[R-sig-ME] Modelling heterogeneity and crossed random effects
Amelie Lescroel
amelie.lescroel at univ-rennes1.fr
Wed Aug 18 10:40:54 CEST 2010
Dear Thierry,
Thanks a lot for your answer. I was hoping that year as a random effect
would 1) account for the study design (I have several points per individual
for each year and I wanted to quantify the correlation of 2 observations
from the same individual within a year vs. across years) and 2) capture
other year effects that would not be accounted for by my fixed effects. And
indeed, all my models including year as a random effect performed better, in
terms of AIC, than those that did not include year. Otherwise, yes, it would
easier to model the variance in nlme. In either package though, I'm not sure
that I found the right structure model that would correspond to the study
design (longitudinal study with replicated points within years) and I would
welcome any suggestion.
Best,
Amelie
-----Original Message-----
From: ONKELINX, Thierry [mailto:Thierry.ONKELINX at inbo.be]
Sent: Wednesday, August 18, 2010 10:30 AM
To: Amelie Lescroel; r-sig-mixed-models at r-project.org
Subject: RE: [R-sig-ME] Modelling heterogeneity and crossed random effects
Dear Amelie,
Do you expect a common effect of year on all individuals that is not
captured by your fixed effects? If not, you do not need to add year as a
random effect and only a random effect of individual will do. Hence you
could switch back to nlme which has more features in terms of variance and
correlation structures.
HTH,
Thierry
----------------------------------------------------------------------------
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie & Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium
Research Institute for Nature and Forest
team Biometrics & Quality Assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium
tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be
www.inbo.be
To call in the statistician after the experiment is done may be no more than
asking him to perform a post-mortem examination: he may be able to say what
the experiment died of.
~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data.
~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
> -----Oorspronkelijk bericht-----
> Van: r-sig-mixed-models-bounces at r-project.org
> [mailto:r-sig-mixed-models-bounces at r-project.org] Namens
> Amelie Lescroel
> Verzonden: woensdag 18 augustus 2010 10:06
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: Re: [R-sig-ME] Modelling heterogeneity and crossed
> random effects
>
> Dear all,
> I did not receive any answer to my questions below. Not that
> I consider that anybody "owes" me an answer but I would
> really need advices from people more knowledgeable than I am.
> Please let me know if I need to reformulate / shorten my
> questions or examples or if they are too "naïve".
> Best regards,
> Amelie
>
> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org
> [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf
> Of Amelie Lescroel
> Sent: Tuesday, August 17, 2010 10:16 PM
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] Modelling heterogeneity and crossed random effects
>
> Dear all,
>
>
>
> I am currently trying to model the behavioural response of
> individual seabirds (in terms of foraging efficiency) to the
> variation in sea ice cover
> (SICdr) of their foraging environment. I have 13 years of
> data, birds are individually marked and followed, I have
> several records (= foraging efficiency data = CPUEr in my
> code) per individual (IDr) for each year
> (YEARr) and individuals are followed across years.
>
>
>
> I am trying to find the right random effect structure
> (biologically meaningful and dealing with problems of
> independence) and to deal with heterogeneity of the residual
> variance at the same time (for all my models, the variance of
> the residuals increases with increasing fitted values).
> Regarding the random effect structure, would you say that
> crossed random effects of the form (1|IDr) + (1|YEARr) would
> correctly reflect the study design? Is there any way to model
> the variance heterogeneity in lmer that would be analogous to
> the varIdent or varFixed functions in nlme? So far, I can
> model the variance heterogeneity with nlme only and the
> (hopefully) appropriate random effect structure with lmer
> only. Would you have other suggestions for dealing with this
> heteroscedasticity?
>
>
>
> Here are a couple of examples regarding the random effect
> structure with some associated questions:
>
>
>
> > M1 <- lmer(CPUEr~SEXr+SICdr+(1|IDr))
>
> > summary(M1)
>
>
>
> Linear mixed model fit by REML
>
> Formula: CPUEr ~ SEXr + SICdr + (1 | IDr)
>
> AIC BIC logLik deviance REMLdev
>
> 270.2 297.6 -130.1 234.5 260.2
>
> Random effects:
>
> Groups Name Variance Std.Dev.
>
> IDr (Intercept) 0.010906 0.10443
>
> Residual 0.060610 0.24619
>
> Number of obs: 1759, groups: IDr, 229
>
>
>
> Fixed effects:
>
> Estimate Std. Error t value
>
> (Intercept) 0.3070164 0.0155734 19.714
>
> SEXrM 0.0961795 0.0195420 4.922
>
> SICdr 0.0026240 0.0008478 3.095
>
>
>
> Correlation of Fixed Effects:
>
> (Intr) SEXrM
>
> SEXrM -0.612
>
> SICdr -0.478 -0.006
>
>
>
> Here, the correlation between 2 observations from the same
> individual (irrespective of year) is:
> 0.010906/(0.010906+0.060610)=0.15
>
>
>
> > M2 <- lmer(CPUEr~SEXr+SICdr+(1|YEARr))
>
> > summary(M2)
>
> Linear mixed model fit by REML
>
> Formula: CPUEr ~ SEXr + SICdr + (1 | YEARr)
>
> AIC BIC logLik deviance REMLdev
>
> 117.1 144.5 -53.55 84.8 107.1
>
> Random effects:
>
> Groups Name Variance Std.Dev.
>
> YEARr (Intercept) 0.020395 0.14281
>
> Residual 0.059892 0.24473
>
> Number of obs: 1759, groups: YEARr, 13
>
>
>
> Fixed effects:
>
> Estimate Std. Error t value
>
> (Intercept) 0.36443 0.04367 8.345
>
> SEXrM 0.10819 0.01175 9.207
>
> SICdr -0.00920 0.00192 -4.793
>
>
>
> Correlation of Fixed Effects:
>
> (Intr) SEXrM
>
> SEXrM -0.134
>
> SICdr -0.367 0.009
>
>
>
> Here, the correlation between 2 observations from the same
> year (irrespective of the bird) is:
> 0.020395/(0.020395+0.059892)=0.25 How do I get the
> correlation of 2 observations from the same individual within
> a year? By modeling CPUEr~SEXr+SICdr+(1|YEARr/IDr)?
>
>
>
> > M3 <- lmer(CPUEr~SEXr+SICdr+(1|YEARr/IDr))
>
> > summary(M3)
>
> Linear mixed model fit by REML
>
> Formula: CPUEr ~ SEXr + SICdr + (1 | YEARr/IDr)
>
> AIC BIC logLik deviance REMLdev
>
> 51.29 84.12 -19.64 17.21 39.29
>
> Random effects:
>
> Groups Name Variance Std.Dev.
>
> IDr:YEARr (Intercept) 0.0097178 0.09858
>
> YEARr (Intercept) 0.0188065 0.13714
>
> Residual 0.0500727 0.22377
>
> Number of obs: 1759, groups: IDr:YEARr, 543; YEARr, 13
>
>
>
> Fixed effects:
>
> Estimate Std. Error t value
>
> (Intercept) 0.357318 0.042408 8.426
>
> SEXrM 0.104650 0.014207 7.366
>
> SICdr -0.008960 0.001855 -4.831
>
>
>
> Correlation of Fixed Effects:
>
> (Intr) SEXrM
>
> SEXrM -0.166
>
> SICdr -0.365 0.004
>
>
>
> Then, would the correlation of 2 observations from the same
> individual within a year be 0.0097178/(0.0097178+0.0500727)=0.16?
>
>
>
> My best model (in terms of AIC) so far is the following:
>
>
>
> > M4 <- lmer(CPUEr~SEXr+SICdr+(SICdr|IDr)+(1|YEARr))
>
> > summary(M4)
>
> Linear mixed model fit by REML
>
> Formula: CPUEr ~ SEXr + SICdr + (SICdr | IDr) + (1 | YEARr)
>
> AIC BIC logLik deviance REMLdev
>
> 12.88 56.66 1.559 -24.55 -3.119
>
> Random effects:
>
> Groups Name Variance Std.Dev. Corr
>
> IDr (Intercept) 8.9314e-03 0.0945058
>
> SICdr 2.3781e-05 0.0048766 -0.464
>
> YEARr (Intercept) 2.1401e-02 0.1462922
>
> Residual 5.0765e-02 0.2253112
>
> Number of obs: 1759, groups: IDr, 229; YEARr, 13
>
>
>
> Fixed effects:
>
> Estimate Std. Error t value
>
> (Intercept) 0.363366 0.045471 7.991
>
> SEXrM 0.100215 0.017188 5.830
>
> SICdr -0.009910 0.001974 -5.021
>
>
>
> Correlation of Fixed Effects:
>
> (Intr) SEXrM
>
> SEXrM -0.189
>
> SICdr -0.357 0.010
>
>
>
> How should I interpret the random effects?
>
>
>
> I am using the R package version 0.999375-31 of lme4 and R
> version 2.9.2.
>
>
>
> Thanks in advance for your help!
>
>
>
> Cheers,
>
>
>
> Amelie
>
>
>
>
>
>
>
>
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
Druk dit bericht a.u.b. niet onnodig af.
Please do not print this message unnecessarily.
Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver weer
en binden het INBO onder geen enkel beding, zolang dit bericht niet
bevestigd is
door een geldig ondertekend document. The views expressed in this message
and any annex are purely those of the writer and may not be regarded as
stating
an official position of INBO, as long as the message is not confirmed by a
duly
signed document.
More information about the R-sig-mixed-models
mailing list