Confidence interval for sum of coefficients

-----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