4 research outputs found
Optimal discrimination designs
We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular T-optimality criterion are derived, which in many circumstances allow an explicit determination of T-optimal designs. It is also demonstrated, that in nested linear models the number of support points of T-optimal designs is usually too small to estimate all parameters in the extended model. In many cases T-optimal designs are usually not unique, and we give a characterization of all T-optimal designs. Finally, T-optimal designs are compared with optimal discriminating designs with respect to alternative criteria by means of a small simulation study. --Model discrimination,optimal design,T-optimality,Ds-optimality,nonlinear approximation
Optimal discrimination designs
We consider the problem of constructing optimal designs for model
discrimination between competing regression models. Various new properties of
optimal designs with respect to the popular -optimality criterion are
derived, which in many circumstances allow an explicit determination of
-optimal designs. It is also demonstrated, that in nested linear models the
number of support points of -optimal designs is usually too small to
estimate all parameters in the extended model. In many cases -optimal
designs are usually not unique, and in this situation we give a
characterization of all -optimal designs. Finally, -optimal designs are
compared with optimal discriminating designs with respect to alternative
criteria by means of a small simulation study.Comment: Published in at http://dx.doi.org/10.1214/08-AOS635 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Model identification for dose response signal detection
We consider the problem of detecting a dose response signal if several competing
regression models are available to describe the dose response relationship. In particular,
we re-analyze the MCP-Mod approach from Bretz et al. (2005), which has become a
very popular tool for this problem in recent years. We propose an improvement based
on likelihood ratio tests and prove that in linear models this approach is always at least
as powerful as the MCP-Mod method. This result remains valid in nonlinear regression
models with identi able parameters. However, for many commonly used nonlinear dose
response models the regression parameters are not identi able and standard likelihood
ratio test theory is not applicable. We thus derive the asymptotic distribution of
likelihood ratio tests in regression models with a lack of identifiability and use this
result to simulate the quantiles based on Gaussian processes. The new method is
illustrated with a real data example and compared to the MCP-Mod procedure using
theoretical investigations as well as simulations
Likelihood-Quotiententests zur Modellidentifikation
Die Grundlage dieser Arbeit bildet die Modellwahl, ein von vielen Autoren untersuchtes Teilgebiet der Regressionsanalyse. Aus einer gegebenen Klasse von Regressionsmodellen soll mit Hilfe statistischer Testverfahren dasjenige Modell ausgewählt werden, das einen vorliegenden Datensatz am geeignetsten beschreibt. Es werden zwei Testverfahren vorgestellt, der sogenannte Kontrasttest und der Likelihood-Quotiententest, wobei letzterer im Vordergrund der Untersuchungen steht. Insbesondere wird das asymptotische Verhalten der Likelihood-Quotiententeststatistik für den Fall untersucht, dass unter Gültigkeit der Nullhypothese einige Modellparameter nicht identifizierbar sind. Für beide Testverfahren werden die Eigenschaften zur Modelldiskriminierung erarbeitet und sowohl theoretisch als auch abschließend innerhalb einer Simulationsstudie miteinander verglichen