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Title: Free-knot splines for generalized linear models Authors:  Jing Wang - University of Illinois at Chicago (United States) [presenting]
Abstract: A computational study of bootstrap confidence bands based on a free-knot spline regression is explored for the Generalized Linear Model. In free-knot spline regression, the knot locations as additional parameters offers greater flexibility and the potential to better account for rapid shifts in slope and other important structures in the target function. However, in freeing up the knots, the search for optimal solutions becomes very complicated. In particular, the lethargy property in the objective function results in many local optima with replicate knot solutions. To prevent solutions with identical knots, a penalized Quasi-likelihood estimating equation is proposed that relies on both a Jupp transformation of knot locations and an added penalty on solutions with small minimal distances between knots. Focusing on logistic regression for binary outcome data, a parametric bootstrap is used to study the variability of the proposed estimator and to construct confidence bands for the unknown form of the logistic regression link function. A real example is also studied.