I am running a fairly basic growth model and have two questions:
1. I know my data is not totally linear (there is a flattening out over time). I tried to enter a quadradic term and it didn't work because the quadradic had a negative mean. I think it is because it is only a slight non-linearity. So I allowed it to etimate time for the last two of five time points. This model fit pretty well but I am confused about how to discuss the results which I need to be able to present to policy makers. How can I discuss this and how can I meaningfully relate it to the covariates in the model?
2. My modification indices suggest correlating the indicators (which in this model are math scores over time) but when I do this I keep getting an error that my theta matrix is not positive definite and it shows that the residual variance on the indicator(s) is negative. Why could this be and what should I do about it. I am certain that the errors of the indicators are correlated since they are the same measure across time. How do I account for this?
1. The fact that you get a negative mean for a quadratic growth factor does not sound like a problem but would seem to reflect a flattening out of the development. The interpretation of results with estimated time scores is a topic that is larger than fits in Mplus Discussion - we discuss it in "Day 2" of our short course (next occasion is October 20 at the Johns Hopkins course); see the Day 2 handout.
2. The combination of free time scores and correlated residuals (I assume adjacent residuals only) make for a flexible but often weakly-defined model. To stabilize the model, you could try to postulate the same residual correlation across time and also the same residual variance across time.