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.> 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 -- |> // | \\ [***********************************] | ( ?? ?? ) [Ronaldo Reis J??nior ] |> V [UFV/DBA-Entomologia ] | / \ [36570-000 Vi??osa - MG ] |> /(.''`.)\ [Fone: 31-3899-4007 ] | /(: :' :)\ [chrysopa at insecta.ufv.br ] |>/ (`. `'` ) \[ICQ#: 5692561 | LinuxUser#: 205366 ] | ( `- ) [***********************************] |>> _/ \_Powered by GNU/Debian Woody/Sarge
On 12/26/05, Ronaldo Reis-Jr. <chrysopa at 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 > -- > |> // | \\ [***********************************] > | ( ?? ?? ) [Ronaldo Reis J??nior ] > |> V [UFV/DBA-Entomologia ] > | / \ [36570-000 Vi??osa - MG ] > |> /(.''`.)\ [Fone: 31-3899-4007 ] > | /(: :' :)\ [chrysopa at insecta.ufv.br ] > |>/ (`. `'` ) \[ICQ#: 5692561 | LinuxUser#: 205366 ] > | ( `- ) [***********************************] > |>> _/ \_Powered by GNU/Debian Woody/Sarge > > ______________________________________________ > R-help at 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 >
On 12/28/05, Douglas Bates <dmbates at gmail.com> miswrote:> 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.I should have written "fixed effects", not "random effects" at the end of that sentence.
Surely there is a correct denominator degrees of freedom if the design is balanced, as Ronaldo's design seems to be. Assuming that he has specified the design correctly to lme() and that lme() is getting the df right, the difference is between 2 df and 878 df. If the t-statistic for the second level of Xvar had been 3.0 rather than 1.1, the difference would be between a t-statistic equal to 0.095 and 1e-6. In a design where there are 10 observations on each experimental unit, and all comparisons are at the level of experimental units or above, df for all comparisons will be inflated by a factor of at least 9. Rather than giving df that for the comparison(s) of interest may be highly inflated, I'd prefer to give no degrees of freedom at all, & to encourage users to work out df for themselves if at all possible. If they are not able to do this, then mcmcsamp() is a good alternative, and may be the way to go in any case. This has the further advantage of allowing assessments in cases where the relevant distribution is hard to get at. I'd think a warning in order that the df are upper bounds, and may be grossly inflated. Incidentally, does mcmcsamp() do its calculations pretty well independently of the lmer results? John Maindonald. On 29 Dec 2005, at 10:00 PM, r-help-request at stat.math.ethz.ch wrote:> From: Douglas Bates <dmbates at gmail.com> > Date: 29 December 2005 5:59:07 AM > To: "Ronaldo Reis-Jr." <chrysopa at gmail.com> > Cc: R-Help <r-help at stat.math.ethz.ch> > Subject: Re: [R] lme X lmer results > > > On 12/26/05, Ronaldo Reis-Jr. <chrysopa at 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
Message: 18 Date: Fri, 30 Dec 2005 12:51:59 -0600 From: Douglas Bates <dmbates at gmail.com> Subject: Re: [R] lme X lmer results To: John Maindonald <john.maindonald at anu.edu.au> Cc: r-help at stat.math.ethz.ch Message-ID: <40e66e0b0512301051i2dc0f257r745c70e749c250f0 at mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1 On 12/29/05, John Maindonald <john.maindonald at anu.edu.au> wrote: >> Surely there is a correct denominator degrees of freedom if the design >> is balanced, as Ronaldo's design seems to be. Assuming that he has >> specified the design correctly to lme() and that lme() is getting the df >> right, the difference is between 2 df and 878 df. If the t-statistic >> for the >> second level of Xvar had been 3.0 rather than 1.1, the difference >> would be between a t-statistic equal to 0.095 and 1e-6. In a design >> where there are 10 observations on each experimental unit, and all >> comparisons are at the level of experimental units or above, df for >> all comparisons will be inflated by a factor of at least 9. Doug Bates commented: I don't want to be obtuse and argumentative but I still am not convinced that there is a correct denominator degrees of freedom for _this_ F statistic. I may be wrong about this but I think you are referring to an F statistic based on a denominator from a different error stratum, which is not what is being quoted. (Those are not given because they don't generalize to unbalanced designs.) This is why I would like to see someone undertake a simulation study to compare various approaches to inference for the fixed effects terms in a mixed model, using realistic (i.e. unbalanced) examples. Doug-- Here is a paper that focused on the various alternatives to denominator degrees of freedom in SAS and does report some simulation results: http://www2.sas.com/proceedings/sugi26/p262-26.pdf Not sure whether it argues convincingly one way or the other in the present discussion. cheers, Dave -- Dave Atkins, PhD datkins at u.washington.edu