howeer wrote:In a set of 24 candidate models with 5 predictors of survival in a known fate analysis, I have 1 factor that shows up in all 4 models with AICc weights < 2, and has a Sum of Akaike weights = 0.76 (factor was included in 1/2 of the candidate models), so I can infer that this factor affects survival. However, I also have 2 other factors which each appear in half the models with AICc weights < 2.0, and have Sums of Akaike weights close to 0.5 (they were each included in 1/2 of the models in the candidate set). What inferences can I make about the importance of these factors based on these values? What other evidence can I use to decide whether these are significant/relevant predictors of survival?
Assessment of the relative importance of variables has often been based only on the best model (e.g., often selected using a stepwise testing procedure). Variables in that best model are considered “important,” while excluded variables are considered not important. This is too simplistic. Importance of a variable can be refined by making inference from all the models in the candidate set (see Burnham and Anderson 2002, chaps. 4–6). Akaike weights are summed for all models containing predictor variable x(j), j = 1, . . . , R; denote these sums as w_+(j ). The predictor variable with the largest predictor weight, w_+(j ), is estimated to be the most important; the variable with the smallest sum is estimated to be the least important predictor.
This procedure is superior to making inferences concerning the relative importance of variables based only on the best model. This is particularly important when the second or third best model is nearly as well supported as the best model or when all models have nearly equal support. (There are “design” considerations about the set ofmodels to consider when a goal is assessing variable importance. See Burnahm and Anderson)