Natural Resource Management: How do I estimate the odds ratio and confidence intervals from model-averaged estimates? I'm currently working on a model selection analysis in the field of natural resource management. My research question is: what variables are important to an avian species nest site selection. My variables include: vegetation metrics collected at the nest site and landscape metrics (e.g., % mature pine) collected at larger spatial scales. My sample size is 72 nests (used) and 72 random locations where I extracted the same habitat variables. I then built 18 models in R using the GLM procedure and a logistic regression framework. I then used the information-theoretic approach (Burnham and Anderson 2002) and Akaike's Information Criteria adjusted for small sample size (AICc) to compare models. The model with the lowest AICc was considered to be the best model, and all models with AICc < 4.0 units from the best model as the best set of approximating models. The Akaike weight (wi) for each model was calculated as an estimate of the probability of the model being the most parsimonious of the developed models. I then used model-averaging using package MUMin in R to calculate parameter estimates, conditional standard errors, and variable weights of the top-performing models within 4 AICc units based on their adjusted Akaike weights (wi) (Burnham and Anderson 2002). The derived parameter estimates and associated standard errors are listed below. 


How do you calculate the odds ratio and confidence intervals given that these estimates were derived from model-averaging and the typical code exp(cbind(OR = coef(results), confint(results))will not work because this code relies on a model whereas the estimates above were derived from 4 different models. 
 A: First off, what's the nature of the outcome? You have sampled nesting sites, did you then count the number of nests at that site? Or did you systematically choose map locations and measure the presence/absence of nests? Or how have these data otherwise been coded into 0/1 outcomes? A count outcome can be handled with loglinear models.
How many nesting attributes have you considered for the analysis? Is there a notion that some measures can be combined such as "access to fresh water" being presence/absence of lakes, rivers, ponds within 0-1km, 1-5km, or 5-10km? Reducing measures like these can improve analysis.
Assuming you have an appropriate choice of model and outcome and regressors, let's return to the issue of model selection. It sounds like this question has interests in both prediction and inference. Let's focus on the inference first. What are the summaries of these variables in terms of significance levels for their wald tests? In multivariate models, significant effects for ORs tell you that the expected proportions of nests at a site differing by 1 unit in that regressor are different, holding all things 
What results do you get from a regression model controlling for all or most of the nesting site variables? (Alternately, you may consider controlling for each in a univariate model). Not that complicated prediction approaches don't have their place, but it's a little hard to trust the importance of a factor that doesn't show up in a "simpler" model.
