Re: [R] lme X lmer results

From: Douglas Bates <dmbates_at_gmail.com>
Date: Thu 29 Dec 2005 - 05:59:07 EST

On 12/26/05, Ronaldo Reis-Jr. <chrysopa@gmail.com> wrote:
> Hi,
>
> this is not a new doubt, but is a doubt that I cant find a good response.
>
> Look this output:
>
> > m.lme <- lme(Yvar~Xvar,random=~1|Plot1/Plot2/Plot3)
>
> > anova(m.lme)
> numDF denDF F-value p-value
> (Intercept) 1 860 210.2457 <.0001
> Xvar 1 2 1.2352 0.3821
> > summary(m.lme)
> Linear mixed-effects model fit by REML
> Data: NULL
> AIC BIC logLik
> 5416.59 5445.256 -2702.295
>
> Random effects:
> Formula: ~1 | Plot1
> (Intercept)
> StdDev: 0.000745924
>
> Formula: ~1 | Plot2 %in% Plot1
> (Intercept)
> StdDev: 0.000158718
>
> Formula: ~1 | Plot3 %in% Plot2 %in% Plot1
> (Intercept) Residual
> StdDev: 0.000196583 5.216954
>
> Fixed effects: Yvar ~ Xvar
> Value Std.Error DF t-value p-value
> (Intercept) 2.3545454 0.2487091 860 9.467066 0.0000
> XvarFactor2 0.3909091 0.3517278 2 1.111397 0.3821
>
> Number of Observations: 880
> Number of Groups:
> Plot1 Plot2 %in% Plot1
> 4 8
> Plot3 %in% Plot2 %in% Plot1
> 20
>
> This is the correct result, de correct denDF for Xvar.
>
> I make this using lmer.
>
> > m.lmer <- lmer(Yvar~Xvar+(1|Plot1)+(1|Plot1:Plot2)+(1|Plot3))
> > anova(m.lmer)
> Analysis of Variance Table
> Df Sum Sq Mean Sq Denom F value Pr(>F)
> Xvar 1 33.62 33.62 878.00 1.2352 0.2667
> > summary(m.lmer)
> Linear mixed-effects model fit by REML
> Formula: Yvar ~ Xvar + (1 | Plot1) + (1 | Plot1:Plot2) + (1 | Plot3)
> AIC BIC logLik MLdeviance REMLdeviance
> 5416.59 5445.27 -2702.295 5402.698 5404.59
> Random effects:
> Groups Name Variance Std.Dev.
> Plot3 (Intercept) 1.3608e-08 0.00011665
> Plot1:Plot2 (Intercept) 1.3608e-08 0.00011665
> Plot1 (Intercept) 1.3608e-08 0.00011665
> Residual 2.7217e+01 5.21695390
> # of obs: 880, groups: Plot3, 20; Plot1:Plot2, 8; Plot1, 4
>
> Fixed effects:
> Estimate Std. Error DF t value Pr(>|t|)
> (Intercept) 2.35455 0.24871 878 9.4671 <2e-16 ***
> XvarFactor2 0.39091 0.35173 878 1.1114 0.2667
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Look the wrong P value, I know that it is wrong because the DF used. But, In
> this case, the result is not correct. Dont have any difference of the result
> using random effects with lmer and using a simple analyses with lm.

You are assuming that there is a correct value of the denominator degrees of freedom. I don't believe there is. The statistic that is quoted there doesn't have exactly an F distribution so there is no correct degrees of freedom.

One thing you can do with lmer is to form a Markov Chain Monte Carlo sample from the posterior distribution of the parameters so you can check to see whether the value of zero is in the middle of the distribution of XvarFactor2 or not.

It would be possible for me to recreate in lmer the rules used in lme for calculating denominator degrees of freedom associated with terms of the random effects. However, the class of models fit by lmer is larger than the class of models fit by lme (at least as far as the structure of the random-effects terms goes). In particular lmer allows for random effects associated with crossed or partially crossed grouping factors and the rules for denominator degrees of freedom in lme only apply cleanly to nested grouping factors. I would prefer to have a set of rules that would apply to the general case.

Right now I would prefer to devote my time to other aspects of lmer - in particular I am still working on code for generalized linear mixed models using a supernodal Cholesky factorization. I am willing to put this aside and code up the rules for denominator degrees of freedom with nested grouping factors BUT first I want someone to show me an example demonstrating that there really is a problem. The example must show that the p-value calculated in the anova table or the parameter estimates table for lmer is seriously wrong compared to an empirical p-value - obtained from simulation under the null distribution or through MCMC sampling or something like that. Saying that "Software XYZ says there are n denominator d.f. and lmer says there are m" does NOT count as an example. I will readily concede that the denominator degrees of freedom reported by lmer are wrong but so are the degrees of freedom reported by Software XYZ because there is no right answer (in general - in a few simple balanced designs there may be a right answer).

>
> > m.lm <- lm(Yvar~Xvar)
> >
> > anova(m.lm)
> Analysis of Variance Table
>
> Response: Nadultos
> Df Sum Sq Mean Sq F value Pr(>F)
> Xvar 1 33.6 33.6 1.2352 0.2667
> Residuals 878 23896.2 27.2
> >
> > summary(m.lm)
>
> Call:
> lm(formula = Yvar ~ Xvar)
>
> Residuals:
> Min 1Q Median 3Q Max
> -2.7455 -2.3545 -1.7455 0.2545 69.6455
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 2.3545 0.2487 9.467 <2e-16 ***
> XvarFactor2 0.3909 0.3517 1.111 0.267
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 5.217 on 878 degrees of freedom
> Multiple R-Squared: 0.001405, Adjusted R-squared: 0.0002675
> F-statistic: 1.235 on 1 and 878 DF, p-value: 0.2667
>
> I read the rnews about this use of the full DF in lmer, but I dont undestand
> this use with a gaussian error, I undestand this with glm data.
>
> I need more explanations, please.
>
> Thanks
> Ronaldo
> --
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R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Dec 29 06:07:07 2005

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