Identification of Linear Directions in Multivariate Adaptive Spline Models

Identifying linear directions in multivariate regression has been a statistical challenge and has attracted particular attention since projection pursuit was developed. To this end, we propose and investigate the use of linear discriminant analysis and projection Hessian directions in conjunction with multivariate adaptive regression splines. Simulation studies in a variety of settings demonstrate the usefulness of our approach in revealing both the functional forms and the linear substructures based on the observed data. Mathematical results are also provided to support our approach. Comparisons are made between our approach and existing approaches, and the improvements are evident. Depending on the circumstance, the extent of improvement can be substantial.

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