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I am doing occupancy analysis for mammals using data derived from camera traps. I've fit the model using Rmark, dredged for the p covariates by fixing psi covariates, then performed model averaging to determine which p covariates I should keep. the results for the full averaged model gives me this relative variable importance:

Relative variable importance: 
                     Psi(Phase) p(WeekDay) p(Trail) Psi(Zone) p(DetectionDist) Psi(Phase:Zone)
Importance:          0.53       0.47       0.38     0.34      0.28             0.01           
N containing models:   24         20         19       24        20                8  

Is there a rule of thumb about what the importance should be for those covariates which I should discard? To me, it looks like all the p covariates should be retained but the Psi covariate of (Phase:Zone) should be discarded, although I dont know if I can make this assumption since this was dredged fixing the psi covariates. Thoughts?

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I'm not sure the "importance" is that useful when model averaging. What if your co-variates occur in few models, but those models were the best ones?

Why don't you look at the AIC scores of the models - you could calculate Akaike weights based on these scores. Multiply the coefficients for each co-variate by the Akaike weight, and then sum those products to give a model-averaged coefficient for each co-variate. You could then keep all of them in your model, or calculate confidence intervals to see if each of them is significant or not (i.e. do the confidence intervals cross zero).

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