Dear List,

I was after some advice on model selection,

I am using AIC model selection rather than P-value based stepwise regression as i feel it is more robust (Burnham & Anderson, 2002). However there seems to be a huge difference in my results.

The factors with the highest p-values , and therefore retained in the MAM, when i did an explanatory stepwise regression, do not appear in the model with the lowest AIC value - do the two approaches generally not match?

The factors retained by the MAM are theoretically what i would expect, so i am a bit surprised as to why the model with the lowest AIC doesn't contain them? I have ranked the AIC models with Akaike weights, but still the top ranked models don't incorporate the traits i would expect / retained in the MAM.

LOWEST AIC MODEL

model43 <- lmer(threatornot~1+(1|order/family) + geophyte + seasonality + pollendispersal + woodyness, family=binomial)
> model43
Generalized linear mixed model fit by the Laplace approximation 
Formula: threatornot ~ 1 + (1 | order/family) + geophyte + seasonality +      pollendispersal + woodyness 
  AIC  BIC logLik deviance
 1395 1430 -690.6     1381
Random effects:
 Groups       Name        Variance Std.Dev.
 family:order (Intercept) 0.37447  0.61194 
 order        (Intercept) 0.00000  0.00000 
Number of obs: 1116, groups: family:order, 43; order, 9

Fixed effects:
                 Estimate Std. Error z value Pr(>|z|)   
(Intercept)       0.40234    0.43237   0.931  0.35208   
geophyte2         0.06453    0.19616   0.329  0.74218   
seasonality2     -1.06900    0.34241  -3.122  0.00180 **
pollendispersal2  0.64474    0.31089   2.074  0.03809 * 
woodyness2        0.47599    0.25646   1.856  0.06346 . 

BEST STEPWISE MAM

Generalized linear mixed model fit by the Laplace approximation 
Formula: threatornot ~ 1 + (1 | order/family) + breedingsystem * fruit +      woodyness 
  AIC  BIC logLik deviance
 1409 1454 -695.3     1391
Random effects:
 Groups       Name        Variance Std.Dev.
 family:order (Intercept) 0.52475  0.7244  
 order        (Intercept) 0.00000  0.0000  
Number of obs: 1116, groups: family:order, 43; order, 9

Fixed effects:
                       Estimate Std. Error z value Pr(>|z|)  
(Intercept)             -1.1290     0.4909  -2.300   0.0215 *
breedingsystem2          0.8123     0.4756   1.708   0.0876 .
breedingsystem3          0.9449     0.5246   1.801   0.0717 .
fruit2                   1.3885     0.6221   2.232   0.0256 *
woodyness2               0.5484     0.2627   2.088   0.0368 *
breedingsystem2:fruit2  -1.6218     0.6577  -2.466   0.0137 *
breedingsystem3:fruit2  -1.6645     0.7449  -2.235   0.0255 *


The breedingsystem* fruit interaction, should, based on theory be important so why is it not in the model with the lowest AIC but is in the MAM?

I am not sure if it is because i did not set out my candidate models correctly, I did a different model for every combination of traits (2 to the power of 7) -1 as i was unsure of which models would be important. I was given the data, i didn't collect it, therefore i have to work with what i have.

Any advice would be greatly appreciated.


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