I would like to know the definition of measurement model in SEM. Is it only about the latent variables? (THat's what I seemed to see what I google.) But I remember long time ago I read somewhere that we need to include all the variables in the SEM with bi-directional arrows too. I do not know which one I should follow...
For instance, I have a model with 3 latent variables (2 predictors, 1 outcome), and one exogenous predictor, one exogenous outcome, together with age and gender that I include in the structural model. The model fit of the structural model is good. But I am stuck at the measurement model, do I need to include those exogenous variables, age and gender? It is very bad if I include them, but if I just use all the latent variables, the measurement model is also good.
model <- specifyModel() love -> L1, lam1, NA love -> L2, lam2, NA hate -> H1, lam3, NA hate -> H2, lam4, NA L1 <-> L1, e3, NA L2 <-> L2, e4, NA H2 <-> H2, e5, NA H2 <-> H2, e6, NA Gender <-> Gender, e1, NA Income <-> Income, e2, NA love <-> love, NA, 1 hate <-> hate, NA, 1 hate <-> love, lh, NA Gender <-> Income, gi, NA Gender <-> love, gl, NA Gender <-> hate, gh, NA Income <-> love, li, NA Income <-> hate, hi, NA #
(By the way, I don't know how to represent this "love <-> love, NA, 1" in the path diagram)