Dear list members,

I am analyzing data on Golden eagle productivity (PROD = number of  
chicks fledging for each eagle couple each year) to see how it is  
influenced by various meteorological factors, Nearest neighbor  
distance (NND) and reproductive success the year before (back1) and  
two years before (back2). for each nest/couple (Nterr) we have one  
PROD measure for each year of the study (about 20 years). PROD varies  
between 0 and 3.

I therefore fitted a full glmm model with family=poisson(link = "log")  
like the following:

aquile09full.lmer<-lmer(PROD~back1+back2+NND+as.factor(clas3)+neve 
+Twinter+Tprecova+Tcova+Tcrescita+Pwinter+Pprecova+Pcova+Pcrescita+(1| 
Nterr)+(1|anno),data=aquile09,family=poisson(link = "log"))

neve+Twinter+Tprecova+Tcova+Tcrescita+Pwinter+Pprecova+Pcova+Pcrescita  
are all meterological variables,
"clas3" is a categorial index of the territory quality, and "anno" is  
the year.

I then went to see the difference in AIC of removing one single  
variable from the full model. I put this variable back before removing  
the next. If the AIC of the Full model -1 increases sensibly compared  
to the full model, I keep the removed variable in the final model:

removed 	df  AIC	    BIC	    Loglik
FULL		17  255.59  316.51 -110.80
Back1  		16  268.05  326.43 -118.02
Back2	        16  266.81  325.31 -117.41
NND		16  286.48  346.58 -127.24		
clas3		15  255.87  309.62 -112.94
neve		16  254.56  311.90 -111.28
Twinter		16  254.67  312.01 -111.34
Tprecova	16  254.03  311.36 -111.01
Tcova		16  254.09  311.43 -111.05
Tcrescita	16  254.43  311.77 -111.22
Pwinter		16  254.84  312.18 -111.42
Pprecova	16  253.59  310.93 -110.80
Pcova		16  255.14  312.48 -111.57
Pcrescita	16  272.62  331.28 -120.31

I therefore refitted a final model with only the kept variables:

Generalized linear mixed model fit by the Laplace approximation
Formula: cl   Data: aquile09
    AIC   BIC logLik deviance
  246.7 271.8 -116.4    232.7
Random effects:
  Groups Name        Variance  Std.Dev.
  anno   (Intercept) 0.0056248 0.074999
  Nterr  (Intercept) 0.0324398 0.180111
Number of obs: 266, groups: anno, 24; Nterr, 22

Fixed effects:
              Estimate Std. Error
(Intercept) -1.016941   0.279004
back1       -0.067498   0.146796
back2        0.181103   0.136243
NND          0.029392   0.053093
Pcrescita    0.003070   0.003008

removed 	df AIC	   BIC	  Loglik
FULL		7  246.73  271.82 -116.37
Back1		6  257.79  279.68 -122.89
Back2		6  259.03  280.97 -123.52
NND		6  281.81  304.34 -134.91
Pcrescita	6  276.86  299.16 -132.43


I would really like to know if you think this model selection  
procedure is correct.

Thank you in advance,

best regards,

Dr. Achaz von Hardenberg

Centro Studi Fauna Alpina - Alpine Wildlife Research Centre
Servizio Sanitario e della Ricerca Scientifica
Parco Nazionale Gran Paradiso, Degioz, 11, 11010-Valsavarenche (Ao),  
Italy



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