Error-in-variable modeling and latent variable modeling

[Chao Xu]

Hi folks,

Below is a simple error-in-variable (EIV) model. There are a lot of ways to estimate this linear structural equation.
x_obs = x_latent + e1
y_obs = beta0 + beta1*x_latent + e2

However, it seems to me that this model can also be estimated in a CFA framework. Namely, the slopes for x_obs and y_obs are 0 and beta0, respectively. The factor loadings for them are 1 and beta1, respectively. This is quite natural and intuitive but I haven't seen a paper in which EIV model is estimated this way. Can anybody confirm or repudiate the equivalence between these two models?

Thank you and Happy New Year to everybody in this warm community.

Chao

[Terrence Jorgensen]

x_obs = x_latent + e1
y_obs = beta0 + beta1*x_latent + e2

However, it seems to me that this model can also be estimated in a CFA framework.

Only if you fix the variance of e1 to zero or a particular value based on previously estimated reliability of x_obs.

Can anybody confirm or repudiate the equivalence between these two models?

Yes.  Is this helpful?

http://daob.nl/wp-content/uploads/2013/03/Oberski-Satorra-Measurement-error-models-with-uncertainty-about-the-error-variance-2013.pdf

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

[Chao Xu]

Hi Dr. Terrence,

Thank you so much for confirming this. This is emphatically helpful. And thank you for the link to that paper. 

Chao

[Chao Xu]

Oh no, it should be Dr. Jorgensen. Sorry for the mix-up.