I am using a parallel growth curve model with 5 waves longitudinal data to evaluate correlated change among 2 traits. For models that showed the effects of correlated change among traits, I'm wondering whether I can estimate a common latent slope factor for both traits' measures in addition to the individual intercept/slope for each trait. I assumed such a common slope would capture the variance across traits that grow together, suggesting that there are underlying mechanism(s) influencing the traits at the same rate.
As I have not find much evidence of such process, anyone directing me to the related discussions would be highly appreciated. Thanks in advance.