Sun, 09/02/2012 - 22:43

Hello

Given that the longitudinal simplex model has measurement error at each time point built in, and that there can be transmissions from E at one time point to another,I am wondering if, at time points other than time 1 in the Simplex model, the innovation for E can be set to 0?

Many thanks

Karen

Based on my reading of the Dolan, Molenaar & Boomsba (1991) paper, I'd say no. The error term in E(t) (i.e. "innovation", or zeta(t)) differs from the phenotypic error term epsilon(t) in that zeta(t) is allowed to affect the autoregressive term at subsequent timepoints whereas epsilon is pure white noise.

E(t) = B(e) * E(t-1) + z(t)

Make some substitutions:

E(t) = B(e) * (B(e)*E(t-2) + z(t-1)) + z(t)

And you see that the zeta term is part of the E autoregression, where epsilon has zero correlation with anything. If you want, you can do the math and define E(t) as a summation reaching back all the way to E(1) and the effects of all of the zeta parameters.

*Edit: Left out a B(e) in the second equation*

Sorry for the delay. I had to find the right paper that defined "innovation" for me.

ryne

Thank you so much for your time on this, and for your response. It is really helpful and greatly appreciated.

Karen