Estimating Binary Monotonic Regression Models and Their Uncertainty by Incorporating Kernel Smoothers

Monotonic regression (MR) is a method that is used for fitting a model to multivariate data in which a response is increasing or decreasing with respect to several explanatory variables. Recently, MR methods were substantially improved, and a group of algorithms can now produce monotonic fits to multivariate datasets containing over a million observations. It is demonstrated here that the accuracy of the monotonic fits produced by these algorithms is unacceptable when the response variable is binary, and kernel smoothers are incorporated into these algorithms to increase the accuracy. A standard approach for estimating confidence limits for the models obtained by these algorithms is to use a resampling technique that applies the same modeling algorithm to each of the numerous bootstrap sets. However, the computational complexity of this approach becomes prohibitively large in the large-scale MR setting. Here, the standard resampling approach is modified to estimate confidence limits efficiently.