[R-sig-ME] lmer output shows laplace approximation not reml
Joshua Wiley
jwiley.psych at gmail.com
Fri Jul 20 18:56:11 CEST 2012
Hi Yolande,
It is not clear what REML is with GLMMs. In LMMs, REML maximizes the
liklihood that only depends only on the variance components by
conditioning on the fixed effects. AFAIK (Dr. Bates will hopefully
correct me if I am wrong or step in with a more thorough explanation)
it is unclear what the conditional distribution that depends only on
variance components would be with nonlinear models. The only
approaches I know of that still do something REMLish use iterative
linear approximations (e.g., the glimmix macro did this with repeated
underlying calls to proc mixed in SAS).
So, I do not think it is surprising that with a GLMM (which mixed
effects poisson is), REML does nothing.
Cheers,
Josh
On Fri, Jul 20, 2012 at 9:39 AM, Yolande Tra <yolande.tra at gmail.com> wrote:
> Thank you for your reply.
> Even though I specify REML=TRUE in the code, the fit was not done with REML.
> My last question also was why I could not get an ANOVA output for the fixed
> effects
>
>> anova(g)
> Error in anova(g) : single argument anova for GLMMs not yet implemented
>
> Y
> On Fri, Jul 20, 2012 at 11:51 AM, Douglas Bates <bates at stat.wisc.edu> wrote:
>
>> On Thu, Jul 19, 2012 at 9:20 PM, Yolande Tra <yolande.tra at gmail.com>
>> wrote:
>> >
>> > Dear Douglas,
>> >
>> > I am sorry to bother you but this is very important. I posted the
>> following question (in a slight different version) at r-sig-ME question
>> list but it seems no one is able to answer it.
>>
>> But Ben answered it. When you specify family="poisson" you are
>> fitting a generalized linear mixed model. The parameter estimates
>> provided for such a model by lme4 are the maximum likelihood
>> estimates, up to an approximation. The default approximation is the
>> Laplace approximation.
>>
>>
>> This data has quite complicated design. I did not find any example
>> that is similar in the literature on lme4. According to the
>> investigator this is a partial nested design. Counts were collected at
>> different transects, different depths and different sites at different
>> times. Time is continuous and assumed to be random, all the others are
>> categorical fixed where transect is nested within depth which is
>> nested within site. Definitely the three factors are nested within
>> each other but based on the the attached files and the table below, it
>> looks like this a repeated measurement design where time (dive_id) is
>> nested within the three factor level combination. So far if I am
>> wrong, please correct me. I believe the main effect is site (b) and
>> level (a) is nested within depth(b) which in turn is nested within
>> site(b). dive_id which represents also time is random.
>> > I read some examples you gave. My output is different.
>> > 1. The fit is done with Laplace approximation, not REML
>> > 2. There is no residual random effect
>> > 3. anova(g) did not give any output
>> >
>> > In this table the cell represents the number of times each combination
>> was used to obtain the counts (based on the attached file).
>> >
>> >
>> >
>> >
>> > Hopkins
>> >
>> > Lovers Point
>> >
>> > Point Pinos
>> >
>> > Total
>> >
>> > 5
>> >
>> > B
>> >
>> > 8
>> >
>> > 6
>> >
>> > 6
>> >
>> > 20
>> >
>> > M
>> >
>> > 8
>> >
>> > 6
>> >
>> > 6
>> >
>> > 20
>> >
>> > Total
>> >
>> > 16
>> >
>> > 12
>> >
>> > 12
>> >
>> > 40
>> >
>> > 10
>> >
>> > B
>> >
>> > 7
>> >
>> > 6
>> >
>> > 7
>> >
>> > 20
>> >
>> > M
>> >
>> > 7
>> >
>> > 6
>> >
>> > 7
>> >
>> > 20
>> >
>> > Total
>> >
>> > 14
>> >
>> > 12
>> >
>> > 14
>> >
>> > 40
>> >
>> > 15
>> >
>> > B
>> >
>> > 7
>> >
>> > 6
>> >
>> > 8
>> >
>> > 21
>> >
>> > M
>> >
>> > 7
>> >
>> > 6
>> >
>> > 8
>> >
>> > 21
>> >
>> > Total
>> >
>> > 14
>> >
>> > 12
>> >
>> > 16
>> >
>> > 42
>> >
>> > Total
>> >
>> > 44
>> >
>> > 36
>> >
>> > 42
>> >
>> > 122
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> >
>> > d2 <- read.csv(file.path(dataDir,"aggregate_2008.csv"), as.is=T,stringsAsFactors
>> = FALSE)
>> > > a<-factor(d2$level)
>> > > b<-factor(d2$site)
>> > > c<-factor(d2$depth)
>> > > g=lmer(total_count ~ b+(1|b:c)+(1|b:c:a)+(1|dive_id), d2,
>> REML=TRUE,family = "poisson")
>> > > summary(g)
>> > Generalized linear mixed model fit by the Laplace approximation
>> > Formula: total_count ~ b + (1 | b:c) + (1 | b:c:a) + (1 | dive_id)
>> > Data: d2
>> > AIC BIC logLik deviance
>> > 1153 1169 -570.3 1141
>> > Random effects:
>> > Groups Name Variance Std.Dev.
>> > dive_id (Intercept) 0.60707 0.77915
>> > b:c:a (Intercept) 0.16273 0.40340
>> > b:c (Intercept) 0.16273 0.40340
>> > Number of obs: 122, groups: dive_id, 61; b:c:a, 9; b:c, 9
>> >
>> > Fixed effects:
>> > Estimate Std. Error z value Pr(>|z|)
>> > (Intercept) 1.98724 0.37388 5.315 1.07e-07 ***
>> > bLovers Point 0.02358 0.53618 0.044 0.965
>> > bPoint Pinos -0.43114 0.53273 -0.809 0.418
>> > ---
>> > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>> >
>> > Correlation of Fixed Effects:
>> > (Intr) bLvrsP
>> > bLoversPont -0.697
>> > bPointPinos -0.702 0.489
>> >
>> > > anova(g)
>> > Error in anova(g) : single argument anova for GLMMs not yet implemented
>> >
>> > I really appreciate any of your insight as author of the package lme4.
>> >
>> > Yolande
>>
>
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>
>
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--
Joshua Wiley
Ph.D. Student, Health Psychology
Programmer Analyst II, Statistical Consulting Group
University of California, Los Angeles
https://joshuawiley.com/
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