I am attempting to model a 2 potentially reinforcing feedback processes. This relates to addictive smoking behavior in adolescence: does amount of smoking at time1 increase the level of addiction at time2, and vice versa. There are eleven measurements each, of the frequency of smoking and the number of reported symptoms of addiction to nicotine (most of the kids did not smoke). I have attempted several modeling approaches: 2 parallel growth processes and regressing the slope of one on the intercept of the other as similar to example 6.13 in the userís guide - NOT Chapter 13! I tried several extensions of Poisson distribution (settled on the hurdle). Finally settled on a stochastic modeling framework, as shown below (there is also a survival component to this model). Is this a valid approach for the processes? Is there a better approach to the problem?
MODEL: tte1 ON predvr1 female hispanic raceo age_in ;
hncsxr2 ON lcimnt1 (1); hncsxr3 ON lcimnt2 (1); .......................... hncsxr10 ON lcimnt9 (1);
lcimnt2 ON hncsxr1 (2); lcimnt3 ON hncsxr2 (2); .......................... lcimnt9 ON hncsxr8 (2); lcimnt10 ON hncsxr9 (2);
It looks like you are taking a cross-lagged panel modeling approach. This is quite common, although I am sure it has been criticized and there may be a better approach. Maybe you don't want the equality constraints. See also the Bollen-Long book and the ALT model. The parallel process growth modeling is possible but doesn't seem to capture the time-specific cross-lagged influences.