[R-sig-ME] calculation of confidence intervals for random slope model

[W. Duncan Wadsworth]

Dr. Bolker,

Could you possibly expand on the statement "The other alternative is
to use bootMer
+ predict to get confidence intervals ..."? In particular, what do you mean
by using `predict` here?

My first stab at this would look like:

library(lme4)
library(ggplot2)
library(dplyr)
data("sleepstudy")
## visualize individual slopes
ggplot(sleepstudy, aes(x = Days, y = Reaction, group = factor(Subject))) +
  geom_smooth(aes(color = factor(Subject)), method = "lm", se = F) +
  theme(legend.position = "none")
sleepy = lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy)
## bootstrap summary function
sumfun = function(.){
  overall = fixef(.)
  individuals = ranef(.)$Subject
  return(c(overall["Days"] + individuals[,"Days"]))
}
## where the fun happens
booty = as.data.frame(bootMer(sleepy, sumfun, nsim = 99))
## for plotting
colnames(booty) = rownames(ranef(sleepy)$Subject)
slope_bs_distros = booty %>% tidyr::gather("Subject", "Value")
## bootstrap distributions of individual slope parameters (??)
ggplot(slope_bs_distros, aes(x = Value)) + geom_histogram() +
  facet_wrap(~ Subject, ncol = 5) +
  geom_vline(xintercept = 0, color = "red", size = 1.5)

But this doesn't seem correct since Subject 335 appears to have a negative
slope. Are we seeing some kind of shrinkage effect here or am I just doing
the bootstrapping wrong?



On Mon, Nov 16, 2015 at 7:58 AM, Ben Bolker <bbolker at gmail.com> wrote:

> On Mon, Nov 16, 2015 at 5:56 AM, Henry Travers
> <henry.travers at zoo.ox.ac.uk> wrote:
> > I have what I hope is a relatively straightforward question about how to
> interpret the results of a mixed effects model of the form:
> >
> > fm1 <- lmer(Reaction ~ Days + (Days | Subject))
> >
> > I am running an experiment such that I am most interested in the
> (equivalent of the) effect of Days for each Subject, rather than say fitted
> values. I understand how to derive the point estimates for this effect, but
> I am struggling to see how to calculate confidence intervals for these
> estimates that take account of both the standard error in the parameter
> estimate for Days and the uncertainty in the corresponding slope estimates
> for each Subject.
> >
> > I would be very grateful if someone could point me in the right
> direction or to a suitable reference.
>
>   This is a surprisingly difficult question to answer.
>   There have been extended discussions in the mailing list (which I
> don't have time to dig for now) about whether it's OK to add the
> conditional variances of the conditional modes to the variances of the
> fixed-effect predictions, and the circumstances under which this would
> be (in)accurate/(anti)conservative.  The other alternative is to use
> bootMer + predict to get confidence intervals ...
>
>   This should probably be added to the FAQ ...
>
> >
> > ------------------------------------------------
> > Henry Travers, PhD
> > Research Associate
> >
> > Interdisciplinary Centre for Conservation Science
> > Department of Zoology
> > University of Oxford
> >
> >
> >
> >
> >
> >
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> >
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