# Calculating point estimates from model-averaged parameters

I'm using an IT-approach and multi-model inference with some count data.

I have used model averaging to obtain parameter estimates from several GLMMs with Poisson-lognormal errors (Poisson family plus observation-level random effect). Model-averaged parameter estimates are as follows:

(Intercept) 1.9522
landuse -2.0318
treatment -0.8861
hedge -0.6943
sun -0.5191
landuse:treatment 1.0529
bound.area -0.2389

I am now trying to work out point estimates from these.

Landuse is a two level factor (a and p). Treatment is a two level factor (AF and MC). Hedge, sun and bound.area are all continuous variables.

So the intercept is treatment = AF and landuse = a. I am interested in working out point estimates for:

1. treatment = AF when landuse = a
2. treatment = AF when landuse = p
3. treatment = MC when landuse = a
4. treatment = MC when landuse = p

I have Grueber et al’s 2011 paper on MMI but I am not sure whether I have correctly managed to work out how to apply their methods (detailed in the paper's appendix) to my parameter estimates. My predictors were standardised to a mean of 0 and SD of 0.5, so I understand that I have to substitute standardized predictors and then solve the model for the required estimate at the mean (i.e. 0) of all the other predictors.

So for example for a point estimate of treatment=AF when landuse=a, can I simply do exp(intercept)? [Which is the same as exp(1.9522 – 2.0318*0 - 0.8861*0 - 0.6943*0 - 0.5191*0 + 1.0529*0*0 – 0.2389*0).]

But how do I work it out for any of the other combinations? Would treatment=AF and landuse=p be worked out like this? : exp(1.9522 – 2.0318 - 0.8861*0 - 0.6943*0 - 0.5191*0 + 1.0529 – 0.2389*0)

I have a feeling I’m missing something / have misunderstood...

Finally, am I right in thinking that I can’t work out a treatment effect by itself (as it’s included in an interaction)?

Any help much appreciated.