# Exploratory Factor Analysis Tables in R

I am currently taking a psychometrics courses, and in this psychometrics course we have just finished reviewing exploratory factor analysis (EFA), where we mostly used the `psych`

package. I was surprised that the `fa`

function did not produce a clean table to display EFA results. So, with a little exploration and help on stack exchange, two great ways to create tables for eigenvalue tables (include percentage of variance explained) and factor loadings with item suppression at whatever value we tell it to suppress.

Let’s begin.

## The Factor Analysis

For this example, I am going to use Allison Horst’s `palmerpenguins`

package for the data and produce a simple and meaningless factor structure. This is for demonstration purposes only

```
# load key packages
library(palmerpenguins)
library(tidyverse)
library(psych)
library(flextable)
# load data
data <- penguins %>%
select(bill_length_mm:body_mass_g)
# factor analysis
efa <- fa(data, nfactors=4, rotate="oblimin")
```

Saving the factor analysis as `efa`

creates a list with a number of useful elements:

`names(efa)`

```
## [1] "residual" "dof" "chi" "nh"
## [5] "rms" "EPVAL" "crms" "EBIC"
## [9] "ESABIC" "fit" "fit.off" "sd"
## [13] "factors" "complexity" "n.obs" "objective"
## [17] "criteria" "STATISTIC" "PVAL" "Call"
## [21] "null.model" "null.dof" "null.chisq" "TLI"
## [25] "F0" "r.scores" "R2" "valid"
## [29] "score.cor" "weights" "rotation" "communality"
## [33] "communalities" "uniquenesses" "values" "e.values"
## [37] "loadings" "model" "fm" "rot.mat"
## [41] "Phi" "Structure" "method" "scores"
## [45] "R2.scores" "r" "np.obs" "fn"
## [49] "Vaccounted"
```

For our purposes, we are going to focus on `Vaccounted`

and `loadings`

. `Vaccounted`

is comprised of a table of eigenvalues and their respective variances accounted for:

`efa$Vaccounted`

```
## MR1 MR2 MR3 MR4
## SS loadings 2.1807053 0.5820772 0.11719588 4.667710e-17
## Proportion Var 0.5451763 0.1455193 0.02929897 1.166928e-17
## Cumulative Var 0.5451763 0.6906956 0.71999460 7.199946e-01
## Proportion Explained 0.7571950 0.2021117 0.04069332 1.620745e-17
## Cumulative Proportion 0.7571950 0.9593067 1.00000000 1.000000e+00
```

For this table, we are simply going to convert it to a data frame and then make it a little bit fancier with `flextable`

. I have been including the `flex`

function in a lot of my assignment files lately. `flex`

is a function that takes a data frame and uses `flextable`

to style it in a Word-friendly, APA-like format:

```
# table set-up ----
flex <- function(data, title=NULL) {
# this grabs the data and converts it to a flextbale
flextable(data) %>%
# this makes the table fill the page width
set_table_properties(layout = "autofit", width = 1) %>%
# font size
fontsize(size=10, part="all") %>%
#this adds a ttitlecreates an automatic table number
set_caption(title,
autonum = officer::run_autonum(seq_id = "tab",
pre_label = "Table ",
post_label = "\n",
bkm = "anytable")) %>%
# font type
font(fontname="Times New Roman", part="all")
}
```

I use the `flex`

function to print tables that are automatically numbered in word. You will need to add the following to your YAML to make that work:

`output: bookdown::word_document2`

Returning to our table, the following code works easily:

```
efa[["Vaccounted"]] %>%
as.data.frame() %>%
#select(1:5) %>% Use this if you have many factors and only want to show a certain number
rownames_to_column("Property") %>%
mutate(across(where(is.numeric), round, 3)) %>%
flex("Eigenvalues and Variance Explained for Rotated Factor Solution")
```

Property | MR1 | MR2 | MR3 | MR4 |

SS loadings | 2.181 | 0.582 | 0.117 | 0.00 |

Proportion Var | 0.545 | 0.146 | 0.029 | 0.00 |

Cumulative Var | 0.545 | 0.691 | 0.720 | 0.72 |

Proportion Explained | 0.757 | 0.202 | 0.041 | 0.00 |

Cumulative Proportion | 0.757 | 0.959 | 1.000 | 1.00 |

Simple enough, right?

Now, on to a more slightly more complicated table. The loadings are stored in the `loadings`

element, but we also might want to communalities, uniqueness, and complexity score for each item too. Those are stored in different elements. In addition, we will want to sort the factor analysis so that it is easy to read. We’ll need to use `fa.sort`

for that. We also want to show factor loadings and suppress anything under .32 (a standard cut-off value). Finally, we will want to make this a simple function call so that we can use it multiple times with easy - factor analysis is an iterative process, after all. Here is the `fa_table`

function:

```
fa_table <- function(x, cut) {
#get sorted loadings
loadings <- fa.sort(x)$loadings %>% round(3)
#supress loadings
loadings[loadings < cut] <- ""
#get additional info
add_info <- cbind(x$communalities,
x$uniquenesses,
x$complexity) %>%
# make it a data frame
as.data.frame() %>%
# column names
rename("Communality" = V1,
"Uniqueness" = V2,
"Complexity" = V3) %>%
#get the item names from the vector
rownames_to_column("item")
#build table
loadings %>%
unclass() %>%
as.data.frame() %>%
rownames_to_column("item") %>%
left_join(add_info) %>%
mutate(across(where(is.numeric), round, 3))
}
```

And here is the result:

`fa_table(efa, .32)`

`## Joining, by = "item"`

```
## item MR1 MR2 MR3 MR4 Communality Uniqueness Complexity
## 1 body_mass_g 0.932 0.799 0.201 1.030
## 2 flipper_length_mm 0.791 0.995 0.005 1.252
## 3 bill_length_mm 0.718 0.584 0.416 1.311
## 4 bill_depth_mm 0.606 0.502 0.498 1.126
```

And here is the table:

```
fa_table(efa, .32) %>%
flex("A Pretty Factor Analysis Table")
```

item | MR1 | MR2 | MR3 | MR4 | Communality | Uniqueness | Complexity |

body_mass_g | 0.932 | 0.799 | 0.201 | 1.030 | |||

flipper_length_mm | 0.791 | 0.995 | 0.005 | 1.252 | |||

bill_length_mm | 0.718 | 0.584 | 0.416 | 1.311 | |||

bill_depth_mm | 0.606 | 0.502 | 0.498 | 1.126 |

Any factor loadings under .32 were suppressed, meaning they are an empty character string that shows as blanks. Had this been a long table with many more factors, the default output in R would have been unwieldy to view and difficult to print. Using the `fa_table`

function makes it easier.