Statistics and Data Science Seminar
Timothy E. O'Brien
Loyola University
Curvature, Robustness and Optimal Design in Applied Generalized Nonlinear Regression Modelling
Abstract: Researchers often find that nonlinear regression models are more applicable for
modelling various biological, physical and chemical processes than are linear ones since
they tend to fit the data well and since these models (and model parameters) are more
scientifically meaningful. These researchers are thus often in a position of requiring
optimal or near-optimal designs for a given nonlinear model. A common shortcoming of
most optimal designs for nonlinear models used in practical settings, however, is that
these designs typically focus only on (first-order) parameter variance or predicted
variance, and thus ignore the inherent nonlinear of the assumed model function.
Another shortcoming of optimal designs is that they often have only p support points,
where p is the number of model parameters.
Measures of marginal curvature, first introduced in Clarke (1987) and further developed
in Haines et al (2004), provide a useful means of assessing this nonlinearity. Other
relevant developments are the second-order volume design criterion introduced in
Hamilton and Watts (1985) and extended in O'Brien (1992, 2010), and the second-order
MSE criterion developed and illustrated in Clarke and Haines (1995).
This talk examines various robust design criteria and those based on second-order
(curvature) considerations. These techniques, coded in the GAUSS and SAS/IML
software packages, are illustrated with several examples including one from a preclinical
dose-response setting encountered in a recent consulting session.
Wednesday September 29, 2010 at 3:00 PM in SEO 636