Hello, all.  I have two questions about combining fixed effects with  
their random effects in a multilevel model in order to look at the  
effects of a treatment at multiple levels.  Note, I'm particularly  
interested in this so that I can later make comparisons between  
different groups.  But, let's use the sleep study as an example.   
Using lme4 and Gelman's arm library, I can obtain both the fixed  
effects and deviations due to their different grouping variables.  I  
can also obtain the error around my estimate of both the fixed and  
random effect.  E.g.,

library(arm)
fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)

#gets fixed effect and the error in it's estimate
fixef(fm1)
se.fixef(fm1)

#gets deviation from fixed effect means and the error in that estimate
ranef(fm1)
se.ranef(fm1)

However, what if I wish to look at, say, the error of the intercept  
for each subject?  Or the estimate of error around the effect of Days  
for each subject?  One does not merely add se.fixed and se.ranef to  
get an estimate of error around those parameters, right?  While this  
may not be as big a problem for the sleepstudy data, it becomes more  
important for unbalanced data.

It seems like mcmcsamp could be a great solution to that, but,  
mcmcsamp does not give estimates of each individual parameter.   
Rather, it again also gives estimates of the random effects using  
saveb=T.  I must admit, however, I am unclear one which random effect  
goes with which fixed effect (they're all b.1, b2, etc in the output  
of mcmcsamp - can I get some clarification?)

Although, hrm, could one merely add the fixed effect estimates to the  
random effect estimates from mcmcsamp to obtain the values for each  
parameter value?

Note, I'm trying to use the method presented below for multiple  
comparisons with lmer.  Any other thoughts would be appreciated.
http://www.stat.columbia.edu/~cook/movabletype/archives/2008/03/why_i_dont_usua_1.html


-Jarrett




----------------------------------------
Jarrett Byrnes
Population Biology Graduate Group, UC Davis
Bodega Marine Lab
707-875-1969
http://www-eve.ucdavis.edu/stachowicz/byrnes.shtml


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