[R-sig-ME] lmer model for repeated measure in RCB design

[Ben Bolker]

  [cc'ing back to r-sig-mixed-models]


On 12-01-11 03:47 PM, Schreiber, Stefan wrote:
> Thanks Ben!
> 
> Yes, you are right, n=56. I don't know what happened there ;)
> 
> As for the ID, yes it is unique for each observation and identifies
> the sampled genotype in its respective block. The ID is build as
> "Genotype_Block".

  Technically, I would say that ID is not technically unique for each
observation since there are three observations (fall, winter, and
spring) for each ID ... ?  (You confirm this below: "each ID is
replicated three times ...") (By "observation", I mean the smallest
sampling unit -- one row of the data frame, in long format)

> Each genotype was replicated 5 times within each
> block. That way I was able to sample 8 genotypes by only having 5
> blocks. That means I sampled three blocks twice for the respective
> genotype.

  Makes sense.
> 
> Then I measured a physiological response on these genotypes in fall,
> winter and spring, representing different climate conditions. I
> always measured the same IDs over three different conditions (56*3).
> So each ID is replicated three times in my ID column.
> 
> Also, I grouped these 7 genotypes into 3 groups since I would rather
> compare the groups within each climatic condition and across the
> climatic conditions instead of all the genotypes.

  That makes perfect sense.
> 
> Since the ID is replicated 3 times, id is nested within genotype,
> correct?
> 
> response ~ group*climate + (1|block) + (1|genotype/id)

  This looks reasonable, although since id is *implicitly* nested (i.e.
it contains the genotype info) you should also be able to write it as
(1|genotype) + (1|id) .

   When you run this, lmer should report appropriate numbers of levels
in each group (block=5, genotype=8, genotype:id = 56? or 40? I'm not
sure ...) ... check these values and see that they are as you expect.
> 
> 
> Thanks again! Stefan
> 
> 
> 
> -----Original Message----- From:
> r-sig-mixed-models-bounces at r-project.org on behalf of Ben Bolker 
> Sent: Wed 1/11/2012 12:13 PM To: r-sig-mixed-models at r-project.org 
> Subject: Re: [R-sig-ME] lmer model for repeated measure in RCB
> design
> 
> Schreiber, Stefan <Stefan.Schreiber at ...> writes:
> 
>> 
>> 
>> Hi all,
>> 
>> I have a questions about the following situation and was hoping to
>> find clarification here.
>> 
>> I have a data frame with the following variables:
>> 
>> id, genotype, group, block, climate, response
>> 
>> I measured a response of 7 genotypes in a randomized complete
>> block design. I measured each genotype 8 times (n=48).
> 
> You have some missing combinations?  (8*7=56, right?)
> 
>> I grouped my 7 genotypes into 3 for me more reasonable groups. I
>> measured the response on the same 7 genotypes 3 times under
>> different climatic conditions.
>> 
>> I specified block and genotype as random and group as fixed.  I
>> believe the proper random statement should look like: block,
>> genotype nested within group.
>> 
>> I came up with the following code:
>> 
>> fit1 <- lmer(weight ~ group*climate + (1|block) +
>> (1|group/genotype) , data=df)
>> 
>> The problem I have now is how can I include the fact that I
>> measured the same genotypes at three different times? Can I say
>> (1|group/genotype/id) instead of (1|group/genotype)?
> 
> Is id a unique identifier for each observation?  In that case it's
> definitely redundant with the residual variance and should not be
> included in the model statement.
> 
> I'm still a little bit uncertain about your experimental design 
> (thanks for the careful explanation, though).  I'm going to make up 
> one possible explanation.  How unbalanced is it?  Does climate 
> represent another level of replication (e.g. are there three climate 
> conditions that are measured for each group*genotype*block 
> combination), or does it vary in an unbalanced way across 
> group*genotype*block combinations?  Would your total number of
> observations be 8 (blocks) * 7 (genotypes) * 3 (climate conditions)?
> 
> You shouldn't include group both as a fixed effect (your fixed
> group*climate term expands to group+climate+group:climate) and a
> random effect (your group/genotype term expands to 
> group+group:genotype).  You should probably use (1|group:genotype)
> instead (make sure group and genotype are both stored as factors).
> 
> Even if it weren't redundant, including a random effect of group
> (with only three groups) is likely to give you an estimated
> group-level variance of zero -- there aren't enough levels to
> estimate variance reliably.
> 
> If genotypes have unique IDs then you don't need the explicit nesting
> or interaction syntax.  If so, my best guess is that
> 
> weight ~ group*climate + (1|block) + (1|genotype)
> 
> is what you want.
> 
> You might consider whether it's worth including other random terms
> -- the most complex model would include (group*climate|block) and
> (climate|genotype) -- but you might find that you were running out of
> signal ...
> 
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