What is the case for defining latents in an SEM? Why do results differ when I don't define?

[Andreas G.]

Hello,

I am doing an MSEM as follows (based on this video: link) after having aggregated the constructs beforehand:

level: 1

performance ~ a*wellbeing + c*leadership + [several controls]

wellbeing ~ b*leadership + [several controls]

level: 2

gr_performance ~ d*gr_wellbeing + f*gr_leadership

gr_wellbeing ~ e*gr_leadership

# indirect and total effects:

ab:=a*b

totalwithin:=ab+c

de:=d*e

total between:=de+f

Now, obviously those are latent variables, second-order latents in fact. In the tutorial (link) Rosseel adds the definitions or measurement model of the latents. However, in the video linked above this is not done.

What is the case for doing this or not doing this?

In my example, if I define both the first-order latents (dimensions of my variables) and then the second-order latents the model looks huge and the regression results are completely different to when I just run the model written above with the aggregated variables.

Why is that?

[Terrence Jorgensen]

obviously those are latent variables, second-order latents in fact

What is obvious about that? "Latent" is vague; technically, the within- and between-level components of each observed variable in your model are latent variables, but I don't see any common factors or growth factors defined with multiple indicators in your syntax, which is what we usually mean by "latent variables" in SEM. 

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