Factor Analysis

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Exploratory Factor Analysis

n <- 500
dt <- data.table(
    x1 = rnorm(n)
  , x2 = rnorm(n) + 1
  , x3 = rnorm(n) + 2
)

dt <- dt[, x4 := x1 + x2 * 3
         ][, x5 := x2 + x3 ^ 2
           ][, x6 := x3 * 4 + x1 * x2]
  
  


library(psych)
fa3 <- fa(dt, nfactors=3, rotate="oblimin", fm="minres")

fa_table <- function(obj){
    t <- unclass(obj$loadings)
    rtn <- data.table(t)
    colnames(rtn) <- dimnames(t)[[2]]
    rtn$variable <- dimnames(t)[[1]]
    vars <- c("variable", dimnames(t)[[2]])
    invisible(rtn[, ..vars])
}

 fa_table(fa3) %>%
    prt(caption="Loadings with Three Factors")

Loadings with Three Factors
variable	MR1	MR2	MR3
x1	0.1291541	0.3209858	0.9356915
x2	0.2819707	0.9040814	-0.3168037
x3	0.9433285	-0.3199487	-0.0642847
x4	0.3054854	0.9508368	-0.0108175
x5	0.9427486	-0.0871145	-0.1274846
x6	0.9363983	-0.2166857	0.1629788

fa3$Vaccounted %>% unclass %>% prt(caption="Variance Explained")

Variance Explained
	MR1	MR2	MR3
SS loadings	2.8449949	1.9813944	1.0229471
Proportion Var	0.4741658	0.3302324	0.1704912
Cumulative Var	0.4741658	0.8043982	0.9748894
Proportion Explained	0.4863791	0.3387383	0.1748826
Cumulative Proportion	0.4863791	0.8251174	1.0000000

R sessionInfo

sessionInfo()

R version 4.2.0 (2022-04-22) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu 20.04.3 LTS

Matrix products: default BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0 LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

locale: [1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
[4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
[7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C

attached base packages: [1] stats graphics grDevices utils datasets methods base

other attached packages: [1] psych_2.2.5 Wu_0.0.0.9000 flexdashboard_0.5.2 [4] lme4_1.1-29 Matrix_1.4-0 mgcv_1.8-38
[7] nlme_3.1-152 png_0.1-7 scales_1.2.0
[10] nnet_7.3-16 labelled_2.9.1 kableExtra_1.3.4
[13] plotly_4.10.0 gridExtra_2.3 ggplot2_3.3.6
[16] DT_0.23 tableone_0.13.2 magrittr_2.0.3
[19] lubridate_1.8.0 dplyr_1.0.9 plyr_1.8.7
[22] data.table_1.14.2 rmdformats_1.0.4 knitr_1.39

loaded via a namespace (and not attached): [1] httr_1.4.3 sass_0.4.1 tidyr_1.2.0 jsonlite_1.8.0
[5] viridisLite_0.4.0 splines_4.2.0 bslib_0.3.1 assertthat_0.2.1 [9] highr_0.9 yaml_2.3.5 pillar_1.8.0 lattice_0.20-45
[13] glue_1.6.2 digest_0.6.29 rvest_1.0.2 minqa_1.2.4
[17] colorspace_2.0-3 htmltools_0.5.3 survey_4.1-1 pkgconfig_2.0.3
[21] haven_2.5.0 bookdown_0.27 purrr_0.3.4 webshot_0.5.3
[25] svglite_2.1.0 tibble_3.1.8 generics_0.1.3 ellipsis_0.3.2
[29] withr_2.5.0 klippy_0.0.0.9500 lazyeval_0.2.2 mnormt_2.1.0
[33] cli_3.3.0 survival_3.2-13 evaluate_0.15 fansi_1.0.3
[37] MASS_7.3-54 forcats_0.5.1 xml2_1.3.3 tools_4.2.0
[41] hms_1.1.1 mitools_2.4 lifecycle_1.0.1 stringr_1.4.0
[45] munsell_0.5.0 compiler_4.2.0 jquerylib_0.1.4 systemfonts_1.0.4 [49] rlang_1.0.4 grid_4.2.0 nloptr_2.0.3 rstudioapi_0.13
[53] htmlwidgets_1.5.4 rmarkdown_2.14 boot_1.3-28 gtable_0.3.0
[57] DBI_1.1.2 R6_2.5.1 fastmap_1.1.0 utf8_1.2.2
[61] stringi_1.7.8 parallel_4.2.0 Rcpp_1.0.9 vctrs_0.4.1
[65] tidyselect_1.1.2 xfun_0.31