter rho. One of "AIC", "BIC", "CAIC", or "EBIC". Default is "BIC".

gamma

The value of gamma.

scores

Logical flag for outputting the factor scores. Defalut is FALSE.

df.method

Two types of degrees of freedom are supported. If "active", the degrees of freedom of are the number of nonzero parameters. If "reparametrization", the degrees of freedom of the MC+ are reparametrized based on the degrees of freedom of the lasso.

Value

loadings

factor loadings
uniquenesses

unique variances
Phi

factor correlation
scores

factor scores
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
rho

a value of rho
gamma

a value of gamma

Author(s)

Kei Hirose
[email protected]

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

fanc and plot.fanc objects.