[R-sig-ME] lme: random effect nested within fixed effect

[Ben Bolker]

  in general "nested" is used to apply to the relationship between
random effects, not to the relationship between fixed & random effects
-- the relationship between random (population) and fixed (type) would
actually be an interaction between random and fixed.

  I'm still not 100% sure of the meaning of the design, but I would
strongly consider whether simply pooling (i.e., taking means) of
individuals within populations would make sense -- there's a nice paper
by Murtaugh (2009) in Ecology or Ecological Applications that makes this
point.  Then you wouldn't have to mess with mixed models at all, you
would just have 'populations' as your sample points.

Andrew Dolman wrote:
> I wouldn't consider population to be nested within type or type to be a
> random effect. You've measured growth of individuals of three different
> types (a fixed effect) and the individuals were grouped in populations so
> perhaps should not be considered totally independent data points. The random
> structure ~ 1 | population  reflects this sampling structure.
> 
> Andy.
> 
> andydolman at gmail.com
> 
> 
> On 6 April 2010 21:24, Itay Mayrose <itaymay at gmail.com> wrote:
> 
>> thanks Andy!
>>
>> what I am a bit confused about is that I am not sure how does this account
>> for population nested within type so I thought the second option is the most
>> sensible:
>>
>>
>> z1 <- lme(growth ~ type, random = ~ 1 | type/population, data =
>> times,method="ML")
>>
>> itay
>>
>>
>>
>> On Tue, Apr 6, 2010 at 12:13 PM, Andrew Dolman <andydolman at gmail.com>wrote:
>>
>>> Hi Itay,
>>>
>>> I think what you want is the following.
>>>
>>>
>>> z0 <- lme(growth ~ 1,     random = ~ 1 | population, data =
>>> times,method="ML")
>>>
>>>
>>> z1 <- lme(growth ~ type, random = ~ 1 | population, data =
>>> times,method="ML")
>>>
>>> anova(z0,z1)
>>>
>>>
>>> This tests for differences in growth between plant types while allowing
>>> growth rates to vary randomly between populations - or to look at it a
>>> different way, it accounts for individuals within populations being more
>>> similar to each other on average than individuals from different
>>> populations.
>>>
>>>
>>> A construction like this
>>>
>>> z1 <- lme(growth ~ type, random = ~ type | population, data =
>>> times,method="ML")
>>>
>>> allows the difference in growth between plant types to vary randomly
>>> between populations. But this would only makes sense if different plant
>>> types existed in the same populations, which does not sound to be the case
>>> here, and is asking a different question.
>>>
>>>
>>>
>>> Andy.
>>>
>>>
>>>
>>>
>>>
>>>
>>> andydolman at gmail.com
>>>
>>>
>>> On 6 April 2010 20:45, Itay Mayrose <itaymay at gmail.com> wrote:
>>>
>>>> Hi all,
>>>>
>>>>  This should be a somewhat trivial question but I am new to R and I am a
>>>> bit
>>>> puzzled with the lme syntax.
>>>>
>>>>  I would like to test for growth difference between three types of
>>>> plants.
>>>> For each plant type I randomly sampled four populations and for each
>>>> population several individuals.
>>>>
>>>>  First, I used lme where type is the fixed effect and population is
>>>> random
>>>> nested within type, but I am not sure which of the three options the
>>>> correct
>>>> syntax is:
>>>>
>>>> (1)
>>>>
>>>> z1 <- lme(growth ~ type, random = ~ 1 | population, data =
>>>> times,method="ML")
>>>>
>>>>  (2)
>>>>
>>>> z1 <- lme(growth ~ type, random = ~ 1 | type/population, data =
>>>> times,method="ML")
>>>>
>>>>  (3)
>>>>
>>>> z1 <- lme(growth ~ type, random = ~ type | population, data =
>>>> times,method="ML")
>>>>
>>>>
>>>>
>>>> I am using the ML method because I would like to contrast this model
>>>> against
>>>> a NULL model where growth does not depend on plant type (assuming the
>>>> first
>>>> syntax is correct):
>>>>
>>>> z0 <- lme(growth ~ 1, random = ~ type | population, data =
>>>> times,method="ML")
>>>>
>>>> anova(z0,z1)
>>>>
>>>>
>>>>
>>>> Thanks!
>>>> Khilik
>>>>
>>>>        [[alternative HTML version deleted]]
>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>
>>>
>>
>> --
>> _________________________________
>> Itay Mayrose
>> http://www.zoology.ubc.ca/~mayrose/<http://www.zoology.ubc.ca/%7Emayrose/>
>> Department of Zoology,
>> University of British Columbia
>> email: itaymay at gmail.com
>>
> 
> 	[[alternative HTML version deleted]]
> 
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-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / people.biology.ufl.edu/bolker
GPG key: people.biology.ufl.edu/bolker/benbolker-publickey.asc