Creating a Measurement Model for a Si...
Message/Author
 acumberl posted on Tuesday, November 02, 2004 - 2:31 pm
Hi Bengt and Linda. I have an question for you about creating a measurement model based on one single composite latent varialbe. We had oringially hpothesized that all the indicators would go into the latent varialbe(success)instead of coming out of the latent construct.We have been reading about formative vs. reflective models and we had theorized a formative model. I also thought that I had specified a formative model, but what it is saying in papers is that the model wouldn't be identified unless there were refletive items going out of the success construct or other latent constructs coming out of the success construct. In the model that I specified, it was identifed and I had one measure set to 1.0 with measurement erro set to 0 and now I'm worried that it's not specified as a formative model. Is there a way to do a formative model in mplus using the by statements or does it automatically do a reflective model with by statements?

Thanks so much!
Amanda
 Linda K. Muthen posted on Tuesday, November 02, 2004 - 2:40 pm
This is from an earlier post by Bengt:

"In some applications it may be more natural to let a factor be defined as being influenced by indicators, rather than influencing the indicators. An example is SES. Mplus handles this modeling by the following model statements.

f by y*;
f@0;
f on x1@1 x2 x3;

Note that f by y* (that is, freeing the factor loading for the single indicator y) is the same as y on f. f has to be defined by some y - if instead you use the dummy definition

f by y@0;
y on f;

the estimate shows up in f by y."
 acumberl posted on Tuesday, November 02, 2004 - 7:17 pm
Hi Linda. Thank you for your response. Is the y an overall measure of the f and the x's the rest of the indicators that we think goes into the f? Can there only be one y? Could you give me an example with say SES in terms of what the y is and what the x's are?
Thank you!
Amanda
 bmuthen posted on Wednesday, November 03, 2004 - 11:02 am
y is just an example of a variable that you want to predict using f. It can be a factor measured by several indicators. For example, the x's may be education, SEI, and income, and y may be achievement.