[R-sig-ME] prediction intervals from a mixed-effects models?

[Spencer Graves]

Dear Reinhold: 

      Thanks for the suggestion.  The index of Gelman and Hill for 
"prediction" for "multilevel model" mentions pp. 272-275 and 361-363.  
P. 362 starts with "predicting a new unit in an existing group", which 
sounds like what I want.  Now all I need to do is study that book enough 
to be able to do what it says. 

      Thanks again. 
      Spencer

Reinhold Kliegl wrote:
> Spencer,
>
> I think the Gelman & Hill (2007) book has examples that look less
> complicated to me in comparison to what you describe (i.e. simply
> sample from the estimated distributions). I have some code for
> computation of power, also following examples in this book. Perhaps, I
> am overlooking something.
>
> Reinhold
>
> On Sun, Apr 13, 2008 at 7:10 PM, Spencer Graves <spencer.graves at pdf.com> wrote:
>   
>>       How can I get prediction intervals from a mixed-effects model?
>>  Consider the following example:
>>
>>  library(nlme)
>>  fm3 <- lme(distance ~ age*Sex, data = Orthodont, random = ~ 1)
>>  df3.1 <- with(Orthodont, data.frame(age=seq(5, 20, 5),
>>                     Subject=rep(Subject[1], 4),
>>                     Sex=rep(Sex[1], 4)))
>>  predict(fm3, df3.1, interval='prediction')
>>  #      M01      M01      M01      M01
>>  # 22.69012 26.61199 30.53387 34.45574
>>
>>  # NOTE:  The 'interval' argument to the 'predict' function was ignored.
>>  # It works works for an 'lm' object, but not an 'lme' object.
>>
>>       One way to do this might be via mcmcsamp of the corresponding
>>  'lmer' model:
>>
>>  library(lme4)
>>  set.seed(3)
>>  samp3r <- mcmcsamp(fm3r, n=10000)
>>  samp3r[1:2,]
>>
>>       Then use library(coda) to check convergence and write a function
>>  to simulate a single observation from each set of simulated parameters
>>  and compute quantile(..., c(.025, .975)) for each prediction level
>>  desired.
>>
>>       However, before I coded that, I thought I would ask if some easier
>>  method might be available.
>>
>>       Thanks,
>>       Spencer
>>  p.s.  RSiteSearch("lme prediction intervals") produced 3 hits including
>>  2 from James A Rogers over 3 years ago.  In one, he said, "I am not
>>  aware of any published R function that gives you prediction intervals or
>>  tolerance intervals for lme models."
>>  (http://finzi.psych.upenn.edu/R/Rhelp02a/archive/42781.html)   In the
>>  other, he provided sample code for prediction or tolerance intervals of
>>  lme variance components.
>>  (http://finzi.psych.upenn.edu/R/Rhelp02a/archive/44675.html)
>>
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>>
>>     
>
>