Hi,
I'm trying to work out plotting effect confidence intervals for a
mixed effects design. For example, when measuring heights over age
one will get two kinds of confidence intervals from the resulting
model (using intervals in lme), a broad inference interval from the
random intercept, and a narrow inference interval about the fixed
effect slope.
I've been considering what this confidence interval about only the
slope means in a graphical way and am asking for advice. I know that
in a standard linear model one can make sort of curved dashed lines a
la Prism's plotting capabilities (something I haven't seen in R). But
I'm not sure this makes sense because it would mean conflating two
kinds of variance I want to keep separate. In a regular regression
the intercept and slope have similar inference qualities. But, in
repeated measures mixed effects models the slope (narrow inference
about effect only) will likely be a different kind of inference than
the intercept (absolute value measurement). Therefore combining those
two to make traditional curves seems inappropriate, especially for
undertanding the slope variance.
I have considered plotting the intercept and, at that point only,
putting the broad inference CI error bars. Then, I could plot the
narrow inference effect around the regression line. However, there
doesn't seem to be a way to place such bars without being misleading.
They certainly can't all start at the same intercept, that implies
increasing variability in measurement over time (and increasing
accuracy back in time). But, what's the alternative because the
intercept and slope our now separate?
(BTW, the curved error bars in regression seem problematic in any
event because if the slope variance is very high with a small
intercept variance then it implies somewhere about the middle of the
line there is this artificially very high accuracy)
