[R-sig-ME] Zero random effect variance?

[Ben Bolker]

On 13-10-17 08:28 PM, Dave Marvin wrote:
> Sorry, I included it as a text file attachment. Guessing the
> list-serv strips attachments... Here is a link to the text file:
> http://goo.gl/e5q2hO
> 
> If that is the issue (which after looking back at my boxplot is
> probably the case) should I still expect literally zero variance
> attributed to the chambers?

  Yes.  This is a case, I think (referred to from time to time in
threads on this list), where the classical method of moments estimates
would give a negative among-group variance, or a compound symmetry model
would give negative within-group correlations; the framework used in
lme4 can't do either of those things easily.  (It would be entertaining
but totally impractical to try to figure out what kind of imaginary- or
complex-valued values one would need in the computations to get this to
work out).

  Ben Bolker

> 
> 
> On Oct 17, 2013, at 8:16 PM, Ben Bolker wrote:
> 
>> Dave Marvin <marvs at ...> writes:
>> 
>>> 
>>> For the following dataset (described at the bottom of this
>>> email),
>> 
>> Did you mean to include an actual data set, or just the text
>> description? Without the data set itself, we can't do better than
>> guessing.
>> 
>>> a boxplot of the data by chamber
>>> 
>>>> height=read.table("height.txt",header=TRUE) 
>>>> boxplot(HtChg~Chamber,data=height)
>> 
>>> shows there is clearly a lot of chamber-to-chamber variation in
>>> the response variable. However, if I run a random intercept-only
>>> model:
>> 
>>>> lmer(HtChg~1+(1|Chamber),data=height)
>>> 
>>> I get 0 variance for the random intercept. Same is true if I then
>>>  include any categorical fixed effects. Does this seem correct,
>>> and if so why? -Dave
>> 
>>>> I am analyzing the growth response (Height Change) of two
>>>> plant
>>> types (vines vs. trees) to different CO2 levels, for a mix of 
>>> species of each plant type in plant growth chambers (Chamber).
>>> CO2 and FT are categorical predictors, each with two levels 
>>> (elevated/ambient CO2, vine/tree plant Functional Types). Each 
>>> growth chamber had the same mix of 8 species (Spp).
>> 
>> Presumably the within-chamber variation is large enough that it
>> adequately accounts for the among-chamber variation? Again, hard to
>> say without seeing the data ... you could do the math yourself
>> (e.g. is variance among >= (variance within)/(n within)?), or
>> simulate some representative examples ...
>> 
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>