Hypothetically, say I have I have three manifest variables measuring anxiety and three manifest variables (items) measuring stress. Then I want to use both to predict scores on depression, which I'm also assessing via three manifest variables.
I could simply add the scores on each of the manifest variables and create composite scores for Anxiety/Stress/Depress, then run a multiple regression. That approach is depicted in the following figure.
Alternatively I could do latent variable modelling, as in the figure below.
Whenever I've done this the R Squared has increased.
Why does this happen? Are the reasons such that is it possible for the R Squared to instead stay the same, or reduce?