9.4 Constant and linear response
By default, PyMC-BART will fit trees that return a single value at each leaf node. This is a simple approach that usually works just fine. However, it is important to understand its implications. For instance, this means that predictions for any value outside the range of the observed data used to fit the model will be constants. To see this, go back and check Figure 9.2. This tree will return 1.9 for any value below c1
. Notice that this will still be the case if we, instead, sum a bunch of trees, because summing a bunch of constant values results in yet another constant value.
Whether this is a problem or not is up to you and the context in which you apply the BART model. Nevertheless, PyMC-BART offers a response
argument that you pass to the BART random variable. Its default value is "constant"
. You can change it to "linear"
, in which case PyMC-BART will return a linear fit at each leaf node or "mix"
, which will propose...