Fast and stable smoothing spline analysis of variance models for large samples with applications to electroencephalography data analysis

The current parameterization and algorithm used to fit a smoothing spline analysis of variance (SSANOVA) model are computationally expensive, making a generalized additive model (GAM) the preferred method for multivariate smoothing. In this thesis, I propose various approximations and algorithms to stabilize and speed-up the fitting of two-way (or higher-way) SSANOVA models. In particular, I propose (a) an efficient reparameterization of the smoothing parameters in SSANOVA models, (b) using strategically-selected knot grids instead of randomly selected knots, (c) including rounding parameters in the model, and (d) scalable algorithms for multiple-smoothing parameter selection in SSANOVA models. To validate my approximations and algorithms, I conduct three simulation studies comparing my methods to current implementations of SSANOVAs and GAMs that are available in R. The simulation results demonstrate that my approximations and algorithms can perform as well as the typical SSANOVA approximation, and can do so in a fraction of the time; furthermore, the simulation results reveal that a strategic SSANOVA can perform as well as or better than a GAM, and (using my algorithm) the strategic SSANOVA can be fit in a similar amount of time as a GAM. Finally, I present how these new approximations and algorithms make it possible to holistically analyze electroencephalography data collected during event-related potential experiments.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Psychology

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Helwig, Nathaniel

Contributors dc:contributor

• Ma, Ping
• Hubert, Lawrence J.
• Anderson, Carolyn J.
• Douglas, Jeffrey A.
• Kohn, Hans-Friedrich

• Smoothing Splines
• smoothing spline analysis of variance (SSANOVA)
• Multivariate Smoothing
• Large Sample Method
• Electroencephalography Data Analysis

Statement dc:rights

• Copyright 2013 by Nathaniel E. Helwig. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/44454

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/44454