Multi-level qualitative (fixed-effects) factors

Hi David and Ben, thanks for your help -

I was worried this would make little sense!

I have set out my candidate models

A+B+C+D
B+C+D
A+C+D
etc etc

And am running through them in lmer. Factor A for instance is Habit, which takes 3 forms - aquatic, terrestrial or epiphyte.

When i run the model with A as a factor i get the breakdown of the individual levels habitat 1, habitat 2 and habitat 3 and a corresponding AIC score. However if i just run it with habitat 3 - aquatic - i get a lower AIC score, therefore the model fits the data better?

I am unsure how to, without splitting my factors into their constituent levels at the beginning - A1+A2+A3 + B1 + B2 etc, arrive at the model with the lowest AIC?

Thanks

Peter

On 3 Aug 2010, at 00:16, David Duffy wrote:

On Mon, 2 Aug 2010, Peter Francis wrote:

I have many multi level factors i.e habit - aquatic, terrestrial, epiphyte etc

I ran the model with habit as a factor

model111 <-lmer(threatornot~1+(1|a/b) + habit, family=binomial)

Generalized linear mixed model fit by the Laplace approximation
Formula: threatornot ~ 1 + (1 | order/family) + habit
?AIC ?BIC logLik deviance
1406 1436 -696.9 ? ? 1394
Random effects:
Groups ? ? ? Name ? ? ? ?Variance ? Std.Dev.
family:order (Intercept) 6.9892e-01 8.3602e-01
order ? ? ? ?(Intercept) 4.2292e-14 2.0565e-07
Number of obs: 1116, groups: family:order, 43; order, 9

Fixed effects:
? ? ? ? ? ?Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.04803 ? ?0.19174 ?-0.250 ?0.80219
habit2 ? ? ? 1.10627 ? ?0.41607 ? 2.659 ?0.00784 **
habit3 ? ? ? 0.92578 ? ?0.78141 ? 1.185 ?0.23611
habit4 ? ? ? 0.14383 ? ?0.38477 ? 0.374 ?0.70856

---
Which had a AIC of 1406

I then re-ran the model with only aquatic and got a lower AIC value - which i guess is to be expected as aquatic is highly significant and aquatic species are more prone to threat ( my response).

model112 <-lmer(threatornot~1+(1|a/b) + aquatic, family=binomial)
model112

Generalized linear mixed model fit by the Laplace approximation
Formula: threatornot ~ 1 + (1 | order/family) + aquatic
?AIC ?BIC logLik deviance
1395 1415 -693.4 ? ? 1387
Random effects:
Groups ? ? ? Name ? ? ? ?Variance Std.Dev.
family:order (Intercept) 0.60007 ?0.77464
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) ? 0.1572 ? ? 0.1827 ? 0.860 0.389613
aquatic ? ? ?-0.6683 ? ? 0.1737 ?-3.847 0.000119 ***

My question is - when i developed the candidate models i thought using multilevel factors would be OK and i would be able to tease out the individual levels. If i split the factors into levels from the beginning then i am left with a huge amount of candidate models? This would not be a problem in stepwise regression as i could just remove the habit with the least significant P Value.

If i remove habits i "feel" are unimportant from the beginning i feel i would be limiting the model too much.

I hope this makes sense!

I don't understand at all, I'm afraid. ?Is aquatic the same as habit=2, or something? ?If so, there is something funny about the model fits.

If family and order are "nuisance" variables, then a stepwise approach is quite reasonable (if you are someone who thinks stepwise regression is reasonable, of course ;)).

Just 2c, David Duffy.

--
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