[R-sig-ME] VERY simple question about NESTING in experimental designs (for glm, lme, lmer, etc.)

[ONKELINX, Thierry]

Dear Toby,

lmer(Birdlength ~ Country + (1|locnum/bnum)) # Is the correct model in your case
lmer(Birdlength ~ Country  + (1|locnum) + (1|locnum/bnum)) # is identical to the model above

The difference between (1|locnum/bnum) and (1|bnum) is that the former allows for location-specific effects (common to all birds on the same location). The random effect in the latter combines both the location-specific and the bird-specific effects.

(Country|locnum) is IMHO not a good idea because each location can be in only one country.

Best regards,

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 Toby Marthews
> Verzonden: donderdag 20 januari 2011 15:24
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: [R-sig-ME] VERY simple question about NESTING in 
> experimental designs (for glm, lme, lmer, etc.)
> 
> Dear R-sig-mixed-models,
> 
> This is probably a painfully simple question, but I can't 
> seem to pin it down from any source. About NESTING.
> 
> Imagine I carry out a nested experiment on birds. I measure 
> the size (say in cm beak to tail) of birds from 6 different 
> locations in Country A with 20 birds in each location. I then 
> also repeat this experiment in Country B with the same 
> replication. Crucially, because the work at each of the 12 
> locations was being carried out by a different collaborating 
> group, they all numbered their individual birds simply 1-20. 
> The data I eventually receive for my metastudy is something like:
> 
> Country	Location	Birdnum	Birdlength
>    A	1	1	7.3
>    A	1	2	6.7
>    ...	...	...	...
>    A	1	20	7.9
>    A	2	1	6.7
>    A	2	2	6.9
>    ...	...	...	...
>    B	1	1	6.7
>    B	1	2	6.6
> 
> The bird numbers and location numbers here are not unique 
> across the experimental design (bird #1 at location 1 is not 
> the same individual as bird #1 at location 2). Hearing what 
> Prof Bates said about not using "implicit nesting" in 2005 
> (http://cran.r-project.org/doc/Rnews/Rnews_2005-1.pdf ), I 
> construct new variables 
> bnum=factor(paste(Country,"-",Location,"-",Birdnum,sep="")) 
> which contains levels "A-1-1","A-1-2", ..., "B-1-2", etc., 
> and locnum=factor(paste(Country,"-",Location,sep="")) which 
> contains levels "A-1","A-1", ..., "B-1", etc. and that means 
> I can use locnum and bnum instead of Location and Birdnum and 
> I have a unique numbering system.
> 
> Say I am interested in the differences between birds in 
> countries A and B with location and birdnumber being random 
> effects. I believe I should try to use a command like
>   lme(fixed=Birdlength~Country,random=~1|bnum)
>   or glm(Birdlength~Country)
>   or lmer(Birdlength~Country+(1|bnum))
> however I have been criticised on two counts for this by 
> colleagues-who-shall-remain-nameless:
> 
>     (1) This is a nested design so I should replace bnum with 
> Country/locnum/bnum or Country/Location/Birdnum in both the 
> lme and the lmer command. (I'm pretty sure I can just use 
> bnum on its own because by knowing bnum I automatically know 
> the corresponding country and location of the measurement so 
> Country and Location are effectively redundant (surely?) 
> however, if I'm right then that means that I will only ever 
> need "/" if my nesting is somehow implicit (i.e. because I 
> usually use paste in the way described, I should never have 
> to use "/" even in nested experiments (which seems odd?))
>     (2) Because Country (my fixed predictor) is being used to 
> calculate bnum, I am mixing fixed and random effects 
> inappropriately. (I am less sure about this one: perhaps 
> "random=~Country|bnum" would be more correct or something else?)
> 
> Even with this very simple experimental setup, a number of 
> possible alternatives have been suggested by my colleagues including
>   glm(Birdlength~Country+Country/locnum+Country/locnum/bnum)
>   lmer(Birdlength~Country+Country|locnum+Country|(locnum/bnum))
>   lmer(Birdlength~Country+Country|locnum+Country|(bnum))
>   lmer(Birdlength~Country+1|locnum+1|(locnum/bnum))
> with the result that I'm getting very confused!
> 
> I'm pretty sure I'm making a meal of this little question so 
> I'll stop there, but any comments would be very welcome!
> 
> Best,
> Toby Marthews
> 
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