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

[Michael Cone]

Dear list,

Lorenz has pointed out to me Ben's suggestion to bootstrap the sums (or 
any linear combiantion) of coefficients I'm interested in. This may be 
the general approach, but I struggle to see why it would be illegitimate 
to simply change the reference level for the treatment contrast coding, 
fit the model again and run confint() a second time (and do so again for 
MachineC):

> Machines$Machine <- relevel(Machines$Machine, 'B')
> fm2 <- lmer(score ~ Machine + (Machine | Worker), data = Machines)
> summary(fm2)
Fixed effects:
             Estimate Std. Error t value
(Intercept)   60.322      3.529  17.096
MachineA      -7.967      2.421  -3.291
MachineC       5.950      2.446   2.432
> confint(fm2)
(Intercept)  52.8500103 67.7944456
MachineA    -13.0931710 -2.8401544
MachineC      0.7692323 11.1307757

Now the CI of the intercept is the confidence interval for the overall 
score of MachineB. Adding lower and upper bounds from fm1 would have 
given somewhat similar, but somewhat wider intervals.
(I probably have a lack of understanding as to how CIs can be calculated 
with. Is there an inuitive explanation for why the bounds don't add?)

> Machines$Machine <- relevel(Machines$Machine, 'C')
> fm3 <- lmer(score ~ Machine + (Machine | Worker), data = Machines)
> summary(fm3)
Fixed effects:
             Estimate Std. Error t value
(Intercept)   66.272      1.806   36.69
MachineB      -5.950      2.446   -2.43
MachineA     -13.917      1.540   -9.04
> confint(fm3)
(Intercept)  62.4471752  70.0972752
MachineB    -11.1307677  -0.7692243
MachineA    -17.1780524 -10.6552759

Thanks, and best wishes
Michael

Am 25.09.2014 14:11 schrieb 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
> 
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