Bifactor ESEM - uncorrelated factors

Serena

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Jul 7, 2024, 8:33:48 AM7/7/24

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Hi there,

I found factors cannot be uncorrelated in bifactor ESEM.

I have three factors indicated by 4 items each. Now I would like to run bifactor ESEM. My code is:

biesem_mod <- "
efa('sat')*f1 + efa('sat')*f2 + efa('sat')*f3 =~ var1 + var2 + var3 + var4 +
var5 + var6 + var7 + var8 +
var9 + var10 + var11 + var12

g_f =~ var1 + var2 + var3 + var4 +
var5 + var6 + var7 + var8 +
var9 + var10 + var11 + var12

f1 ~~ 0*f2
f1 ~~ 0*f3
f2 ~~ 0*f3

g_f ~~ 0*f1 + 0*f2 + 0*f3
"
biesem_mod_fit <- cfa(biesem_mod, data = data, cluster = "id", estimator = "MLR", rotation = "geomin")

summary(biesem_mod_fit, fit.measures = TRUE, standardized = TRUE)

After these, in the output:
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f1 ~~
f2 0.455 0.455 0.455
f3 0.289 0.289 0.289
f2 ~~
f3 0.220 0.220 0.220
f1 ~~
g_f 0.000 0.000 0.000
f2 ~~
g_f 0.000 0.000 0.000
f3 ~~
g_f 0.000 0.000 0.000

The covariances between three factors still exist, however, the covariances between specific factors and the general factor are o.

Any ideas about this?

Thanks in advance,
Serena

Daniel Morillo Cuadrado

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Jul 9, 2024, 12:21:57 PM7/9/24

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It's probably due to using a "geomin" rotation, which I think is an oblique rotation. If you want them to be uncorrelated try with an orthogonal rotation instead. According to the `efa()` help page, you may check the GPArotation package for help about the different types of rotations.

In any case, I have my doubts that specific factors should necessarily be constrained to be uncorrelated always, but that may be unrelated to your problem.

Hope it helps!

--

Daniel Morillo, Ph.D.

GitHub | ORCID

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Serena

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Jul 10, 2024, 2:09:37 AM7/10/24

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Hi Daniel,

Thanks for your ideas!

-> It's probably due to using a "geomin" rotation, which I think is an oblique rotation. If you want them to be uncorrelated try with an orthogonal rotation instead.

I did try the 'target' rotation, which is an orthogonal rotation, but the results are similar (i.e., they still cannot be uncorrelated).

Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all

f1 ~~
f2 -0.382   -0.382    -0.382
f3 0.729    0.729       0.729
f2 ~~
f3 -0.260 -0.260       -0.260

f1 ~~
g_f 0.000 0.000 0.000
f2 ~~
g_f 0.000 0.000 0.000
f3 ~~
g_f 0.000 0.000 0.000

-> In any case, I have my doubts that specific factors should necessarily be constrained to be uncorrelated always, but that may be unrelated to your problem.

My understanding is that they capture different information and thus should be uncorrelated. However, I am open to discussing this further.