[R] anova statistics in lmer

Mon May 15 19:54:14 CEST 2006

Note the intrusion of modeling "philosophy" here: is it better to give an
exact but likely quite wrong answer, or to give an incomplete or no answer?
The latter seems to me to be an honest statement about the limits of one's
knowledge that the former obscures by a fog of exactitude. 

Obviously, others may disagree, but I applaud Doug Bates's forthright
approach.

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA

"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Doran, Harold
> Sent: Monday, May 15, 2006 9:15 AM
> To: Diego Vázquez; r-help at stat.math.ethz.ch
> Subject: Re: [R] anova statistics in lmer
> 
> The issue is not unresolved within lmer, but with the 
> statistical model itself. SAS gives you alternatives for the 
> ddf such as Kenward-Roger. But, as I have noted on the list 
> before, this makes the assumption that the ratio of the 
> variances follow an F distribution and that the only 
> remaining challenge is to then estimate the ddf. Then, one 
> can get all the p-values you want.
> 
> If you believe that is true, then the SAS options will give 
> you some statistics to use--not to say that they are correct, though. 
> 
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch 
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Diego Vázquez
> > Sent: Monday, May 15, 2006 11:53 AM
> > To: r-help at stat.math.ethz.ch
> > Subject: [R] anova statistics in lmer
> > 
> > Dear list members,
> > 
> > I am new to R and to the R-help list. I am trying to perform 
> > a mixed-model analysis using the lmer() function. I have a 
> > problem with the output anova table when using the anova() 
> > function on the lmer output object: I only get the numerator 
> > d.f., the sum of squares and the mean squares, but not the 
> > denominator d.f., F statistics and P values.
> > Below is a sample output, following D. Bates' SASmixed 
> > example in his paper "Fitting linear mixed models in R" 
> > (R-News 5: 27-30).
> > 
> > By reading the R-help archive, I see that this problem has 
> > come up before (e.g., 
> > http://tolstoy.newcastle.edu.au/R/help/06/04/25013.html).
> > What I understand from the replies to this message is that 
> > this incomplete output results from some unresolved issues 
> > with lmer, and that it is currently not possible to use it to 
> > obtain full anova statistics. Is this correct? And is this 
> > still unresolved? If so, what is the best current alternative 
> > to conduct a mixed model analysis, other than going back to SAS?
> > 
> > I would greatly appreciate some help.
> > 
> > Diego
> > 
> > ----
> > 
> > Example using SASmixed "HR" data (see D. Bates, "Fitting 
> > linear mixed models in R", R-News 5: 27-30)
> > 
> > > data("HR",package="SASmixed")
> > > library(lme4)
> > Loading required package: Matrix
> > Loading required package: lattice
> > 
> > Attaching package: 'lattice'
> > 
> > 
> >         The following object(s) are masked from package:Matrix :
> > 
> >          qqmath
> > 
> > > (fm1<-lmer(HR~baseHR+Time*Drug+(1|Patient),HR))
> > Linear mixed-effects model fit by REML
> > Formula: HR ~ baseHR + Time * Drug + (1 | Patient)
> >           Data: HR
> >       AIC      BIC    logLik MLdeviance REMLdeviance
> >  788.6769 810.9768 -386.3384   791.8952     772.6769
> > Random effects:
> >  Groups   Name        Variance Std.Dev.
> >  Patient  (Intercept) 44.541   6.6739
> >  Residual             29.780   5.4571
> > number of obs: 120, groups: Patient, 24
> > 
> > Fixed effects:
> >              Estimate Std. Error t value
> > (Intercept)  33.96209    9.93059  3.4199
> > baseHR        0.58819    0.11846  4.9653
> > Time        -10.69835    2.42079 -4.4194
> > Drugb         3.38013    3.78372  0.8933
> > Drugp        -3.77824    3.80176 -0.9938
> > Time:Drugb    3.51189    3.42352  1.0258
> > Time:Drugp    7.50131    3.42352  2.1911
> > 
> > Correlation of Fixed Effects:
> >            (Intr) baseHR Time   Drugb  Drugp  Tm:Drgb
> > baseHR     -0.963
> > Time       -0.090  0.000
> > Drugb      -0.114 -0.078  0.237
> > Drugp      -0.068 -0.125  0.236  0.504
> > Time:Drugb  0.064  0.000 -0.707 -0.335 -0.167 Time:Drugp  
> > 0.064  0.000 -0.707 -0.167 -0.333  0.500
> > > anova(fm1)
> > Analysis of Variance Table
> >           Df Sum Sq Mean Sq
> > baseHR     1 745.99  745.99
> > Time       1 752.86  752.86
> > Drug       2  86.80   43.40
> > Time:Drug  2 143.17   71.58
> > 
> > 
> > --
> > Diego Vázquez
> > Instituto Argentino de Investigaciones de las Zonas Áridas 
> > Centro Regional de Investigaciones Científicas y Tecnológicas 
> > CC 507, (5500) Mendoza, Argentina 
> > http://www.cricyt.edu.ar/interactio/dvazquez/
> > 
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> 
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