In the structural equation model, the definition variables are usually added in the regression of thresholds, such as age and sex. But I don't thoroughly figure out the meanings of them.
For instance, I want to estimate the heritability of smoking( binary variable) and age is added to adjust the threshold.
I notice that the β of age in MZ and DZ is the same, so I wonder if the age is used to adjust the prevalence of smoking in order to make sure the thresholds of MZ equal to that of DZ?
In that case, the definition variables should be influencial factors of smoking, as well as distribute differently between MZ and DZ, is right?
However, because the difference of co-twins' correlations between MZ and DZ are central to the SEM in twin study, so I have to make sure that the definition variables could not change co-twins' correlations, otherwise the heritability would be wrongly estimated, is that right?
So it should be prudent to choose definition variables, and that's why people usually only select age and sex as definition variables. I wonder if I am right.
These are my confusions about the meanings of definition variables and how to choose them appropriately.
Look forward to your reply!
Many thanks!