JSM 2005 - Toronto

Abstract #302895

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 219
Type: Topic Contributed
Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #302895
Title: Quantile Dispersion Graphs for Comparing Designs for Multivariate Generalized Linear Models
Author(s): Siuli Mukhopadhyay*+ and André I. Khuri
Companies: University of Florida and University of Florida
Address: Department of Statistics, Gainesville, FL, 32611-8545, United States
Keywords: quantile dispersion graphs ; multiresponse ; generalized linear models ; E-optimality ; mean-squared error of prediction
Abstract:

In this paper, we use the method of quantile dispersion graphs (QDGs) to compare multiresponse designs for generalized linear models (GLMs). Designs for fitting a GLM depend on the unknown parameters of the model. Thus, the use of any design optimality criterion would require prior knowledge of the parameters. The criterion chosen here is similar to E-optimality in linear models, namely the minimization of the maximum eigenvalue of the mean-squared error of prediction (MSEP) matrix. The QDGs for comparing multiresponse designs for GLMs are based on this criterion. Quantiles of the maximum eigenvalue of the MSEP are obtained on concentric surfaces inside a region of interest, $R$. For a given design, these quantiles depend on the model's parameters. Plots of the maxima and minima of the quantiles, over a subset of the parameter space, produce the quantile dispersion graphs. The plots provide a comprehensive assessment of the overall prediction capability of the design within the region $R$. They also depict the dependence of the design on the model's unknown parameters.

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