# Why does AIC model rank order change in lme models with standardization of predictor variables?

I can't figure this out. The AIC/AICc rank of my mixed effect models are different whether or not I standardize my predictor values using rescale.

Note, I'm not concerned that AICc is changing, as that is expected, but I am concerned that the model rank order is changing.

The standardization method being used is subtracting the mean and dividing by 2 standard deviations.

As expected, p-values and t-values do not vary between standardized and unstandardized models, just AICc, and most importantly, AICc model rank.

All variables a-k are positive continuous numeric (0-∞) and a1 and b1 are proportions with range 0-1.


# unstandardized
data_n <- data

# standardize variables
data$$k <- arm::rescale(data$$k)
data$$a <- arm::rescale(data$$a)
data$$b <- arm::rescale(data$$b)
data$$c <- arm::rescale(data$$c)
data$$d <- arm::rescale(data$$d)
data$$e <- arm::rescale(data$$e)
data$$f <- arm::rescale(data$$f)
data$$g <- arm::rescale(data$$g)
data$$a1 <- arm::rescale(data$$a1)
data$$b1 <- arm::rescale(data$$b1)


Testing AICc Rank with and without standardization

M_17 <- lme(fixed = log(y) ~ k + d + a1, data=data, random = ~ 1|Plot_No)
AICc(M_17)

##  174.8177

M_17_n <- lme(fixed = log(y) ~ k + d + a1, data=data_n, random = ~ 1|Plot_No)
AICc(M17_n)

##  184.1404


M_31 <- lme(fixed = log(y) ~ k + f + d, data=data, random = ~ 1|Plot_No)
AICc(M_31)

##  178.2103

M_31_n <- lme(fixed = log(y) ~ k + f + d, data=data_n, random = ~ 1|Plot_No)
AICc(M31_n)

##  191.7922

M_71 <- lme(fixed = log(y) ~ k + b, data=data, random = ~ 1|Plot_No)
AICc(M_71)

##  179.2528

M_71_n <- lme(fixed = log(y) ~ k + b, data=data_n, random = ~ 1|Plot_No)
AICc(M71_n)

##  190.5091


As shown, the ranking of M_31 and M_71 changes whether I use standardization or not.