Package 'fad'

Title: Factor Analysis for Data
Description: Compute maximum likelihood estimators of parameters in a Gaussian factor model using the the matrix-free methodology described in Dai et al. (2020) <doi:10.1080/10618600.2019.1704296>. In contrast to the factanal() function from 'stats' package, fad() can handle high-dimensional datasets where number of variables exceed the sample size and is also substantially faster than the EM algorithms.
Authors: Somak Dutta [aut, cre], Fan Dai [aut], Ranjan Maitra [ctb]
Maintainer: Somak Dutta <[email protected]>
License: GPL-3
Version: 0.9-1
Built: 2024-11-21 06:40:42 UTC
Source: CRAN

Help Index

Factor Analysis for data (high or low dimensional).

Description

Perform fast matrix-free maximum-likelihood factor analysis on a covariance matrix or data matrix, works if number of variables is more than number of observations.

Usage

fad(
  x,
  factors,
  data = NULL,
  covmat = NULL,
  n.obs = NA,
  subset,
  na.action,
  start = NULL,
  scores = c("none", "regression", "Bartlett"),
  rotation = "varimax",
  control = NULL,
  lower = 0.005,
  ...
)

Arguments

x

A formula or a numeric matrix or an object that can be coerced to a numeric matrix.
factors

The number of factors to be fitted.
data

An optional data frame (or similar: see model.frame), used only if x is a formula. By default the variables are taken from environment(formula).
covmat

A covariance matrix, or a covariance list as returned by cov.wt. Of course, correlation matrices are covariance matrices.
n.obs

The number of observations, used if covmat is a covariance matrix.
subset

A specification of the cases to be used, if x is used as a matrix or formula.
na.action

The na.action to be used if x is used as a formula.
start

NULL or a matrix of starting values, each column giving an initial set of uniquenesses.
scores

Type of scores to produce, if any. The default is none, "regression" gives Thompson's scores, "Bartlett" given Bartlett's weighted least-squares scores. Partial matching allows these names to be abbreviated. Also note that some of the scores-types are not applicable when p > n.
rotation

character. "none" or the name of a function to be used to rotate the factors: it will be called with first argument the loadings matrix, and should return a list with component loadings giving the rotated loadings, or just the rotated loadings. The options included in the package are: varimax, promax, quartimax, equamax.
control

A list of control values:

nstart

The number of starting values to be tried if start = NULL. Default 1.

trace

logical. Output tracing information? Default FALSE.

opt

A list of control values to be passed to optim's control argument.

rotate

a list of additional arguments for the rotation function.
lower

The lower bound for uniquenesses during optimization. Should be > 0. Default 0.005.
...

Components of control can also be supplied as named arguments to fad.

Value

An object of class "fad" with components

loadings

A matrix of loadings on the correlation scale, one column for each factor. The factors are ordered in decreasing order of sums of squares of loadings, and given the sign that will make the sum of the loadings positive. This is of class "loadings"
uniquenesses

The uniquenesses computed on the correlation scale.
sd

The estimated standard deviations.
criteria

The results of the optimization: the value of the criterion (a linear function of the negative log-likelihood) and information on the iterations used.
factors

The argument factors.
dof

The number of degrees of freedom of the factor analysis model.
method

The method: always "mle".
rotmat

The rotation matrix if relevant.
scores

If requested, a matrix of scores. napredict is applied to handle the treatment of values omitted by the na.action.
n.obs

The number of observations if available, or NA.
call

The matched call.
na.action

If relevant.
loglik, BIC

The maximum log-likelihood and the Bayesian Information Criteria.

See Also

factanal

Examples

set.seed(1234)

## Simulate a 200 x 3 loadings matrix ~i.i.d N(0,1)
L <- matrix(rnorm(200*3),200,3) 

## Simulate the uniquenesses i.i.d U(0.2,0.9)
D <- runif(200,0.2,0.9) 

## Generate a data matrix of size 50 x 200 with rows
## ~i.i.d. N(0,LL'+diag(D))
X <- tcrossprod(matrix(rnorm(50*3),50,3),L) + matrix(rnorm(50*200),50,200) %*% diag(sqrt(D))

## Fit a factor model with 3 factors:
fit = fad(X,3)


## Print the loadings:
print(fit$loadings)

Factor Analysis for data on a sphere (high or low dimensional).

Description

Perform fast matrix-free maximum-likelihood factor analysis on data on sphere, works if number of variables is more than number of observations.

Usage

fads(
  inputs,
  q,
  ii = 123,
  M = NULL,
  L = NULL,
  D = NULL,
  gamma = NA,
  maxiter = 10000,
  epsi = 1e-04
)

Arguments

inputs

A numeric matrix or an object that can be coerced to a numeric matrix.
q

The number of factors to be fitted.
ii

The random seeds for initialization. Default 123 if no initial values of parameters are imported.
M

The initial values of mean.
L

The initial values of loading matrix.
D

The initial values of uniquenesses.
gamma

The common constant used in the eBIC formula. Default 'NA'.
maxiter

The maximum iterations. Default 10,000
epsi

The absolute difference between final data log-likelihood values on consecutive step. Default 0.0001.

Value

An object of class "fads" with components

mu

The estimate mean.
loadings

A matrix of loadings on the correlation scale, one column for each factor. The factors are ordered in decreasing order of sums of squares of loadings, and given the sign that will make the sum of the loadings positive.This is of class "loadings"
uniquenesses

The uniquenesses computed on the correlation scale.
sd

The estimated standard deviations.
iter

The number of iterations
gerr

the difference between the gradients on consecutive step.
loglik, eBIC

The maximum log-likelihood the extended Bayesian Information Criteria (Chen and Chen,2008).

Print the Output of Factor Analysis

Description

Prints the output of the fad.

Usage

## S3 method for class 'fad'
print(x, digits = 3, ...)

Arguments

x

an object of class fad.
digits

number of decimal places to use in printing uniquenesses and loadings.
...

further arguments to print.

Value

None.

Print the Output of Factor Analysis

Description

Prints the output of the fads.

Usage

## S3 method for class 'fads'
print(x, digits = 3, ...)

Arguments

x

an object of class fads.
digits

number of decimal places to use in printing uniquenesses and loadings.
...

further arguments to print.

Value

None.