title: randomForest importance measure percent MSE has different results depending on how it is called?
body: <p>I was doing something with the <code>randomForest</code> package in R and I came across the following and was wondering why it happened.</p>
  <p>If I create a random forest using the Boston housing data like so:</p>
  <pre><code>library(MASS)
  library(randomForest)
  
  data(&quot;Boston&quot;)
  
  set.seed(101) 
  rf &lt;- randomForest(medv ~ ., data = Boston, importance = TRUE)
  </code></pre>
  <p>Then if I want to take a look at the importance (specifically the percent increase in MSE) I can do this:</p>
  <pre><code>&gt; rf$importance
             %IncMSE IncNodePurity
  crim     9.1072362     2556.4934
  zn       0.6773818      269.0987
  indus    5.5466086     2372.3983
  chas     0.8297999      260.9694
  nox     11.2673993     2870.7901
  rm      35.1327635    12738.1708
  age      3.6626845     1067.3055
  dis      7.4365111     2497.2382
  rad      1.5139761      394.6151
  tax      3.9388712     1478.1129
  ptratio  7.3573333     2789.9989
  black    1.6405931      787.7995
  lstat   57.1932326    11921.4248
  </code></pre>
  <p>however, if I call the specific importance function from <code>randomForest</code> I get this:</p>
  <pre><code>&gt; randomForest::importance(rf)
            %IncMSE IncNodePurity
  crim    17.748309     2556.4934
  zn       3.333258      269.0987
  indus   11.227245     2372.3983
  chas     5.267923      260.9694
  nox     19.850569     2870.7901
  rm      36.633648    12738.1708
  age     15.084757     1067.3055
  dis     19.368978     2497.2382
  rad      6.333343      394.6151
  tax     12.125730     1478.1129
  ptratio 15.120461     2789.9989
  black    8.863837      787.7995
  lstat   30.674737    11921.4248
  </code></pre>
  <p>As you can see the results for <code>%IncMSE</code> are different. For example, when using <code>rf$importance</code> the variable <code>lstat</code> is clearly the most important variable. However, when using <code>randomForest::importance(rf)</code>, this method ranks <code>rm</code> the most important, followed closely by <code>lstat</code>.</p>
  <p>Why am I getting different results for the <code>%IncMSE</code> on the same model fit?</p>