second-order cfa model working for lavaan but not for blavaan

[Lang Lang]

Hi,

I am fitting the following second order factor model, where constraints were added on latent variable variances for identification:

model <- '
  F1 =~ NA*X1 + X2 + X3 + X4
  F2 =~ NA*X5 + X6 + X7
  F3 =~ NA*X8 + X9 + X10
  G =~ NA*c1*F1 + c2*F2 + c3*F3
 
  F1 ~~ var_F1*F1
  F2 ~~ var_F2*F2
  F3 ~~ var_F3*F3

  var_F1 == 1 - c1^2
  var_F2 == 1 - c2^2
  var_F3 == 1 - c3^2
 
  G ~~ 1*G
'

It works fine with cfa function from lavaan, but when I use the exact same model with bcfa I got the following error: 

Error in prisplit[[1]] : subscript out of bounds

I spent some time in the source code but still have no clue why this happen or how to fix it.

Thanks in advance for any suggestions or comments.

[Ed Merkle]

I think this happens because of the constraints on var_F1 to var_F3. The default estimation method (target = "stan") cannot handle these constraints. It should work with target = "jags", though. (And the error message could also be improved here.)

One other thing: instead of manually fixing the variance of G to 1, it is better to use std.lv = TRUE. This is because, with std.lv = TRUE, blavaan will do some things to try to ensure model convergence (i.e., one loading per latent variable needs to be sign-constrained during estimation).

Ed

[Lang Lang]

Hi Ed, thanks for your comments. I tried jags but somehow it still doesn't work. I am guessing that this might also be due to cross-matrix constraint? since c1-c3 are loadings while  var_F1 to  var_F3 are from the variance matrix.

The reason I did not use the  std.lv = TRUE is that this will set all of my lv to variance 1 (both first order and second order lvs). The identification constraints I applied here is to have a marginal variance of onefor latent variables, could there be alternative ways to set up the constraints maybe?

Thank you so much!

Lang

[Ed Merkle]

I believe the problem is that var_F1 to var_F3 can potentially become negative, which are the "invalid" parent values. The constraints below might work with target = "jags":

var_F1 == max(.01, 1 - c1^2)

var_F2 == max(.01, 1 - c2^2)

var_F3 == max(.01, 1 - c3^2)

but then it seems there is a further blavaan problem after that. I will need to look at it some more.

Ed

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[Ed Merkle]

Lang,

I just made a small fix to the github version of blavaan so that target="jags" works, see installation instructions at the bottom of this page:

https://ecmerkle.github.io/blavaan/

I think you want the syntax below (separating the "NA" and parameter label on the "G =~" line, with std.lv = FALSE). You might also consider mildly informative priors on the loadings and latent variances to help ensure that the total variance does not go above 1 (though, if your data are standardized, maybe it is not an issue).

Ed

model <- '

F1 =~ NA*X1 + X2 + X3 + X4

F2 =~ NA*X5 + X6 + X7

F3 =~ NA*X8 + X9 + X10

G =~ NA*F1 + c1*F1 + c2*F2 + c3*F3

F1 ~~ NA*var_F1*F1

F2 ~~ NA*var_F2*F2

F3 ~~ NA*var_F3*F3

var_F1 == max(.01, 1 - c1^2)

var_F2 == max(.01, 1 - c2^2)

var_F3 == max(.01, 1 - c3^2)

G ~~ 1*G

'

On Thu, 2024-08-15 at 15:20 -0700, Lang Lang wrote:

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[Lang Lang]

Thank you so much Ed, it works perfectly now!