Confusion about when model is not identified

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Blain Waan

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Nov 8, 2018, 7:05:10 PM11/8/18
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I have several binary variables (say, Y1, Y2, Y3, and Y4) and a few covariates (e.g. X1, X2, X3).

I have made the Y variables ordered (to get DWLS) and ran the following codes in lavaan.

mod1 <- '
    Y1 ~ Y2 + Y3 + X1 + X2 + X3

    Y2 ~ Y1 + Y3
 + X1 + X2 + X3
    Y3 ~ Y1 + Y2 + X1 + X2 + X3
    Y4 ~ Y1 + Y2 + Y3 + X1 + X2 + X3
'
fit1 
<- sem(mod1, data=dat)
summary
(fit1, standardized=TRUE)

But that shows me the following warning:

Warning message:
In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  :
  lavaan WARNING
: could not compute standard errors!
  lavaan NOTE
: this may be a symptom that the model is not identified.

I saw on the web that when the number of "knowns" is fewer than the number of "unknowns" then the model becomes "not identified". So, I removed all covariates to reduce the number of parameters to be estimated. 

mod2 <- '
    Y1 ~ Y2 + Y3
    Y2 ~ Y1 + Y3
    Y3 ~ Y1 + Y2
    Y4 ~ Y1 + Y2 + Y3
'

fit2 
<- sem(mod2, data=dat)
summary
(fit2, standardized=TRUE)

But this still shows me the same warnings. 

However, when I run the model (note, with all covariates but not testing bidirectional relationships) as follows:

mod3 <- '
    Y1 ~ X1 + X2 + X3
    Y2 ~ Y1 + X1 + X2 + X3
    Y3 ~ Y1 + Y2 + X1 + X2 + X3
    Y4 ~ Y1 + Y2 + Y3 + X1 + X2 + X3
'

fit3 
<- sem(mod3, data=dat)
summary
(fit3, standardized=TRUE)

this doesn't show me the warning anymore. But this is not what I wanted to test. 

I cannot understand what are the knowns and unknowns here and why my second attempt (mod2) doesn't work even after reducing the number of parameters to be estimated. 

It seems to me like either testing bidirectional relationships are not allowed or that I'm making a mistake here. Could anyone please clarify why it is happening? I really appreciate your comments. 


Terrence Jorgensen

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Nov 9, 2018, 6:43:33 AM11/9/18
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The issue is that you only observed 1 covariance between Y1 and Y2, and another between Y2 and Y3.  So you don't have enough information to estimate 2 relationships between Y1 and Y2, and 2 relationship between Y2 and Y4, unless you impose some arbitrary constraints (e.g., setting the reciprocal paths to be equal by giving them the same label).

If you want to see how 2 variables affect each other, you should measure them on at least 2 occasions (which is how causation unfolds anyway), which will provide a way to get around this limitation.

Cole, D. A., & Maxwell, S. E. (2003). Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling. Journal of abnormal psychology112(4), 558.

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

Nabil Awan

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Nov 9, 2018, 10:44:49 AM11/9/18
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Dear Terrence,

Thanks for your clear explanation!

Kind regards

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