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I have many predictors and therefore created a cforest and used varimp to determine the most important variable. However, it is not easy for me to interpret the results. One concrete thing I do not understand is:

I ran it several times (I also tried different values for mtry) and Predictor A is constistently ranked rather high (around 0.08), whereas Predictor B always has an importance score around 0.

However, if I crosstab the response variable with Predictor A and B respectively and run a a Fisher-exact test, I get a p-value of 0.2 for Predictor A and a p-value of 0.02 for predictor B.

I guess that significance and variable importance are different concepts, but still it seems quite counterintuitive to me that there is a significant association between Predictor B and the response, but apparently, according to the varimp-ranking, Predictor B has no impact at all.

Could you give me a hint why such a result can occur?

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It's hard to say without a concrete example as the details may depend on both the data and the variable importance measure. Possible reasons could include:

  • A cross-table between the response and a predictor assesses the marginal effect. However, in a random forest you can also capture more complex patterns involving other regressors as well.
  • Possibly, there is a good surrogate variable for B but not A among the other predictors.
  • Possibly, A has more categories than B which might be "penalized" more in a significance test compared to a variable importance measure.
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