Modelling heterogeneity and crossed random effects

-----Oorspronkelijk bericht-----
Van: Amelie Lescroel [mailto:amelie.lescroel at univ-rennes1.fr]
Verzonden: woensdag 18 augustus 2010 10:41
Aan: ONKELINX, Thierry; r-sig-mixed-models at r-project.org
Onderwerp: RE: [R-sig-ME] Modelling heterogeneity and crossed 
random effects

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 "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:

 

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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