Elsevier

Journal of Multivariate Analysis

Volume 124, February 2014, Pages 57-69
Journal of Multivariate Analysis

D-optimal designs for multiresponse linear models with a qualitative factor

https://doi.org/10.1016/j.jmva.2013.10.011Get rights and content
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Highlights

  • Determinant of information matrix of a product design is separated into two parts.

  • The optimal marginal design is uniform on the index set of the qualitative levels.

  • D-optimal design for a hierarchically ordered system of multiresponses is given.

Abstract

Consider a linear regression model with both quantitative and qualitative factors and an k-dimensional response variable y whose components are equicorrelated for each observation. The D-optimal design problem is investigated when the levels of the qualitative factor interact with the quantitative factors. It is shown that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. It is also shown that for the hierarchically ordered system of regression models, the D-optimal design does not depend on the covariance matrix of y.

AMS subject classifications

62H99
62K05

Keywords

D-optimal designs
Multiresponse linear models
Qualitative factors

Cited by (0)

This work was partially supported by NSFC grant (11071168, 11101077), Special Funds for Doctoral Authorities of Education Ministry (20103127110002), Innovation Program of Shanghai Municipal Education Commission (11zz116), E-Institutes of Shanghai Municipal Education Commission (E03004), Shanghai Leading Academic Discipline Project, the Fundamental Research Funds for the Central Universities.