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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