Latent growth curve model: should you include predictors if the variance for slope and/or intercept factor is not significant?

Question

Hi I am running a series of latent growth curve models.

I am wondering: can predictors of the slope and intercept factor(s) be included when the slope and/or intercept variance are not significant, or should this be avoided?

Further, I am wondering whether the answer to this is impacted by 1) missingness in the data (and whether it is related to predictors/covariates), and 2) if the slope variance has been fixed to a specific number (i.e., it is modelled as a fixed effect); specifically in one model I have fixed the slope variance to be greater than 0 (i.e., 0.00001) after receiving a lavaan warning that the variance was negative.

Answer 1

In principle, you can add predictors even when the variances are small. However, you may not find any effects. In your case, it looks like the slope variance may be very close or even equal to zero in the population. If individuals don't differ in their slopes, then obviously, there are no differences to explain. In other words, predictors cannot account for non-existent inter-individual differences.