Parameter constraints with different SEs

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Andrew Grotzinger

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Nov 10, 2018, 1:07:07 PM11/10/18
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I've been running a series of models in which I use parameter equality constraints for a handful of estimates (e.g., F1 =~ V1 + b*V2 + b*V3 + V4 + V5) and noticed that while the point estimate for the parameters constrained to be equal are the same, like you'd expect, that I will get different standard errors for these same constrained parameters. In Mplus, when running the same model, I've noticed that the standard errors will also be equal for the parameters constrained to be equal. In lavaan, I've also tried specifying a ghost parameter based on the equality constraint (e.g., c := b), and found that in this case the standard error will match that of the variable that is listed first with the equality constraint (in this case the SE for b*V2), as opposed to some weighted average of the standard errors for the constrained parameters like I'd expect. I'm posting to see if you have any suggestions for how to obtain the same SEs for the parameters constrained to equality, or if there is an explanation as to why different SEs would be more appropriate. Thanks very much!

Terrence Jorgensen

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Nov 12, 2018, 8:33:45 AM11/12/18
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I've been running a series of models in which I use parameter equality constraints for a handful of estimates (e.g., F1 =~ V1 + b*V2 + b*V3 + V4 + V5) and noticed that while the point estimate for the parameters constrained to be equal are the same, like you'd expect, that I will get different standard errors for these same constrained parameters.

That is what I'd expect, and it's what I always see.

HS.model <- ' visual  =~ x1 + a*x2 + a*x3
              textual =~ x4 + b*x5 + b*x6
              speed   =~ x7 + c*x8 + c*x9 '

fit
<- cfa(HS.model, data=HolzingerSwineford1939)
summary
(fit, fit.measures=TRUE)


Can you post your full syntax and data so we can see how this happens?

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

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