[R-sig-ME] Confidence interval for sum of coefficients

[Michael Cone]

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