R help - Mar 2008 - Equation for the standard error of a predicted score for a cross-classified model

All,

I have several years of longitudinal test scores for students (many who
switch schools at various points in time). I am using a mixed-effects model
with crossed random effects to model student trajectories. The model
includes time at level 1 and students crossed with schools at level 2. When
I run the model I get the posterior variances on the intercepts and slopes
for students and schools, but I am trying to figure out how to combine these
variance components to determine the standard error for each student's
predicted score at a given point in time.

Say, for a given student
pi = posterior variance for their intercept
ps = posterior variance for their slope
si = posterior variance of the intercept for the school the student was in
at time t
ss = posterior variance of the slope for the school that the student was in
at time t

This is what I'm currently thinking

SE = sqrt(pi+si+(t-x)^2(ps+ss))

where t = time and x = mean number of observations across all students.

Any help anyone can offer would be greatly appreciated.

-- 
Jonathan Weeks
Doctoral Candidate
School of Education
University of Colorado, Boulder
weeksjp@gmail.com
303-517-9666

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