Predicting with residual correlation
Message/Author
 John C posted on Wednesday, June 28, 2017 - 3:20 pm
Hello,

I have an autoregressive model with two outcomes, x1 and x2, each measured at three time points, t0, t1, and t2. The two outcomes typically co-occur so I specify them to be correlated but without any cross-lagged causal effects. The model is as follows:

Model:

x1t1 on x1t0 (x1t0effect);
x1t2 on x1t1 (x1t1effect);

x2t1 on x2t0 (x2t0effect);
x2t2 on x2t1 (x2t1effect);

x1t0 with x2t0 (x1t0Wx2t0);
x1t1 with x2t1 (x1t1Wx2t1);
x1t2 with x2t2 (x1t2Wx2t2);

[x1t1] (x1t1int);
[x1t2] (x1t2int);
[x2t1] (x2t1int);
[x1t2] (x2t2int);

I would like to predict x1 at t2 for a given value of x1 at t0 (x1=10), using a linear constraint.

Model Constraint:
NEW (predictX1);

predictX1 = x1t2int + (x1t1int + x1t0effect*10) * x1t1effect;

However, I want also to do this prediction when the initial value of x2 is high, since the error correlations are all positive and significant.

Are there any templates/examples for doing this so I can be sure I'm doing it properly?
 Bengt O. Muthen posted on Wednesday, June 28, 2017 - 6:30 pm
I don't think you can bring x2 into this prediction if the model doesn't have x2 as a predictor of x1. The residual correlation is included in the sense that it is part the t1 model.