[R-sig-ME] random factor and error messages in the model fitting

Thu Apr 3 01:22:33 CEST 2008

I'd expect that you want to generalize to a difference choice of  
transects within each altitude and age-class.  Were there multiple  
transects for each altitude and age-class combination?  If not, the  
factor Transect is trying to do two things at once -- account for the  
fixed effect of altitude, and account for the random effect of transect.

Two analyses are possible with the data that you seem to have:

A)  lm( SLA ~ Transect + Age + Age:Transect)

The inferences generalize to a different choice of tissue samples  
within those same Age and Transect combinations.  When a prediction is  
made, you have to say which Age and Transect combination you have in  
mind, and inferences apply to the particular Transects that were taken.

B)

lmer(SLA ~ Age + Transect + (1|Transect:Age),
          data=Treeline[Site=="TermasChillan",], na.action=na.omit)

This treats variation between Age:Transect combinations as the  
relevant measure of error, hoping that this will be mach the same as  
the error that you'd get from different transects within Altitude:Age  
combinations.  If there is an Altitude:Age interaction, it may over- 
estimate the error.

[If you do happen to have multiple transects for each Age:Transect  
combination, you'd want something like:

lmer(SLA ~ Age*Altitude+ (1|transect/Age),
          data=Treeline[Site=="TermasChillan",], na.action=na.omit)

(the error term needs to identify individual transect*Age  
combinations) ]

NB also, you might want to try a non-linear term in Age in the fixed  
part of the model.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.

On 3 Apr 2008, at 4:02 AM, Hank Stevens wrote:

> Hi Alex,
> On Apr 2, 2008, at 10:17 AM, Alex Fajardo wrote:
>
>> Dear r-sig-mixed-models webmail list members,
>>
>> I am new in the mixed-effects models world and I am learning from
>> Faraway's
>> and Pinheiro & Bates' books and also from this list.
>> I have 3, very straightforward, questions, but first a brief summary
>> of my
>> analysis objectives. I am trying to analyze my data with mixed  
>> effects
>> models where the fixed factor is represented by altitudinal
>> transects (4
>> transects, where T4 is treeline, and T1, T2 and T3 are below
>> treeline). In
>> each altitudinal transect I collected tissue samples from different
>> age-class trees (a categorical variable with 4 levels, I, II, III,
>> and IV);
>> all this with the main objective to compare specific leaf area -SLA-
>> of the
>> treeline trees with lower elevation transects, and take into account
>> the
>> age-class of the tree being considered. The data set is very
>> unbalanced and
>> reading similar papers I concluded that age-class should be
>> considered a
>> random factor nested in transects.
>>
>> *Question 1*: am I correct by considering age-class a random factor
>> nested
>> within transect? If so, what should be the way to code the model?
>> My suggestion is:
>>> sla.termas = lmer(SLA ~ 1 + Transect + (1|Transect:Age),
>> data=Treeline[Site=="TermasChillan",], na.action=na.omit) or
>>> sla.termas = lmer(SLA ~ 1 + Transect + (Transect|Age),
>> data=Treeline[Site=="TermasChillan",], na.action=na.omit), but I am
>> not
>> sure.
> I would assume that Age is NOT nested; if it is, you are saying that
> the effect of age could depend entirely on which transect you look at.
> Rather, I assume different ages simply have different responses, i.e.,
> (1|Age).
>
> However, I would think that a fixed effect model is just as useful.
> lm( SLA ~ Transect + Age + Age:Transect)
>
> I am not sure why these altitudes or age class are considered a random
> draw from a large number of such classes that you know little about.
> They seem entirely repeated, and usefully so.
>
> My two cents,
> Hank
>>
>>
>>
>> In my learning process I followed examples given in Faraway's book
>> and just
>> for learning purposes I computed my model in the way he does
>> (considering
>> both factors random) and got, for some, variables the following
>> warning
>> message:
>>
>>> sla.termas = lmer(SLA ~ 1 + (1|Transect) + (1|Transect:Age),
>> data=Treeline[Site=="TermasChillan",], na.action=na.omit)
>> *Warning message: In .local(x, ..., value) :
>> Estimated variance-covariance for factor 'Age' is singular*
>>
>> This is not good when I try to test the significance of the
>> variation among
>> ages by ANOVA, since I get a Pr(>Chisq)=1; something must be wrong.
>> This
>> situation happens with some variables and not with all of them:
>> strange?
>>
>> *Question 2*: any idea why this happens? What am I doing wrong?
>>
>> When I do get the model run (no such a warning message and just for
>> some
>> other variables) and compare this model with a reduced version
>> (without the
>> nested random factor, e.g., age-class) I run anova and get a p-
>> value. As
>> suggested by Faraway I should also go for a p-value computing LRT
>> 1000 times
>> (less conservative cf. Faraway) and most of the time I get the
>> following
>> message:
>>
>>> lrstat = numeric(1000)
>>> for(i in 1:1000){
>> + rSLA = unlist(simulate(sla.termas2))
>> + nmod =
>> lmer(rSLA~1+(1|
>> Transect),data=Treeline[Site=="TermasChillan",],na.action=na.omit)
>> + amod =
>> lmer(rSLA~1+(1|Transect)+(1|
>> Transect:Age 
>> ),data=Treeline[Site=="TermasChillan",],na.action=na.omit)
>> + lrstat[i] = 2*(logLik(amod)-logLik(nmod))
>> + }
>> *Error in model.frame.default(data = Treeline[Site ==
>> "TermasChillan",  :
>> variable lengths differ (found for 'Transect')*
>>
>> *Question 3*: any idea why this happens? What am I doing wrong? I
>> made an
>> artificial balanced data set to see whether the unbalanced situation
>> was the
>> responsible for this message but it was not.
>>
>> I am new in the mixed-effects models world but I want to learn; your
>> comments and advice will be greatly appreciated. Cheers,
>>
>>
>>
>> --
>> Alex Fajardo, PhD
>> Investigador Asociado
>> Centro de Investigación en Ecosistemas de la Patagonia
>> Bilbao 449. Coyhaique, CHILE
>> Telefonos: 56-67-244503; (56) 8-4506354
>> Fax: 56-67-244501
>> alex.fajardo at ciep.cl
>>
>>      [[alternative HTML version deleted]]
>>
>> <ATT00001.txt>
>
>
>
> Dr. Hank Stevens, Associate Professor
> 338 Pearson Hall
> Botany Department
> Miami University
> Oxford, OH 45056
>
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> http://www.muohio.edu/botany/
>
> "If the stars should appear one night in a thousand years, how would  
> men
> believe and adore." -Ralph Waldo Emerson, writer and philosopher
> (1803-1882)
>
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