Back To Index Previous Article Next Article Full Text


Statistica Sinica 22 (2012), 1765-1786

doi:http://dx.doi.org/10.5705/ss.2010.261





ON LOCALLY OPTIMAL DESIGNS FOR GENERALIZED

LINEAR MODELS WITH GROUP EFFECTS


John Stufken and Min Yang


University of Georgia and University of Illinois at Chicago


Abstract: Generalized linear models with group effects are commonly used in scientific studies. However, there appear to be no results for selecting optimal designs. In this paper, we identify the structure of locally optimal designs, provide a general strategy to determine the design points and the corresponding weights for optimal designs, and present theoretical results for the special case of $D$-optimality. The results can be applied to many commonly studied models, including the logistic, probit, and loglinear models. The design region can be restricted or unrestricted, and the results can also be applied for a multi-stage approach.



Key words and phrases: A-optimality, binary response, D-optimality, Loewner ordering, logistic model, loglinear model, probit model.





Kuan-Chieh Huang 2012-08-18