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Modelling heterogeneity and crossed random effects

5 messages · Amelie LESCROEL, ONKELINX, Thierry

Original
Amelie LESCROEL
# 
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 "na?ve".
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:
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
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)?
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:
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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ONKELINX, Thierry
# 
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
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signed document.
Amelie LESCROEL
# 
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
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.
ONKELINX, Thierry
# 
Dear Amelie,

In my opinion, a correlation structure (e.g. corAR1(~Year) or corExp(~Year)) will do to represent your design. And it will give you information about the difference in variance in a year and among years.
A second option would be to add year as a random slope per individual. Random = ~ factor(Year) - 1|ID
You could even combine both options.

Note that according to Zuur et al. (2009) is random intercept is equivalent to a compound symmetry correlation structure.

lme(Z ~ ..., random = ~ 1|A) is equivalent to gls(Z ~ ..., correlation = corCompSymm(~A))

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
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.