  We propose a new algorithm called PLUTO for building logistic regression
trees to binary response data. PLUTO can capture the nonlinear and interaction
patterns in messy data by recursively partitioning the sample space. It fits a
simple or a multiple linear logistic regression model in each partition. PLUTO
employs the cyclical coordinate descent method for estimation of multiple
linear logistic regression models with elastic net penalties, which allows it
to deal with high-dimensional data efficiently. The tree structure comprises a
graphical description of the data. Together with the logistic regression
models, it provides an accurate classifier as well as a piecewise smooth
estimate of the probability of "success". PLUTO controls selection bias by: (1)
separating split variable selection from split point selection; (2) applying an
adjusted chi-squared test to find the split variable instead of exhaustive
search. A bootstrap calibration technique is employed to further correct
selection bias. Comparison on real datasets shows that on average, the multiple
linear PLUTO models predict more accurately than other algorithms.
