It seems to me that if forest, meadow, ploughland are proportions adding to
one, then testing them as a three-way interaction is odd. I'm not sure I
understand your hypothesis. If it is that cranial dimension is related to
the amount of ploughland or forest, maybe just using 'meadow' as a main
effect would be a straightforward first test. If it is that sensitivity to
other environmental factors is conditioned upon the amount of ploughland or
forest - I'm not sure, but again, testing with EnvironmentalFactor*meadow as
main effects might work.

 

I'm also not sure whether you've explored all possibilities for random
effects structures. Seems like you might want to treat individual as a
random effect, but nested within population, i.e., (1|pop/ind). 

 

Just a few thoughts, in the spirit of Socratic inquiry

 

--Seth

 

 

From: Milos Blagojevic [mailto:paulidealiste@aol.com] 
Sent: Tuesday, May 07, 2013 3:56 PM
To: seth@swbigelow.net
Subject: Re: [R-sig-ME] lme4 with proportion data and lack of fir otherwise

 

This is a great idea. I`ve been struggling with this for a long time. But
I`m afraid it doesn`t answer my specific question. Namely any diversity
index will score the most diverse habitat with the highest grade. But my
hypothesis is that the cranial dimensions are predicted the most by those
populations in which either forest or plowland prevail. 

 

Unfortunately, any lm models using this type of data were highly
insignificant.

 

Is there possibly a way to summarize the ones with extreme proportions with
the highest grade? 

 

Best regards,

Milos

Then making a model using the index as a continuous,
independent variable.

 

Milos Blagojevic
paulidealiste@aol.com

 

-----Original Message-----
From: Seth Bigelow <seth@swbigelow.net>
To: 'Milos Blagojevic' <paulidealiste@aol.com>; r-sig-mixed-models
<r-sig-mixed-models@r-project.org>
Sent: Tue, May 7, 2013 3:39 pm
Subject: RE: [R-sig-ME] lme4 with proportion data and lack of fir otherwise

Since your dependent variable consists of proportions, you might try
summarizing it with a diversity index like the Shannon-Weaver-Wiener, i.e.,
Index = -Sum(p[i]*log(p[i])), where p[i] is the proportion of meadow,
forest, or ploughland. Then making a model using the index as a continuous,
independent variable. Since this index is a measure of 'information', and
will tend to be largest when the 3 landscape types are in even proportions,
you can even make an argument that there should be a correlation between
landscape information content, and whatever cranial dimensions you are
measuring...
 
--Seth
 
 
 
 
-----Original Message-----
From: r-sig-mixed-models-bounces@r-project.org
[mailto:r-sig-mixed-models-bounces@r-project.org
<mailto:r-sig-mixed-models-bounces@r-project.org?> ] On Behalf Of Milos
Blagojevic
Sent: Monday, May 06, 2013 6:16 AM
To: r-sig-mixed-models@r-project.org
Subject: [R-sig-ME] lme4 with proportion data and lack of fir otherwise
 
 
 
Hi all,
 
 
This is my first post on this list that is motivated by a mixed-effect
problems I experience with my data. I have a dataset with 50 cranial
measurements that was reduced by PCA to six common variables (this step may
be optional for the model). My aim is to formulate a good statistical model
using either individual PC scores or individual characters as dependent
variables. Predictors are environmental variables, population density, total
area and proportions of forest, meadow and plowland expressed as ratios that
add up to one. The last predictors are the most important for my hypotheses.
 
 
 
Since every individual has its own PC score or length value but all
environmental variables are the same for all individuals that belong to the
same population my only solution was to use a mixed-effect model that will
control for this perfect correlations in predictor variables. Random term
should thus be population and predictors should be entered into a model like
this
 
 
lmer(PC1 ~ fore * mead * plo + (1|pop), data = PCscores) where predictors
are proportions. Other predictors excluded. 
 
 
 
Anovas (car type II) report no significance in any of the model terms (I
know this is not the right way of interpreting lmer models).
 
 
I would appreciate any idea on model formulation and a possible graphic
representation of these results.  
 
 
 
This is the output
 
  
Linear mixed model fit by REML
Formula: PC1s ~ fore * mead * plo + (1 | pop) 
   Data: PCscoresLog
  AIC  BIC logLik deviance REMLdev
 2979 3023  -1480     3018    2959
Random effects:
 Groups   Name        Variance Std.Dev.
 pop      (Intercept)  3.0171  1.7370  
 Residual             11.5588  3.3998  
Number of obs: 567, groups: pop, 12
 
Fixed effects:
              Estimate Std. Error t value
(Intercept)    -55.405    147.496  -0.376
fore            45.983    146.222   0.314
mead             4.128    162.703   0.025
plo             55.533    147.743   0.376
fore:mead       98.644    187.813   0.525
fore:plo        16.972     29.573   0.574
mead:plo        71.979    128.921   0.558
fore:mead:plo -115.183    129.659  -0.888
 
Correlation of Fixed Effects:
            (Intr) fore   mead   plo    for:md for:pl med:pl
fore        -0.998                                          
mead        -0.796  0.832                                   
plo         -1.000  0.998  0.798                            
fore:mead   -0.182  0.117 -0.449  0.177                     
fore:plo    -0.065  0.066  0.223  0.059 -0.227              
mead:plo    -0.173  0.111 -0.455  0.168  0.992 -0.236       
fore:med:pl  0.236 -0.237 -0.307 -0.229  0.117 -0.887  0.10
 
 
 
Thanks in advance,
 
 
Milos Blagojevic,
Faculty Of Science,
Kragujevac,
Serbia
email: paulidealiste@aol.com
 
 
 
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