Confidence interval for sum of coefficients

Dear Michael,

This is possibly not what you should do. As has been recently
suggested to me on this list, you could use bootMer with a function
that computes the sum(s) that you are interested in. Then use boot.ci
from the boot package to estimate the confidence intervals

Best wishes, Lorenz

-----Urspr?ngliche Nachricht-----
Von: r-sig-mixed-models-bounces at r-project.org 
[mailto:r-sig-mixed-models-
bounces at r-project.org] Im Auftrag von Michael Cone
Gesendet: Donnerstag, 25. September 2014 14:11
An: r-sig-mixed-models at r-project.org
Betreff: [R-sig-ME] Confidence interval for sum of coefficients

Hello,

I suspect this to be simple, but I can't figure it out.

library(lme4)
data(Machines)
fm1 <- lmer(score ~ Machine + (Machine | Worker), data = Machines)
summary(fm1)

Fixed effects:
             Estimate Std. Error t value
(Intercept)   52.356      1.681  31.151
MachineB       7.967      2.421   3.291
MachineC      13.917      1.540   9.036

confint(fm1)

                  2.5 %     97.5 %
[...]
(Intercept) 48.7964047 55.9147119
MachineB     2.8401623 13.0931789
MachineC    10.6552809 17.1780575

[and 14 warnings, but it's just an example:
In optwrap(optimizer, par = start, fn = function(x) dd(mkpar(npar1,  
...
:
convergence code 1 from bobyqa: bobyqa -- maximum number of function
evaluations exceeded
...
In profile.merMod(object, signames = oldNames, ...) : non-monotonic
profile]

I'd like to have confidence intervals for the overall score of 
MachineA,
MachineB, and MachineB. MachineA is easy (CI of the intercept), but 
how
do I combine the CI of the intercept with the CI of the MachineB
parameter, and likewise the CI of the intercept with the parameter of
MachineC? Can I simply add the lower and upper bounds of the two
intervals or is this naive?

Thank you for your time,

Michael