What does theory tell you?

SEM is about defining your theory as a set of relationships among variables. Usually you set up a path diagram to define what variables you think are causally related and what are not. Some measured variables may be seen as an indicator, or manifestation, of some other underlying condition. That underlying condition is your latent variable. Often, several manifest variables act together to represent one latent variable.

Your university probably has a license for at least one brands of SEM software, or there are some good Open-Source options and several R packages. Here is a partial list: https://openmx.ssri.psu.edu/sem-resources .

After you have defined your theory, then you test to see if reality is consistent with your theory. Reality is your data. If you get a good fit, then you can say that your theory is consistent with reality.

Of course, it is quite possible that some other theory (path model) could also give a good, or better, fit with your data. In my experience, the more complicated the model the more likely it is that another model will fit as well.

Now, if you don't have a clear idea of which measured variables are manifestations of a specific latent variable, then you don't have a good theory. Maybe you want to develop a theory - that is, maybe you want to discover which variables are highly related to each other so that you can join them together to make a new combination variable (the latent variable).

If you want to discover combinations of variables, then you should look into Exploratory Factor Analysis (EFA).

EFA will suggest what variables are closely related so they can be regarded as manifestations of a latent variable, and what variables are closely related to a different latent variable.

Ideally, you should conduct EFA using a different set of data from the data used in the EFA. There is a lot more to think about, but you really should refer to your research methods texts and other guides.

Thank you Hume F. Winzar for your answer. The idea is that i am trying to combine my field of research in health and engineering, with statistical equation modelling. Unlike the constructs in social science that are already predefined with their measured variables (using questionnaires), we have a lack of unders whether all the measured biomedical data can be related to one or more construct. I will be attempting to find out using EFA.

Dear Halim Tannous

Meausurement variables (items, indicators) are predefined in the literature. If you are building a "new" latent variable for which there is no previous evidence about its measurement items, then, try EFA as indicated by Hume F. Winzar.

Regards

Scale development and the application of constructs in SEM are usually two completely different issues. In the social sciences you can frequently use experts' opinions (face validity, content validity) to find out whether a variable belongs to a contstruct. In the natural sciences it makes sense to apply EFA to identify a construct. Just make sure that you are not mixing up those two steps. If you used EFA to identify a construct you should not use the same dataset using a confirmatory procedure, since it is quite obvious that you will find a relationship. Instead, you need new data to confirm your exploratory findings.