Abstract
We propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model. In contrast to the commonly used geometric approach, we use an approach based on algebraic tools. Considerations are restricted to models with two parameters, and the general results are applied to often used special cases, including logistic, probit, double exponential and double reciprocal models for binary data, a loglinear Poisson regression model for count data, and the Michaelis-Menten model. The approach, which is also of value for multi-stage experiments, works both with constrained and unconstrained design regions and is relatively easy to implement.
Original language | English (US) |
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Pages (from-to) | 518-541 |
Number of pages | 24 |
Journal | Annals of Statistics |
Volume | 37 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2009 |
Externally published | Yes |
Keywords
- Binary response
- Count data
- Design of experiments
- Generalized linear model
- Loewner order
- Michaelis-menten model
- Multi-stage experiment
- Optimality
- Poisson model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty