Dear ECOLOG: I think there was an important aspect of Dr. Bigelow's quote from Burnham and Anderson (2002) page 131 that was not highlighted.
THe passage quoted was: "Models having delta-I within 0-2 units of the best model should be examined to see whether they differ from the best model by 1 parameter...in this case, the larger model is not really supported or competitive, but rather is close only because it adds 1 parameter..." As I understand it, this is a means for distinguishing between between two models when one of the models has a higher dAIC and more parameters. However, if a model with the lowest AIC (dAIC = 0) has more parameters than a second model with dAIC<2, the second model cannot be considered to be better than the first on the basis of parsimony. This is because the addition of more parameters to the first model is improving fit and lowering the AIC despite the penalty more parameters incurs. Is this true? Below is an example I sketched out: Say you have four models with wither 2 or three parameters. Model deltaAIC #1 response = B1(x) + B2(y) + B3(z) 0 #2 response = B1(x) + B2(y) 1.2 #3 response = B1(x) + B2(y) + B3(u) 1.8 #4 response = B1(u) + B3(v) + B3(w) 4 First, I believe this is the situation that kicked off this thread on AIC: Two models, the one with the lowest AIC has more parameters, the second with dAIC <2 #1 response = B1(x) + B2(y) + B3(z) 0 #2 response = B1(x) + B2(y) 1.2 So, between #1 and #2, one should not conclude the #2 is better simply because it has fewer parameters. The addition of the third parameters to model #1 improves the fit of the model and has a lower AIC DESPITE the penalty for adding another parameter. Second, two models, the one with higher AIC also has more parameters #2 response = B1(x) + B2(y) 1.2 #3 response = B1(x) + B2(y) + B3(u) 1.8 Here, #2 and #3 both have dAIC <2, but #3 has more parameters. Therefore, model #2 can be favored b/c it is more parsimonious Third, #1 response = B1(x) + B2(y) + B3(z) 0 #3 response = B1(x) + B2(y) + B3(u) 1.8 Here, #1 and #3 have the same number of parameters and are within 2 dAIC units. These models, I believe should be considered equivalent. Finally My question: what do you do if you have all three models under consideration? #1 response = B1(x) + B2(y) + B3(z) 0 #2 response = B1(x) + B2(y) 1.2 #3 response = B1(x) + B2(y) + B3(u) 1.8 Nathan
