[R-sig-ME] Fwd: same old question - lme4 and p-values
bates at stat.wisc.edu
Sun Apr 6 23:38:49 CEST 2008
On Sun, Apr 6, 2008 at 4:02 PM, Andrew Robinson
<A.Robinson at ms.unimelb.edu.au> wrote:
> On Sun, Apr 06, 2008 at 10:15:09AM -0500, Douglas Bates wrote:
> > On Sat, Apr 5, 2008 at 5:10 AM, Reinhold Kliegl
> > <reinhold.kliegl at gmail.com> wrote:
> > > Here is a section that worked in Kliegl, Risse, & Laubrock (2007, J
> > > Exp Psychol:Human Perception and Performance, 33, 1250-1251).
> > >
> > > "Analysis
> > > Inferential statistics are based on a linear mixed-effects model
> > > (lme) specifying participants and items as crossed random effects.
> > > This analysis takes into account differences between participants and
> > > differences between items in a single sweep and has been shown to
> > > suffer substantially less loss of statistical power in unbalanced
> > > designs than traditional ANOVAs over participants (F1) and items (F2;
> > > see Baayen, in press, Pinheiro & Bates, 2000; Quen? & van den Bergh,
> > > 2004, for simulations).
> > > We used the lmer program (lme4 package; Bates & Sarkar, 2006) in
> > > the R system for statistical computing (R Development Core Team, 2006)
> > > and report regression coefficients (b; absolute effect size in ms),
> > > standard errors (SE), and p-values for an upper-bound n of denominator
> > > degrees of freedom computed as n of observations minus n of fixed
> > > effects. As these p-values are potentially anti-conservative, we
> > > generated confidence intervals from the posterior distribution of
> > > parameter estimates with Markov Chain Monte Carlo methods, using the
> > > mcmcsamp program in the lme4 package with default specifications
> > > (e.g., n=1000 samples; locally uniform priors for fixed effects;
> > > locally non-informative priors for random effects). Both procedures
> > > yielded the same results.
> > > Finally, we also computed post-hoc power statistics for the
> > > preview and lexical status main effects and for the interaction effect
> > > on first fixation durations (with effect sizes similar to those
> > > reported earlier, e.g., Kliegl, 2007), and using lme estimates of
> > > between-participant, between-item, and residual variances (Gelman &
> > > Hill, in press). For the observed proportion of random loss of items,
> > > power estimates based on 1000 simulations each were around .85 for
> > > word n and n+2 and .59 for word n+1 (due to the higher skipping
> > > rate)." (page 1251)
> > >
> > > Power statistics were included in response to a reviewer request. I am
> > > not much in favor of post-hoc power statistics; but note that here
> > > they are restricted to the use of estimates of random effects. For
> > > reviewers, we also included traditional F1- and F2-ANOVA tables; they
> > > are not part of the article. In other articles, it has also been
> > > acceptable to report coefficients, their standard errors, and their
> > > ratio, and to say that coefficients larger than 2 SE are interpreted
> > > as significant (e.g., Kliegl, 2007, J Exp Psychol: General, 136,
> > > 530-537), that is, it is possible to leave out p-values completely.
> > >
> > > Corrections and improvements of the above sentences are highly welcome
> > > for future articles. In perspective, I think the p-value problem will
> > > simply go away.
> > >
> > > Best
> > > Reinhold
> > >
> > > PS: Would it be useful to have a site where peer-reviewed articles
> > > using lme4 for statistical inference are listed and, possibly,
> > > retrievable versions are provided?
> > Thanks for the suggestion, Reinhold. I would be delighted to provide
> > a page on http://lme4.r-forge.r-project.org/ to list such references.
> > May I ask for a volunteer to maintain such a listing? I am rather
> > overextended at present trying to get lme4_1.0-0 out and writing a
> > book about what it does. All that is required is to obtain a R-forge
> > login, decide how to organize the pages and then update the pages as
> > new references are submitted.
> I'm happy to do that, Doug. I've registered.
Thanks for the offer, Andrew. Shravan Vasishth has already kindly
taken on the job.
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