SEM with second order latent variables

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Cara Samuel

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May 26, 2018, 10:40:23 AM5/26/18
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Hi all, this is more of a theoretical SEM question than an lavaan question specifically (so my apologies if this is not an appropriate place to post this) but I was wondering if it makes conceptual and statistical sense to include two first order latent variables and a second order latent variable in a SEM analysis (taken from a second order CFA I conducted previously)? There are no error messages when I run the model. It makes sense to me but I'm fairly new to lavaan and SEM in general so I might be missing something! Any input would be much appreciated, I can't find any information on this anywhere! Please see the attached figure for the model I ran, syntax is below.

Thanks!

Cara

sem.model6 <- 
  
  ' 

"first order latent var 1" =~ x1 + x2 + x3
"first order latent var 2" =~ x4 + x5 + x6 + x7

"second order latent var 1" =~ "first order latent var 1" + "second order latent var 2"


y1 ~ "second order latent var 1"
y2 ~ "second order latent var"


'

fit.sem6 <- sem(sem.model6, data=dat, std.lv = TRUE, missing = "FIML", estimator = "MLR")

summary(fit.sem6, fit.measures=TRUE, standardized = TRUE, rsquare=TRUE)
SEM figure.PNG

Jeremy Miles

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May 28, 2018, 12:25:50 AM5/28/18
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In this case, I don't think it does.  The model is equivalent to a model that has arrows from the y1 and y2 to the two first order latent variables.

Here's how I think about it: If that latent variable wasn't there, you'd have four parameters - from the two Y vars to the two latents. When you add a latent variable you are specifying some constraints (usually) on what those four parameters might be. But when you add this latent, you still have four parameters - so you are not adding any constraints  - the two models are equivalent.

(Also, your Y variables are exogenous - it would be clearer if these were called X, and your X variables are endogenous. It would be clearer if these were called Y).

jeremy

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