

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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