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This has been bothering me for a while- when graphing the occupancy values in response to a covariate for presentation purposes, is it more "honest" to use the modeled occupancy values (so, let's say I run a model with just vegetation cover and use those occupancy estimates) OR the best model (now let's say it has veg cover, tree density, and rock cover) and then graph those occupancy estimates versus my covariate of interest (veg cover). I would only graph covariates that did well in the model selection analysis, of course, so let's assume the covariate of interest is important in predicting occupancy, but it isn't the top (univariate) model. It seems like, with the first approach, you generate a sort of trendline in response to the covariate instead of the "best" occupancy values, but sometimes that is more useful. Perhaps either approach can be justified, but I would like to hear some other thoughts- thanks!

Ekalies,
I too have had this problem/concern as this is the problem when one models in more dimensions that we can easily see. Typically, the way I have addressed this (none of which are better or worse in my mind) is either hold one/more of the covariate values at their mean value and plot the predicted response over the value of interest and then see how it changes or use a 3-dimensional plot (usually which is not a good solution as viewing is often not clear).

One alternative maybe would be to plot the prediction function as a point rather than a line plot and use the quantile values for the input data range for each predictor in unison (e.g., the 25%, 50%, 75%, value for each parameter). But, I would have to think about that some more and simulate some examples to see how it would look.

Sorry not more help,

Bret