Thanks Doug,
 
So for my results below:

The Trait + Human + Environment model fits the data best based on AIC  (only just) is it possible to estimate the contribution of each package i.e Trait contributes this much, Human this much and environmental this much?

Would i return to the models where i analysed them individually and rank them according to individual AIC values  -  Environment is the most important factor then Trait then Human? Or use delta AIC to estimate the contribution of each package - as in the method of Burnham and Anderson?

Thanks,

Chris


Model Theme	d.f	AIC
Environment	10	580.8
Human	2	585.1
Spatial	4	604.5
Trait	11	580.2
Envronment+  Spatial	14	583.1
Human + Environment	12	570.9
Human + Spatial	5	588.7
Trait + Environment	21	566.8
Trait + Human	13	561.9
Trait + Spatial	15	581.3
Human + Environment + Spatial	15	574
Trait + Environment + Spatial	25	567.2
Trait + Human + Environment	23	553.7
Trait + Human + Spatial	16	562.4
Trait + Human + Environment + Spatial	26	554.5








On 5 Apr 2011, at 14:31, Douglas Bates wrote:

On Tue, Apr 5, 2011 at 7:01 AM, Chris Mcowen <chrismcowen@gmail.com> wrote:
> Dear List,
> 
> I am relatively new to mixed models and models in general so i apologise in advance
> 
> I have a binary response, 0,1 and two random effects  A & B. I then have a range of predictor values which can be put into groups.
> 
> Biological -C,D,E,F,G,H,I,J,K
> Human - L,M,N,O,P
> Environment - Q,R,S,T,U
> Spatial - V,W,X
> 
> I am interested in asking two questions - Which predictors in each group are the most important
> 
> Biological_Model <- lmer(yesno~1+(1|A/B)+C,D,E,F,G,H,I,J,K, family=binomial)
> I have constructed a series of pre-dfinied models and compared AIC rather than using stepwise regression. I have done this for all the groups.
> 
> I am now interested, and this is where i am struggling, to investigate which of the four groups and combinations therein are most important in determining the response and how much do they each contribute?
> 
> I have tried this, based on the results from above
> 
> Biological <-cbind(C,F,G,J)
> Human <-cbind(M,N)
> Environment <- cbind(R,S,T)
> Spatial <-cbind(X)
> 
> 
> I have then run through the combinations of the groups of predictors i.e
> 
> Human_Environment_model <- lrm(yesno~Human+Environment)
> Spatial_Biological_model <- lrm(yesno~Spatial+Biological)
> 
> I have compared the r-squared values and not surprisingly the greater the number of packages the better the fit. To counter this i also calculated the AIC value of the various models, and this pretty much agrees.

For nested models (meaning that the predictors in the smaller model
are a subset of the predictors in the larger model) the larger model
should explain more of the variability, so your conclusion about the
R-squared values would hold - except that I don't know how one would
define an R-squared value for a model with a binary response.  Or, for
that matter, for a model with random effects.  You could perform some
kind of calculation related to the correlation of the fitted and
observed responses but the interpretation of the R-squared is, as far
as I know, specific to linear models assuming a Gaussian response
distribution.

Information criteria such as AIC, BIC and DIC are designed to compare
more general models and I think I would go with them or with
likelihood ratio tests for the comparisons.

> The idea was to look at how much influence these packages have - can you look at the difference in R-squared values i.e if i have a Biological model with a r-squared value of 0.2 then i add human impact and it goes up to 0.35, can i say the addition of human impact added 0.15 or is this not statistically sensible? Or would it be more sensible to use the AIC values which indicate Human & Environment describe the relationship best?
> 
> Thanks
> 
> Chris
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