Does the sem function in lavaan correct for attenuation bias? (kroon's method, etc...)

[Hoon Pyo Jeon]

 Hi all, 

 I am currently using the lavaan package for a sem analysis in economics. Everything seems good until the cfa parts, where we do factor analysis and get latent variables. But when we use these latent variables in the structural model in sem, does the regression correct for attenuation bias resulting from the measurement error in the latent variables, maybe through something like kroon's method? If it doesn't, is there any way to do it using the lavaan package?

 Thank you for your help!

[Edward Rigdon]

In SEM, the residual variances of the observed variables are taken to be equivalent to measurement error. Since those are separated from the common factors, the common factors are taken to be "purified" so that structural model estimates are free from the effects of measurement error. That is the primary rationale for adopting SEM methods.

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[Hoon Pyo Jeon]

 Hi Edward,

 Thank you very much for your reply! So you mean that when I use the sem function in lavaan package, I do not have to correct for measurement errors when I use the latent variables in a regression, right? 

 

 I also have the code here. The regressions will not suffer from attenuation bias / measurement error  right?

On Thursday, April 11, 2019 at 10:09:05 AM UTC-4, Edward Rigdon wrote:

In SEM, the residual variances of the observed variables are taken to be equivalent to measurement error. Since those are separated from the common factors, the common factors are taken to be "purified" so that structural model estimates are free from the effects of measurement error. That is the primary rationale for adopting SEM methods.

On Wed, Apr 10, 2019 at 9:51 PM Hoon Pyo Jeon <hjeo...@gmail.com> wrote:

 Hi all, 

 I am currently using the lavaan package for a sem analysis in economics. Everything seems good until the cfa parts, where we do factor analysis and get latent variables. But when we use these latent variables in the structural model in sem, does the regression correct for attenuation bias resulting from the measurement error in the latent variables, maybe through something like kroon's method? If it doesn't, is there any way to do it using the lavaan package?

 Thank you for your help!

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[Edward Rigdon]

Yes, that is correct, as long as you are willing to accept the observed variables' factor model residuals as being their "measurement errors." Most people do.

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[Hoon Pyo Jeon]

 Edward, your response is always very helpful. Thank you for that.

 I just had one more question: it seems like we also have a function in Lavaan called fsr (factor score analysis), and it seems like it's different from sem. Shouldn't I use fsr function in order to account for attenuation bias? Or could I still just use sem as well?

[Edward Rigdon]

     Someone else will have to explain why anyone conducts factor score regresion. It makes little sense to me.

     You want to avoid working with factor scores if you can. Because common factors are typically indeterminate, working with factor scores means confronting the indeterminate nature of factors head-on. Bis creeps into factor scores because of failures to account for this indeterminacy--hence the methods to de-bias. In an ordinary SEM analysis, you don't need to estimate factor scores, and the bias will not exist in the first place. This is a lot to explain in an email.

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[Yves Rosseel]

The sem() function does 'correct for attenuation bias' out-of-the-box,
as this is what SEM does.

However, traditional SEM (as implemented in the sem() function) uses a
system-wide estimation approach (usually ML): all parameters are
estimated simultaneously. The idea behind factor-score regression (in
combination with Croon's corrections) is to estimate the parameters in
separate parts: first the measurement models (one latent variable at a
time), and then the structural part. The main motivation is robustness
against (local) model misspecifications: unlike ML where
misspecifications lead to bias all over the place, factor-score
regression keeps it contained, often resulting in unbiased estimates for
many parameters-of-interest, despite the model misspecifications. (An
alternative approach with a similar goal is MIIVsem, developed by Ken
Bollen.)

Despite the name, the 'factor scores' are not really needed; they are
just a means to get to the estimate of the 'true' variance-covariance
matrix of the latent variables, which is then the input for the
structural part.

I never hurts to try out different approaches and compare the results.

Yves.

[Hoon Pyo Jeon]

I see! Thank you Yves for a very helpful answer! I was originally going to use factor score regression using Croon's Method, but I'm now thinking of just using SEM. Thanks for your help!