standardized parameters don't match between std.lv = T and std.lv = F

[Luisa Horsten]

Dear all,

I use SEM to test hypotheses concerning the relation between latent factors. Say my model looks like this:

bifactor <- '
A =~ X1 + X2 + X3 + X4 + X5 + X6
B =~ X7 + X8 + X9 + X10 + X11 + X12
C =~ X13 + X14 + X15 + X16 + X17 + X18


G =~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10 + X11 + X12 + X13 + X14 + X15 + X16 + X17 + X18



D =~ X19 + X20 + X21 + X22 + X23 + X24
H =~ Y1 + Y2 + Y3 + Y4 + Y5 + Y6


D ~~ HH
D ~~ G'

My approach so far was to estimate one model in which the parameters are estimated freely and then one in which I constrain the parameters to be equal (D ~~ a*HH, D ~~ a*G).
My hypothesis would be that r(D, G) > r(D, HH), so I want to look at the standardized parameters.Thus, when fitting the model I set std.lv = TRUE

Now I would expect that the value in the estimate and the std.lv columns are equal (which they are), and that they are also equal to the values in the std.lv-column of the fitted model, in which I did not set std.lv = TRUE. The latter is not the case and I am super confused about that. I had used the exact same approach in a model before, and there the values matched, so I feel like I am not completely off with my expectation... Could anybody shed light on this? Thanks a lot in advance!

[Edward Rigdon]

What is HH? Is it related to H?

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[Terrence Jorgensen]

Ed's question is relevant because HH appears to be either a typo for H, or HH is an observed variable.  If it is the latter, try setting fixed.x=FALSE and comparing Std.lv columns.  Additionally, did you set orthogonal=TRUE?  

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Luisa Horsten]

Oh yes, sorry, my bad. Those are good points, indeed! That was indeed a typo, H and HH are the same. And no, I did not set orthogonal = TRUE, but what I did is set A ~~ 0*B, A ~~ 0*C, A ~~ 0*G, B ~~ 0*C, B ~~ 0*G, C ~~ 0*G. Sorry, should have mentioned that from the start. So the full model is

bifactor <- '

A =~ X1 + X2 + X3 + X4 + X5 + X6
B =~ X7 + X8 + X9 + X10 + X11 + X12
C =~ X13 + X14 + X15 + X16 + X17 + X18


G =~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10 + X11 + X12 + X13 + X14 + X15 + X16 + X17 + X18



D =~ X19 + X20 + X21 + X22 + X23 + X24

HH =~ Y1 + Y2 + Y3 + Y4 + Y5 + Y6

D ~~ HH
D ~~ G

A ~~ 0*B
 A ~~ 0*C
A ~~ 0*G
B ~~ 0*C
B ~~ 0*G
C ~~ 0*G'


bifactor.fit <- cfa(bifactor,
                     data = data,
                     missing = "fiml",
                     std.lv = TRUE,
                     estimator = "MLR")

[Terrence Jorgensen]

Interesting.  I just tried comparing the Std.lv column with std.lv=TRUE and FALSE using the ?cfa example, and found the same issue.  Thanks for point this out.

The problem is due to a new argument, which provides a third option to set the latent scale: effects.coding="loadings"

?lavOptions

The previous behavior set the value of auto.fix.first as the opposite of std.lv (so if one was TRUE, the other was FALSE).  Now, when you set std.lv=TRUE, it leaves auto.fix.first=TRUE.  In your output, did you notice that the latent variances were all 1, but so were all the first factor loadings?  So the reason results were inconsistent is probably that you were comparing models that were not statistically equivalent, because with std.lv=TRUE, there were additional constraints. 

For now, you can get around this by explicitly setting std.lv=TRUE and auto.fix.first=FALSE.  I will bring this to Yves' attention to update the internal checks, to make sure the original behavior automatically sets auto.fix.first=FALSE when std.lv=TRUE.  

https://github.com/yrosseel/lavaan/issues/154

[Luisa Horsten]

No, to be honest I did not double check the factor loadings, but now that you mention it... :D Thanks for your time investigating this, I really appreciate it!