EFA with Mixed Data Types

library(psych)

Select only relevant columns

dat <- mtcars[c("mpg", "disp", "hp", "drat", "wt", "qsec", "vs", "am", "gear")] |> na.omit()

mixedCor(dat,
         c = c("mpg", "disp", "hp", "drat", "wt", "qsec"), 
         p = c("gear"),
         d = c("am", "vs"))
#> Call: mixedCor(data = dat, c = c("mpg", "disp", "hp", "drat", "wt", 
#>     "qsec"), p = c("gear"), d = c("am", "vs"))
#>      mpg   disp  hp    drat  wt    qsec  vs    am    gear 
#> mpg   1.00                                                
#> disp -0.85  1.00                                          
#> hp   -0.78  0.79  1.00                                    
#> drat  0.68 -0.71 -0.45  1.00                              
#> wt   -0.87  0.89  0.66 -0.71  1.00                        
#> qsec  0.42 -0.43 -0.71  0.09 -0.17  1.00                  
#> vs    0.82 -0.88 -0.90  0.55 -0.69  0.92  1.00            
#> am    0.75 -0.74 -0.30  0.89 -0.86 -0.29  0.26  1.00      
#> gear  0.55 -0.63 -0.14  0.80 -0.66 -0.24  0.32  1.00  1.00

Run EFA

efa <- fa(dat, nfactors = 3, 
          fm = "pa", rotate = "oblimin",
          cor = "mixed") # <<<<<< this

I know nothing about cars, so maybe this does make sense?

parameters::model_parameters(efa, sort = TRUE, threshold = 0.45)
#> # Rotated loadings from Factor Analysis (oblimin-rotation)
#> 
#> Variable |  PA1  | PA2  | PA3  | Complexity | Uniqueness
#> --------------------------------------------------------
#> wt       | 0.89  |      |      |    1.03    |    0.11   
#> mpg      | -0.81 |      |      |    1.12    |    0.13   
#> hp       | 0.78  |      |      |    1.84    |    0.13   
#> am       | -0.71 |      | 0.54 |    2.42    |   -0.20   
#> disp     | 0.65  |      |      |    1.77    |    0.09   
#> vs       |       | 0.98 |      |    1.21    |   -0.19   
#> qsec     |       | 0.96 |      |    1.05    |    0.04   
#> gear     |       |      | 1.03 |    1.01    |   -0.04   
#> drat     |       |      | 0.59 |    1.74    |    0.27   
#> 
#> The 3 latent factors (oblimin rotation) accounted for 96.44% of the total variance of the original data (PA1 = 41.80%, PA2 = 28.81%, PA3 = 25.82%).

Get scores

head(efa$scores)
#>                          PA1        PA2        PA3
#> Mazda RX4         -0.7132604 -1.1436652  0.6883296
#> Mazda RX4 Wag     -0.5945421 -1.0484639  0.6801836
#> Datsun 710        -1.8079669  0.9292450  1.1463418
#> Hornet 4 Drive    -0.3823838  1.4346867 -0.8482820
#> Hornet Sportabout  0.9090902 -0.7456465 -1.1785893
#> Valiant           -0.3670598  1.6176777 -0.7955352