calculation of confidence intervals for random slope model

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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