Factor analysis visualization made easy with FAtools

NOTE: THIS PACKAGE IS IN DEVELOPMENT

From choosing the numbers of factors to extract to inspecting loadings, factor analysis can be very visual in nature. The FAtools R package aims to make this process easier by providing functions to do visualizations with ease.

To Download:

library('devtools')
#devtools::install_github('mattkcole/FAtools')
library('FAtools')

Examples:

We can first look at our data (here we are using the possibly cliche but familiar data, mtcars).

library(datasets)
summary(mtcars)
#>       mpg             cyl             disp             hp       
#>  Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0  
#>  1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5  
#>  Median :19.20   Median :6.000   Median :196.3   Median :123.0  
#>  Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7  
#>  3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0  
#>  Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0  
#>       drat             wt             qsec             vs        
#>  Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
#>  1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
#>  Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
#>  Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
#>  3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
#>  Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
#>        am              gear            carb      
#>  Min.   :0.0000   Min.   :3.000   Min.   :1.000  
#>  1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
#>  Median :0.0000   Median :4.000   Median :2.000  
#>  Mean   :0.4062   Mean   :3.688   Mean   :2.812  
#>  3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
#>  Max.   :1.0000   Max.   :5.000   Max.   :8.000

Let's first make our correlation matrix - we wont worry about scaling or investigating our data much for this demonstration (usually a bad idea).

corr.matrix <- cor(mtcars)

Let's load the packages we need for our analysis:

library('psych')    # for statistical methods
library('FAtools')  # for some plotting and EDA
library('dplyr')    # for data wrangling
library('knitr')    # for rmd help

Lets make and plot our scree plot to assess the number of factors present.

s.plot <- FAtools::scree_plot(corr.matrix, nrow(mtcars), ncol(mtcars))
plot(s.plot)

We can conduct our factor analysis with two factors using the psych package.

results <- psych::fa(corr.matrix, 2, rotate = "varimax")
results$loadings
#> 
#> Loadings:
#>      MR1    MR2   
#> mpg   0.675 -0.630
#> cyl  -0.634  0.731
#> disp -0.727  0.607
#> hp   -0.316  0.881
#> drat  0.812 -0.219
#> wt   -0.784  0.454
#> qsec -0.151 -0.873
#> vs    0.295 -0.788
#> am    0.901       
#> gear  0.882  0.150
#> carb         0.809
#> 
#>                  MR1   MR2
#> SS loadings    4.464 4.393
#> Proportion Var 0.406 0.399
#> Cumulative Var 0.406 0.805

The loadings look pretty good, but we can make them more interpretable by excluding low loadings (param: cutoff), rounding (param: roundto), incorporate a data dictionary, and include labels -- And we can use the knitr::kable() function for great looking tables in Rmarkdown documents.

FAtools::loadings_table(results$loadings, 2, cutoff = 0.3, roundto = 2) %>%
        kable()

name	V1	V2
mpg	0.68	-0.63
cyl	-0.63	0.73
disp	-0.73	0.61
hp	-0.32	0.88
drat	0.81
wt	-0.78	0.45
qsec		-0.87
vs	0.3	-0.79
am	0.9
gear	0.88
carb		0.81

Say we had more informative names than colnames(mtcars).

cool_names <- c("Miles Per Gallon", "Cylinders", "Displacement",
                "Gross horsepower", "Rear Axle ratio", "Weight (1K lbs)",
                "1/4 mile time", "V/S", "Manual", "Forward gears",
                "Carburetors")

And say we wern't really all that interested in loadings with an absolute value less than 0.3.

FAtools::loadings_table(loading_frame = results$loadings,
                        cutoff = 0.3, roundto = 2,
                        Name = colnames(mtcars), 
                        description = cool_names) %>%
        kable()

name	description	V1	V2
mpg	Miles Per Gallon	0.68	-0.63
cyl	Cylinders	-0.63	0.73
disp	Displacement	-0.73	0.61
hp	Gross horsepower	-0.32	0.88
drat	Rear Axle ratio	0.81
wt	Weight (1K lbs)	-0.78	0.45
qsec	1/4 mile time		-0.87
vs	V/S	0.3	-0.79
am	Manual	0.9
gear	Forward gears	0.88
carb	Carburetors		0.81

We could also display this graphically, which works well when we have more retained factors or many more variables. (let's say we have 5 factors extracted).

loadings5 <- cor(mtcars) %>%
        psych::fa(2, rotate = "varimax")
        
FAtools::loadings_plot(loadings5$loadings,
                       colorbreaks = c(0, 0.2, 0.4, 0.6, 0.8, 1),
                       labRow = c("F1", "F2"),
                       columnlabels = cool_names)
#> Warning in if (is.na(labRow) == T) {: the condition has length > 1 and only
#> the first element will be used

Looks great!

Submit and issue with any concerns!

Credits: Much of the scree plot functionality comes from code provided by: www.statmethods.net