ifa: Independent Factors Analysis

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

Independent Factors Analysis (IFA) is an extension and synthesis of the factor analysis and independent components analysis methods. Note that rotation is not implemented in this model, as the IFA solution is not invariant under orthogonal rotations. Any orthogonal rotation of independent variables will result in correlated ones, breaking the independence of the latent variables extracted by an independent components or independent factors analysis. Uncorrelatedness is a neccessary, but not sufficient condition for independence. Independence is a stronger condition: a set of random variables has the property of independence when the joint probability density function of the set is the product of each individual variable's probability density function, i.e. f(x_1, x_2, ..., x_p) = ∑ f(x_p). However, the property of being uncorrelated only means that the linear relationship between a set of variables is null, which obviously leaves open other types of relationships. Likewise orthogonality only implies linear independence. While independent components/factors are orthogonal to one another, the basis vectors are not neccessarily orthogonal. This is unlike PCA, where the basis vectors are orthogonal to each other. Therefore, orthogonal rotation of the basis vectors of ICA/IFA will not be guaranteed to preserve orthogonality of the components, as the orthogonal rotation only guarantees linear independence.

Usage

ifa(
  Y,
  nfac = max(nrow(Y) - 2, ncol(Y)),
  ic = NULL,
  scale = TRUE,
  max.iter = 1000,
  tol = 1e-04
)

Arguments

Y	a numeric matrix or data frame of only numeric variables.
nfac	the number of factors to extract.
ic	an integer vector of length nfac detailing how many independent components comprise each factor. for example, c(4,3,3,1). the default is NULL, which yields 2 independent components per factor.
scale	should the variables be scaled prior to analysis? Defaults to TRUE.
max.iter	maximum number of iterations. defaults to 1000.
tol	a tolerance value for convergence. defaults to 1e-4.
rotate	a rotation function from the GPArotation package. Defaults to Varimax.

Value

an object of class "facanal"

References

Attias, H. (1999). Independent factor analysis, Neural Comput. 11(4), 803–851.

Montanari, A. & Viroli, C. (2010). The independent factor analysis approach to latent variable modelling, Statistics, 44:4, 397-416, doi:10.1080/02331880903189125

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.