I've been running an AIC in order to select variables for stepwise regression models that I have been running. The data is landscape data were parts of the landscape in 4 radii (1km, 2km, 3km and 4km) around 19 test locations have been intersected and landscape parameters such as % arable land and % forest cover have been used as variables to predict damages by a certain agricultural pest. When i run AIC on the models with the variables of different radii to see which combination have the best fit I get the same AIC on some combinations.
Ex. Damages from pest against % forest cover (4000m radius), chemical treatment (number of insecticide sprays) and % of arable land in 1000m radius
Df Sum of Sq RSS AIC
<none> 2.6991 -35.079
+ forest cover 1000m 1 0.075342 2.6237 -33.617
+ chemical treatment 1 0.015308 2.6837 -33.187
+ arable land 4000m 1 0.002589 2.6965 -33.098
[1] **20.84039**
--> AIC = 20.84039
If i change the % of arable land variable from a radius of 4000m to a radius of 3000m the AIC is the same.
Df Sum of Sq RSS AIC
<none> 2.6991 -35.079
+ forest cover 1000m 1 0.075342 2.6237 -33.617
+ chemical treatment 1 0.015308 2.6837 -33.187
+ arable land 3000m 1 0.000095 2.6989 -33.080
[1] **20.84039**
--> AIC = 20.84039
So my question is, does anyone know why the AIC is the same for these two models? Can it simply be because the variable changed ( % arable land in a 4000m radius to a 3000m radius is similar? That is, the percentage of arable land does not change too much between the two radiuses?)
Cheers.