Difference between Importance(random forest) and RandomForest$importance

Question

I do not understand what is the difference between importance function (randomForest package) and importance value for a Random Forest model:

I computed a simple RF classification model and tried finding the variable importance through the following code:

 rf_model$importance
         0               1      MeanDecreaseAccuracy    MeanDecreaseGini
 X1  0.096886458    0.032546101    0.055488009             2472.172207
 X2  0.030985037    0.025615202    0.027530078             1338.378297
 X3  0.124302743    0.012551971    0.052402188             3091.891586

importance(rf_model)
            0            1      MeanDecreaseAccuracy    MeanDecreaseGini
 X1 159.9149603    175.6265625        242.424683          2472.172207
 X2 104.8273654    97.09338154        129.5084398         1338.378297
 X3 157.0207876    86.93847182        216.6374153         3091.891586

Why is there a difference between first three columns of the output while the MeanDecreaseGini is same?

Answer 1

When calling importance(rf_model) by default the measures are divided by their “standard errors”. Consider this example:

library(randomForest)
set.seed(4543)
data(mtcars)
mtcars.rf <- randomForest(mpg ~ ., data=mtcars, ntree=1000,
                          keep.forest=FALSE, importance=TRUE)

mtcars.rf$importance
#output
        %IncMSE IncNodePurity
cyl   7.3939431     162.38777
disp 10.0468306     257.46627
hp    7.6801388     200.22729
drat  1.0921653      65.96165
wt    9.7998328     250.94940
qsec  0.6066792      38.52055
vs    0.7048540      24.75183
am    0.6201962      17.27180
gear  0.4110634      16.33811
carb  1.0549523      27.47096

same as above

importance(mtcars.rf, scale = FALSE)
        %IncMSE IncNodePurity
cyl   7.3939431     162.38777
disp 10.0468306     257.46627
hp    7.6801388     200.22729
drat  1.0921653      65.96165
wt    9.7998328     250.94940
qsec  0.6066792      38.52055
vs    0.7048540      24.75183
am    0.6201962      17.27180
gear  0.4110634      16.33811
carb  1.0549523      27.47096

default: 
importance(mtcars.rf)
       %IncMSE IncNodePurity
cyl  15.767986     162.38777
disp 19.885128     257.46627
hp   18.177916     200.22729
drat  7.002942      65.96165
wt   18.479239     250.94940
qsec  5.022593      38.52055
vs    4.427525      24.75183
am    6.435329      17.27180
gear  3.968845      16.33811
carb  8.207903      27.47096

and finally:

importance(mtcars.rf, scale = FALSE)[,1]/mtcars.rf$importanceSD
      cyl      disp        hp      drat        wt      qsec        vs        am      gear      carb 
15.767986 19.885128 18.177916  7.002942 18.479239  5.022593  4.427525  6.435329  3.968845  8.207903

is same as importance(mtcars.rf)[,1]

all.equal(importance(mtcars.rf, scale = FALSE)[,1]/mtcars.rf$importanceSD,
          importance(mtcars.rf)[,1])
#output
TRUE