I am beginning to go through SEM textbooks and research in order to understand the logic and reasoning for the analysis. I believe that I will be using this type of analysis in the near future for my thesis project.
I have a question in regards to the value assigned to latent variables. I understand that in SEM a measurement model must be assessed and approved before moving to a structural model.
Based on my understanding, a measurement model is largely assessing the relationship between a latent variable and the observed variables that are directly measured. An example of a basic equation for the relationship between one LV (Intelligence) and two OVs (Test1 and Test2) would be: Test1 = factor loading *Intelligence + error and Test2 = factor loading * Intelligence + error.
Then for a structural model, the relationship between endogenous and exogenous LVs is assessed. So for instance if the theory of interest is saying that LV Intelligence has a positive affect on LV Achievement, then the equation would be Achievement = structure coefficient * Intelligence + error.
The main issue I have trouble understanding, is since LVs are not directly measured or observed, what value are they assigned? Is it the mean of all the OVs that are said to "measure" the LV? From my example, would the value for Intelligence be the average of Test1 and Test2 scores? Is there a different equation used to calculate the LV value?
Sorry if my question is confusing, but thank you in advance for your help!