Modelling heterogeneity and crossed random effects

-----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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