
I have been running lmer models in R, looking at what effects reproductive success in Ground Hornbills (a South African Bird). My response variable is breeding success and is binomial (0-1) and my random effect is group ID. My response variables include rainfall, vegetation, group size, year, nests, and proportion of open woodland. 
 
I have run numerous models with success but I am confused about what the outputs are. When I run my first model with all my variables (all additive) then i get a low AIC value with only a few of the variables being significant. When i take out the varaibles that are not significant then my AIC becomes higher but I have more significant variables! When I keep taking out the unsignificant variables, I am left with a model that has nests, open woodland, and group size as being extremely significant BUT the AIC is high! Why is my AIC value increasing when I have fewer varaibles that are all significant and seem to be best explaining my data? Do i look at only the AIC when choosing the 'best' model or do I look at only the p-values? or both? The model with the lowest AIC at the moment has the most variables and most are not significant?
 
Please help. Any suggestions would be great!!

 

Here is some more information and some of my outputs:

 

The first model has all my variables included and i get a low AIC with only grp.sz and wood being significant:

 

model1<-lmer(br.su~factor(art.n)+factor(yr)+grp.sz+rain+veg+wood+(1|grp.id),data=hornbill,family=binomial)
> summary(model1)
Generalized linear mixed model fit by the Laplace approximation 
Formula: br.su ~ factor(art.n) + factor(yr) + grp.sz + rain + veg + wood +      (1 | grp.id) 
   Data: hornbill 
   AIC   BIC    logLik   deviance
 138.5 182.3  -55.26    110.5
Random effects:
 Groups Name   Variance Std.Dev.
 grp.id (Intercept) 1.2913   1.1364  
Number of obs: 169, groups: grp.id, 23
 
Fixed effects:
                  Estimate      Std. Error  z value  Pr(>|z|)    
(Intercept)      -3.930736   3.672337  -1.070    0.2845    
factor(art.n)1  1.462829   0.903328   1.619     0.1054    
factor(yr)2002 -2.592315   1.764551  -1.469   0.1418    
factor(yr)2003 -3.169365   1.759981  -1.801   0.0717 .  
factor(yr)2004  0.702210   1.341524   0.523   0.6007    
factor(yr)2005 -2.264257   1.722130  -1.315   0.1886    
factor(yr)2006  2.129728   1.270996   1.676   0.0938 .  
factor(yr)2007 -0.579961   1.390345  -0.417   0.6766    
factor(yr)2008 -1.062933   1.640774  -0.648   0.5171    
grp.sz             1.882616    0.368317   5.111   3.2e-07 ***
rain                -0.005896   0.003561  -1.656   0.0977 .  
veg                 -1.993443   1.948738  -1.023   0.3063    
wood               6.832543   3.050573   2.240   0.0251 *  
 
 
Then i carry on and remove varaibles i think are not having an influence on breeding success like the year, vegetation and rain. And i get this:
 
model3<-lmer(br.su~factor(art.n)+grp.sz+wood+(1|grp.id),data=hornbill,family=binomial)
> summary(model3)
Generalized linear mixed model fit by the Laplace approximation 
Formula: br.su ~ factor(art.n) + grp.sz + wood + (1 | grp.id) 
   Data: hornbill 
   AIC    BIC    logLik deviance
 143.8  159.4  -66.88    133.8
Random effects:
 Groups Name        Variance Std.Dev.
 grp.id (Intercept)     0.75607  0.86953 
Number of obs: 169, groups: grp.id, 23
 
Fixed effects:
                   Estimate Std. Error  z value   Pr(>|z|)    
(Intercept)      -8.6619     1.3528   -6.403   1.52e-10 ***
factor(art.n)1   1.5337     0.6420    2.389    0.0169 *  
grp.sz            1.6631     0.2968    5.604    2.09e-08 ***
wood              3.2177     1.5793    2.037   0.0416 *  
 
So all the variables are significant but the AIC value is higher!
 
I thought that with fewer variables and they are all showing significance which means they are influencing breeding success-then why is my AIC higher in this model??
Do i only look at the AIC values and ignore the p-values? or only look at the p-values??
 
Thanks!!
 
 
 		 	   		  
_________________________________________________________________


	[[alternative HTML version deleted]]


