[R-sig-ME] Modelling heterogeneity and crossed random effects
ONKELINX, Thierry
Thierry.ONKELINX at inbo.be
Wed Aug 18 10:29:48 CEST 2010
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
>
>
>
>
>
>
>
>
>
>
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>
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