the question that I have appears to be simple, because it concerns a basic growth model, yet I cannot find a proper solution.
I would like to run a growth model over 5 time points across two manifest groups, which also includes predictor variables. Descriptive plots show a similar non-linear trend in the means across the two groups over time, which I would like to have captured through the magnitudes of the slope coeffients in the growth model.
I have been successful at calibrating such a model with the coefficients for time points 3, 4, and 5 estimated freely. Now one reviewer of our paper suggested comparing the model to a linear growth model. That makes perfect sense to me, but when I fix the slope coefficients under the same parametrization to 0, 1, 2, 3, 4 for the five time points, respectively, the model does not converge due to a non-definite matrix and problems with the slope latent variable.
When I change the parametrization by omitting the [y1-y5@0 intercept slope] statement about the means/intercepts, the model converges. However, under that parametrization the slope coefficients are almost identical across the time points and do not seem to capture the non-linear trend anymore that I had observed descriptively.
Thus, one parametrization seems to work only for the linear model with all coefficients fixed and one seems to work only for the non-linear model with three coefficients estimated freely. How do I have to specify the models so that I can simply specify the models in the same fashion, which would also have the slope coefficients capture through their magnitude the observed non-linear growth?
As a final note, this problem also occurs when I fit a simple model over the whole data set without any additional predictors. Could you please tell me what I am misunderstanding or doing incorrectly?
The "change in parametrization" that you mention does not give a growth model. It should be possible to fit a linear growth model so you can contrast it to the non-linear model. But to diagnose the convergence problem you are experiencing, you would have to send the data, input, output, and license number to firstname.lastname@example.org.