[R-sig-ME] lme4 with proportion data and lack of fir otherwise

[Seth Bigelow]

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 at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Milos
Blagojevic
Sent: Monday, May 06, 2013 6:16 AM
To: r-sig-mixed-models at 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 at aol.com



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