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 <qz280@cam.ac.uk>) that is optimized for the high dimensional problem where the number of samples n is less than the number of variables p.
factor.analysis(Y, r = 1, method = "pc")data matrix, a n*p matrix
number of factors (default, r =1)
algorithm to be used, "pc" (default) or "ml"
a list of objects
estimated factor loadings
estimated latent factors
estimated noise variance matrix
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.
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>
# Nonparanormal(npn) transformation
als.npn <- transformData(alsData$exprs)$data
#> Conducting the nonparanormal transformation via shrunkun ECDF...done.
## pc
pc<- factor.analysis(Y = als.npn, r = 2, method = "pc")
head(pc$Gamma)
#> [,1] [,2]
#> [1,] 0.3023514 0.60012228
#> [2,] 0.7577627 0.52654004
#> [3,] -0.7554944 -0.26095445
#> [4,] 0.1151171 -0.70688315
#> [5,] 0.4806646 -0.06877752
#> [6,] 0.1340605 -0.58860977
head(pc$Z)
#> [,1] [,2]
#> [1,] -0.33026001 -0.869972921
#> [2,] -0.68976787 -1.361599830
#> [3,] 0.67371880 0.007571711
#> [4,] -1.39466075 -0.688934677
#> [5,] 0.07287238 -1.076990819
#> [6,] -0.99396433 -0.488201691
head(pc$Sigma)
#> 207 208 10000 284 285 317
#> 0.5421869 0.1423013 0.3548809 0.4808143 0.7579812 0.6293163
## ml
ml <- factor.analysis(Y = als.npn, r = 2, method = "ml")
head(ml$Gamma)
#> [,1] [,2]
#> 207 0.2641432 0.55929046
#> 208 0.7728752 0.53838279
#> 10000 -0.7715566 -0.27324054
#> 284 0.1192708 -0.69677472
#> 285 0.4539599 -0.04553308
#> 317 0.1480935 -0.55334494
head(ml$Z)
#> [,1] [,2]
#> ALS2 -0.3086763 -0.7838108
#> ALS3 -0.5541185 -1.2612329
#> ALS4 0.7607658 0.1601732
#> ALS5 -1.3418033 -0.5918722
#> ALS6 0.1523818 -0.9958831
#> ALS7 -1.0637363 -0.3341780
head(ml$Sigma)
#> 207 208 10000 284 285 317
#> 0.6111499 0.1040704 0.3215149 0.4952729 0.7850598 0.6664684