Random rate effect in non-linear grow...
Message/Author
 Chris Stride posted on Thursday, July 02, 2015 - 9:33 am
Hi
I've fitted a logistic growth model to my data using the code below.

However I'd now like to see whether the *rate* of change (i.e. the parameter 'alpha' in the model below) varies amongst participants, since that's my main reserach question.

So.... is there any way of setting a parameter created in MODEL CONSTRAINT to be random? Or is there another way of doing this?
cheers
Chris

MODEL:
i1 by ANX3-ANX8@1;

s1 by ANX3* (L1)
ANX4 (L2)
ANX5 (L3)
ANX6 (L4)
ANX7 (L5)
ANX8 (L6);
i1 s1; i1 with s1; [i1* s1*];

[ANX3-ANX8@0];

ANX3 ANX4 ANX5 ANX6 ANX7 ANX8 (a);

MODEL CONSTRAINT:
NEW(alpha lambda);

L1 = 1/(1 + exp(-(1 - lambda)*alpha));
L2 = 1/(1 + exp(-(2 - lambda)*alpha));
L3 = 1/(1 + exp(-(3 - lambda)*alpha));
L4 = 1/(1 + exp(-(4 - lambda)*alpha));
L5 = 1/(1 + exp(-(5 - lambda)*alpha));
L6 = 1/(1 + exp(-(6 - lambda)*alpha));
 Bengt O. Muthen posted on Thursday, July 02, 2015 - 6:18 pm
A couple of thoughts:

You can try to relate alpha to an observed variable using the Constraint= option and then express alpha as a deterministic fcn of that in Model Constraint.

Or, you can use mixture modeling to give alpha a non-parametric distribution.

Or, perhaps this paper about non-linear growth using Mplus can be helpful:

Grimm, K., Zhang Z., Hamagami, F. & Mazzocco, M. (2013). Modeling nonlinear change via latent change and latent acceleration frameworks: Examining velocity and acceleration of growth trajectories Multivariate Behavioral Research, DOI: 10.1080/00273171.2012.755111.