I fitted a mixed model as following:
$Y = \beta_0 + \beta_1 T + \beta_2 X + \beta_3 X T + \beta_iW_i$
$T$ is time, $X$ is my variable of interest and $W_i$ are various confounding variables. I also used a specific covariance matrix to modelise the random effect of time (
Sp(POW) from SAS).
I want to summarise my data into a regression line of the type.
$Y = aT + b$
with $a = \beta_1 + \beta_3$ and $b = \beta_2$.
Since my betas are estimations and thus random variables, they come along with errors and even their own confidence intervals.
How can I get the CI of $Y$ for any $T$, so I can plot my line with a pretty ribbon ?