[R] Graphic representation of model results

[Guillaume Brutel]

Dear list members,

I am facing difficulties in making a graphics that could show visually 
results of a model.

I have tested the effects of 4 quantitative variables (Z1, Z2, Z3, Z4) 
on a variable Y using a weighted mixed effects GLM with weights W (using 
the glmmPQL function). I applied a blocking approach using factor F2 
nested in factor F1 as a grouping structure on a random intercept in the 
GLMM . The fixed effect are the 4 independent variables simultaneously 
fitted in the inferential model (Z1, ..., Z4).

Three out of the four variables have a significant effect on Y (Z1, Z2, Z3).

My problem is that I want to show graphically my results. If I plot Y 
according to the Z1, this won't take into account the effect of e.g. Z2 
and the fact that the analysis was weighted by W (same with adding a 
weighted lowess). If I add a regression line with the estimate for Z1 
obtained from the weighted mixed effect GLM, this doesn't not properly 
reflect the analysis (since they were obtained with simultaneously 
fitting Z2 and Z3). Making various 3D figures don't help because the 
various plots are too difficult to read.

Any advice (about the conceptual way of making the figure and the 
function(s) that can be used) is welcome.
Thank you very much,
Regards,

Guillaume Brutel.