Many variable selection techniques have been developed that focus on first-order linear regression models. In some applications, such as modeling response surfaces, fitting second-order terms can improve predictive accuracy. However, the number of spurious interactions can be large leading to poor results with many methods. We focus on forward selection, describing algorithms that use the natural hierarchy existing in second-order linear regression models to limit spurious interactions. We then develop stopping rules by extending False Selection Rate methodology to these algorithms. In addition, we describe alternative estimation methods for fitting regression models including the LASSO, CART, and MARS. We also propose a general method for controlling multiple-group false selection rates, which we apply to second-order linear regression models. By estimating a separate entry level for first-order and second-order terms, we obtain equal contributions to the false selection rate from each group. We compare the methods via Monte Carlo simulation and apply them to optimizing response surface experimental designs.
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-04282008-151809 |
| Date | 13 May 2008 |
| Creators | Crews, Hugh Bates |
| Contributors | Howard Bondell, Jason Osborne, Dennis Boos, Leonard Stefanski |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-04282008-151809/ |
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