A colleague of mine ran a basic unconditional growth model using fixed time scores that reflects linear growth. When we looked at the modification indices, it was suggested that overall model fit would improve if the first 2 factor loadings for the intercept factor were freed. This struck me as odd and counterintuitive with respect to everything I have read in this area. It was my sense that factor loadings could not be freed for the intercept factor at all. Do these modification indicates tells us anything meaningful about the intercept factor?
Modification indices are given for all fixed and constrained parameters. Parameters should be freed based on what makes substantive sense. It does not make sense to free the factor loadings of the intercept growth factor because having them fixed at one is part of the parameterization of the growth model. The fact they they come up as possible parameters to free may indicate that the development has a bumpy beginning. I would take a look at the observed data means and individual plots. It may be that the first two timepoints need to be treated differently.