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prediction intervals and lmer

Ben Bolker 
Muldoon, Ariel <Ariel.Muldoon at ...> writes:
If you look carefully at the FAQ code, you'll see that the 
lme and glmmADMB code do include residual variance terms.  The page
itself is a little bit vague about which computed values are
confidence intervals are confidence intervals and which are prediction
intervals; the values given for lme4 are confidence intervals,
incorporating either (1) only the uncertainty on the fixed-effect
parameters (beta) or (2) uncertainty on beta plus variation due
to random effects [this would be a sort-of confidence interval for 
a population-level prediction, i.e. the expected variation
(conditional on the random-effect parameter effects) of the mean
of a large number of samples from a _single_ previously unobserved
block].   The problem (or at least, my problem) with setting up
generic confidence/prediction intervals for mixed models is thinking
clearly about which sources of variation one wants to (1) ignore,
(2) condition on, (3) marginalize over ...  (Also, note that none
of these approaches allows for the uncertainty of the random-effects
parameters.)

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Muldoon, Ariel prediction intervals and lmer Aug 28 Ben Bolker prediction intervals and lmer Aug 30 Muldoon, Ariel prediction intervals and lmer Aug 30