I would like to obtain the initial communalities for an exploratory factor analysis in R (that is, the R squared of each item when predicted by the other items included in the analysis).
Is there a way to do this with either jmv::efa or psych::fa ?
I only see the uniqueness, which informs me of the communalities AFTER factor extraction (1-uniqueness)...
Thank you for your consideration : )
As you note, the initial communalities in a factor analysis are the squared multiple correlations (SMC) of each variable by the remaining variables. Using the built-in attitude dataset as an example they are easily calculated without additional packages via:
1 - 1 / diag(solve(cor(attitude)))
rating complaints privileges learning raises critical advance
0.7326020 0.7700868 0.3831176 0.6194561 0.6770498 0.1881465 0.5186447
The psych package includes the smc() function for convenience:
psych::smc(attitude)
rating complaints privileges learning raises critical advance
0.7326020 0.7700868 0.3831176 0.6194561 0.6770498 0.1881465 0.5186447
Here is the dput for the data I am using, hereafter called hwk:
hwk <- structure(list(V1 = structure(c(4, 4, 2, 2, 2, 2, 2, 2, 4, 4,
2, 3, 2, 3, 4, 2, 2, 2, 3, 3, 2, 3, 1, 3, 3, 3, 3, 4, 1, 2, 4,
1, 2, 3, 2, 3, 1, 1, 2, 2, 4, 3, 2, 1, 2, 3, 3, 4, 3, 3, 2, 3,
1, 4, 3, 2, 3, 4, 1, 3, 3, 3, 2, 2, 1, 2, 3, 4, 4, 2, 4, 3, 2,
3, 3, 3, 3, 2, 4, 3, 3, 3, 2, 2, 3, 4, 2, 4, 4, 2, 2, 3, 3), format.spss = "F8.0"),
V2 = structure(c(4, 4, 3, 4, 3, 4, 3, 2, 4, 1, 3, 3, 3, 4,
3, 3, 2, 3, 4, 3, 1, 4, 2, 3, 4, 2, 4, 3, 3, 2, 3, 2, 3,
3, 4, 3, 3, 3, 3, 3, 3, 2, 4, 2, 2, 2, 4, 3, 4, 4, 2, 4,
2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 4,
3, 4, 3, 3, 3, 4, 2, 4, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 3,
4, 4, 3), format.spss = "F8.0"), V3 = structure(c(4, 4, 4,
4, 4, 4, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4), format.spss = "F8.0"),
V4 = structure(c(4, 4, 3, 4, 3, 4, 2, 1, 3, 2, 3, 1, 4, 4,
2, 3, 2, 2, 2, 4, 1, 2, 2, 2, 3, 2, 3, 2, 2, 1, 3, 1, 1,
2, 4, 1, 1, 2, 3, 2, 2, 1, 1, 1, 3, 2, 4, 3, 3, 3, 3, 3,
3, 4, 3, 1, 4, 3, 4, 3, 2, 3, 2, 1, 4, 1, 4, 1, 2, 4, 4,
4, 3, 3, 3, 2, 2, 1, 4, 3, 2, 3, 2, 1, 3, 4, 1, 2, 4, 3,
4, 2, 2), format.spss = "F8.0"), V5 = structure(c(3, 3, 3,
4, 3, 4, 3, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2,
2, 2, 2, 4, 2, 3, 2, 3, 4, 1, 4, 2, 3, 3, 2, 2, 3, 2, 2,
3, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3,
2, 2, 3, 3, 3, 2, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4,
3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3), format.spss = "F8.0"),
V6 = structure(c(4, 4, 3, 4, 3, 4, 4, 1, 3, 3, 3, 3, 2, 3,
4, 2, 4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 4, 4, 3, 4, 4, 3,
3, 3, 4, 2, 2, 3, 3, 3, 4, 2, 4, 3, 4, 4, 4, 3, 4, 2, 4,
3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 3, 1, 4, 4, 4, 4, 4, 4,
4, 3, 4, 4, 4, 4, 2, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 3,
4, 4, 4), format.spss = "F8.0"), V7 = structure(c(4, 4, 2,
4, 2, 4, 4, 3, 3, 3, 2, 2, 4, 4, 3, 3, 1, 4, 3, 3, 1, 2,
4, 3, 4, 2, 4, 4, 3, 3, 2, 2, 3, 2, 4, 3, 3, 3, 3, 3, 3,
1, 4, 3, 2, 2, 4, 3, 4, 4, 2, 4, 2, 3, 4, 3, 3, 3, 4, 3,
4, 4, 3, 4, 4, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 3, 4, 3, 4,
3, 3, 3, 3, 2, 2, 4, 4, 4, 4, 2, 4, 4, 3), format.spss = "F8.0"),
V8 = structure(c(4, 4, 2, 1, 2, 1, 1, 1, 3, 3, 2, 3, 2, 3,
4, 2, 2, 2, 3, 3, 2, 3, 1, 3, 3, 3, 3, 4, 1, 2, 4, 1, 2,
3, 2, 3, 1, 1, 2, 2, 3, 1, 1, 1, 2, 3, 3, 4, 3, 3, 2, 3,
1, 3, 4, 2, 3, 4, 1, 3, 3, 3, 2, 2, 1, 2, 3, 4, 4, 2, 4,
3, 4, 4, 4, 4, 3, 2, 4, 3, 3, 3, 2, 2, 3, 4, 2, 4, 4, 2,
1, 3, 4), format.spss = "F8.0"), V9 = structure(c(4, 4, 4,
4, 4, 4, 4, 4, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 4, 4,
4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 4, 3, 2, 4, 3, 4,
4, 4, 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 4, 3, 2, 4,
3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4,
4, 3, 4, 4, 4, 4, 4, 3, 2, 4, 4, 4, 4, 4), format.spss = "F8.0"),
V10 = structure(c(4, 4, 2, 4, 2, 4, 3, 2, 3, 3, 3, 2, 4,
4, 2, 2, 1, 3, 4, 4, 1, 4, 2, 3, 3, 2, 4, 3, 2, 3, 3, 1,
3, 2, 4, 3, 2, 3, 3, 3, 3, 1, 2, 4, 2, 3, 4, 4, 3, 3, 2,
4, 2, 4, 3, 3, 4, 3, 4, 3, 4, 4, 4, 1, 4, 3, 3, 4, 3, 4,
4, 3, 3, 3, 3, 3, 4, 1, 4, 3, 3, 3, 3, 2, 3, 4, 4, 2, 4,
2, 4, 4, 3), format.spss = "F8.0"), V11 = structure(c(3,
3, 1, 4, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 2, 2, 1,
2, 3, 1, 2, 3, 3, 2, 1, 2, 2, 2, 3, 2, 2, 3, 2, 1, 2, 2,
1, 1, 4, 3, 1, 3, 2, 3, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 3,
2, 2, 2, 2, 2, 2, 1, 1, 1, 3, 3, 4, 2, 1, 2, 2, 3, 3, 3,
3, 4, 3, 2, 3, 3, 2, 2, 2, 2, 1, 3, 1, 4, 1, 3), format.spss = "F8.0"),
V12 = structure(c(4, 4, 3, 2, 3, 2, 3, 1, 3, 3, 3, 3, 2,
3, 3, 2, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 4, 3, 4, 4,
3, 3, 3, 4, 2, 2, 3, 3, 3, 4, 2, 4, 3, 4, 4, 4, 3, 4, 2,
4, 3, 3, 3, 3, 4, 3, 3, 2, 2, 1, 1, 3, 1, 4, 4, 4, 4, 4,
4, 4, 3, 3, 2, 2, 2, 2, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
3, 2, 3, 4), format.spss = "F8.0")), class = c("tbl_df",
"tbl", "data.frame"), row.names = c(NA, -93L))
I did some research after my initial answer and it appears that there is a package for this called EFA Tools. There is a function called EFA that allows you to specify that you want the initial communalities. First, run the library and the EFA itself below:
# Load EFA Tools library:
library(EFAtools)
# Run EFA:
hwkfa <- EFA(hwk,
n_factors = 3,
start_method = "psych",
method = "PAF",
rotation = "promax",
init_comm = "smc", # selected initial communalities
type = "SPSS")
Then from there you can simply select the initial communalities by using the following code:
hwkfa$h2_init
Which gives you the following vector of output:
V1 V2 V3 V4 V5 V6 V7
0.8034001 0.5583605 0.5487691 0.3255253 0.5685402 0.4643686 0.5227481
V8 V9 V10 V11 V12
0.8050573 0.3474202 0.5564858 0.3496354 0.3783390
I ran the same thing in SPSS and got matching values:
