SEMgraph (version 1.2.2)

factor.analysis: Factor analysis for high dimensional data

Description

Wrapper for Factor Analysis with potentially high dimensional variables implement in the "cate" R package (Author: Jingshu Wang [aut], Qingyuan Zhao [aut, cre] Maintainer: Qingyuan Zhao <[e-mail]>) that is optimized for the high dimensional problem where the number of samples n is less than the number of variables p.

Usage

factor.analysis(Y, r = 1, method = "pc")

Value

a list of objects

Gamma

estimated factor loadings

Z

estimated latent factors

Sigma

estimated noise variance matrix

Arguments

Y

data matrix, a n*p matrix

r

number of factors (default, r =1)

method

algorithm to be used, "pc" (default) or "ml"

Details

The two methods extracted from "cate" are quasi-maximum likelihood (ml), and principal component analysis (pc). The ml is iteratively solved the EM algorithm using the PCA solution as the initial value. See Bai and Li (2012) for more details.

References

Jushan Bai and Kunpeng Li (2012). Statistical Analysis of Factor Models of High Dimension. The Annals of Statistics, 40 (1), 436-465 <https://doi.org/10.1214/11-AOS966>

Jingshu Wang and Qingyuan Zhao (2020). cate: High Dimensional Factor Analysis and Confounder Adjusted Testing and Estimation. R package version 1.1.1. <https://CRAN.R-project.org/package=cate>

Examples

# Nonparanormal(npn) transformation
als.npn <- transformData(alsData$exprs)$data

## pc
pc<- factor.analysis(Y = als.npn, r = 2, method = "pc")
head(pc$Gamma)
head(pc$Z)
head(pc$Sigma)

## ml
ml <- factor.analysis(Y = als.npn, r = 2, method = "ml")
head(ml$Gamma)
head(ml$Z)
head(ml$Sigma)