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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!

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They are not assigned a value. This is the factor indeterminacy problem in factor analysis. (They can be assigned a value, but there is more than one way to do it, and there is not a unique set of values that can be assigned.)

What we are saying is (something like): If this model is correct, this latent variable must exist, and the function of this latent variable is to explain the relationships amongst the other variables. We don't know what each person's score is on this latent variable, we just know that it has these relationships with the measured variables.

The mean and variance of the latent variable are arbitrary, and that's why you need to add constraints to identify them. (Usually fixing a loading to 1.00, and the mean/intercept to 0.00).

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  • $\begingroup$ Jeremy, thank you for your response. Just for clarity, are the standardized regression weights which are displayed in the output of AMOS just a standardized measure of the beta coefficients from a typical multiple regression equation? If the latent variables aren't directly assigned a value, is the beta coefficient essentially measuring the relationship between the observed variables of the independent latent variable with the observed variables of the dependent latent variable? Sorry just trying to wrap my head around this. Thanks again! $\endgroup$ – Derek H. May 29 '15 at 2:33
  • $\begingroup$ "is the beta coefficient essentially measuring the relationship between the observed variables of the independent latent variable with the observed variables of the dependent latent variable?" Sort of, it is trying to account for that relationship. Here's an example. If A and B correlate 0.64, then it is possible that there is an unmeasured latent variable which explains this relationship. It can have loadings of 0.8. We don't know anyone's scores on this latent, but we know that is correlates 0.8 with the two measured variables, and therefore explains the relationship. $\endgroup$ – Jeremy Miles May 29 '15 at 17:14

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