BI-Factor EFA

[ecelik]

Hello,

I replicated the bifactor EFA example from Muthén & Muthén using SEMLj (jamovi). While all fit indices are identical to the Mplus results, I observe small differences in factor loadings and standard errors.

The SEMLj syntax used is:

Code: Select all

efa("efa1")*FG +
efa("efa1")*FF1 +
efa("efa1")*FF2 =~
y1 + y2 + y3 + y4 + y5 + y65 + y6 + y7 + y8 + y9 + y10
FG  ~~ 0*FF1
FG  ~~ 0*FF2
FF1 ~~ 0*FF2

Rotation: Geomin
Geomin epsilon: 0.0001

The model specifies a bifactor structure with one general factor (FG) and two specific factors (FF1, FF2), constrained to be orthogonal.

Given that the fit indices are identical, could the small discrepancies in loadings and SEs be attributed to:

• Numerical optimization in Geomin rotation

• Differences in starting values or rotation algorithms (GPA vs. Mplus defaults)

• Factor scaling or sign indeterminacy

• Numerical computation of standard errors

Is it expected in bifactor EFA / ESEM frameworks that parameter estimates differ slightly while model fit remains identical?

Any insights would be greatly appreciated.

Thank you.

Mplus: https://www.statmodel.com/usersguide/chap5/ex5.29.html
SEMLj: https://drive.google.com/file/d/1ceoDYC ... sp=sharing

[mcfanda@gmail.com]

I do not have access to Mplus (it's not open source). Did you try to check the results with R lavaan?

[ecelik]

Dear Prof. Gallucci,
Thank you very much for your response.
Yes — I replicated the analysis in R using lavaan.
I'm sharing the lavaan and SEMLj syntax I used with you.
I’d be very grateful for suggestions.
Thanks again!

Code: Select all

#SEMlj Bifactor ESEM
efa("efa1")*FG +efa("efa1")*FF1 +efa("efa1")*FF2 
=~y1 + y2 + y3 + y4 + y5 +y6 + y7 + y8 + y9 + y10
FG  ~~ 0*FF1
FG  ~~ 0*FF2
FF1 ~~ 0*FF2

Code: Select all

#lavaan Bifactor ESEM
#Read  data Mplus example  bi-factor EFA
ex5.29 <- read.table("http://statmodel.com/usersguide/chap5/ex5.29.dat")
names(ex5.29) = paste0("y",1:10)

#install packages
library(lavaan)
library(lavaanPlot)
library(GPArotation)
library(semTools)

#Define EFA block
model.BESEM <- '
  efa("efa1")*FG +
  efa("efa1")*F1 +
  efa("efa1")*F2 =~ y1+y2+y3+y4+y5+y6+y7+y8+y9+y10
  '
#fit.BESEM
fit.BESEM <- cfa(
  model = model.BESEM,
  data = ex5.29,
  estimator = "ML",
  rotation = "bigeomin",
  rotation.args = list(
    rstarts = 30,
    algorithm = "gpa",
    orthogonal = TRUE,
    std.ov = TRUE,
    geomin.epsilon = 0.0001
  ),
)
  summary(fit.BESEM, standardized = TRUE)
  #BifactorESEM graph 
  lavaanPlot(name = "BifactorESEM",
             model = fit.BESEM)

[ecelik]

Mplus result :https://www.statmodel.com/usersguide/chap5/ex5.29.html

[mcfanda@gmail.com]

What was the correspondence between lavaan and SEMLj?