I ran a binary growth model using logit regression with 7 waves of data which will later be used in a two-part semicontinuous model. I am trying to calculate the probability of using alcohol and want to make sure that I am doing this correctly.
The relevant results are listed below.
MEANS Int 0.00 Slp 0.684
Variances Int 7.219 Slp 0.330
P(Y=1| x) = 1/[1+exp(-logit)],
where the logit = -threshold +mean(intercept) + t(slope)
This probability involves numerical integration to integrate out the random effects, that is, the intercept and slope latent variables. Because of this, it is not straightforward to computed this yourself. You can compute the probability conditional on the means of i and s if you like - this does not involve integration.