Running a latent growth model using one continuous variable measured five times I am running into a problem with poor model fit. Looking at the modification indices I see that the problem may be in the fixing of the outcome intercepts at zero, so I would like to know if there is another reason for this constrain besides model parametrization as my model would be properly identified after removing these contrains.
As an addition to my previous post, I see in one of the presentations from the website about LGM that "outcome intercepts [are] fixed at zero to represent measurement invariance". Does this mean that the outcome measure is invariant across time? In that case, why is it necessary to fix the intercepts to zero, why not simply contraining them to the equal across time? Also, if invariance testing of the measure shows that there in scalar invariance across time, but not metric invariance then would it not be more accurate to leave the intercepts free as we already know that they are not equal across time?
When mod indices point to the intercepts fixed at zero, it means that the growth model is not suitable, but that the means progress over time in a non-smooth fashion. Freeing them you essentially leave the realm of growth modeling. You can do that with say one intercept (at one time point) if you have some specific substantive reason for a jump at that time point. But it is not standard.
The reason you fix the intercepts to zero rather than holding them equal is that the model already has a level-related parameter, namely the mean of the intercept growth factor - if you let the intercepts be equal you are catching the same one thing by two parameters - it is superflous and therefore non-identified.