Fig. 4

Non-linear dependencies: party vs. permimp implementation. Data sets were sampled with five, nine or seventeen uniformly distributed (min = -3, max = 3) predictors. An additional predictor was created by squaring one of the uniform predictors, so that all but two predictors were independent, and two showed a perfect quadratic relation. This resulted in two quadratically related predictors plus either four, eight or sixteen independent predictors. Sample size was either N=500,1000, or 2500, and either no, half or all the predictors had a linear impact on the continuous outcome variable. The dependence tests within the party and the permimp implementation (i.e., a χ²-test based on the tree-growing split points) were applied only to the two predictors with the perfect quadratic relation. The proportion of p-values lower than.05 within the party and permimp implementation are indicated in blue and pink respectively. The dashed line corresponds to a proportion of.05