# AIC model selection when successive models have ΔAIC <2 compared to next best model

I have a set of linear mixed effects models with which I'm changing fixed effects, and comparing AIC for model selection. Something akin to this hypothetical model set. Sample is ~750 observations so not using AICc.

M0 <- lmer( y ~ x + (1|p) + (1|q/r), data = my.data, REML = FALSE )
M1 <- lmer( y ~ x + y + (1|p) + (1|q/r), data = my.data, REML = FALSE )
M2 <- lmer( y ~ x + z + (1|p) + (1|q/r),  data = my.data, REML = FALSE )
M3 <- lmer( y ~ x + y + z + (1|p) + (1|q/r), data = my.data, REML = FALSE )


When I check the AIC for model selection, the models progressively become a better fit with the data set, with AIC values progressively decreasing in the model set, similar to this.

AIC(MO)
[1] 166.3
AIC(M1)
[1] 165.1
AIC(M2)
[1] 163.4
AIC(M3)
[1] 161.8


According to the general rule applied, two models with ΔAIC <2 are statistically indistinguishable and there is not enough evidence to select a single model over the other.

However, in a situation such as this, where there is ΔAIC >2 between best and worst fitting models, but there is ΔAIC <2 between each model and the next best fitting model, what would be the correct interpretation of AIC values? What would be the appropriate model selection, if any?

One way of thinking about this is to consider model averaging with AIC based weights proportional to $\exp(-AIC/2)$, which would be normalized to sum to 1.