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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.

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Yes, you could do this, but it would be weird.

It would be sort of like having a common factor and specific factors in a confirmatory factor analysis, except the factors are growth factors.

I predict you are going to run into problems identifying this unless your sample is huge. You're asking every mean and covariance to provide you with a lot of information - it's trying to estimate two very similar latent variables, and distinguishing between them will be hard.

You'll also run into problems with estimation - I think that the estimate the model you'll need to correlate the specific factors with one another but leave the common factor uncorrelated.

Instead of doing it this way, would add one additional slope factor which accounts for the correlation of the two slope variables, and an additional intercept factor which accounts for the intercept correlations (with loadings constrained to 1). The variance of that additional factor is the shared slope variance. The means of the slopes and intercepts are the differences between the common mean slope and the individual slopes.

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