English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In discrete choice experiments, the information matrix depends on the modelparameters. Therefore, $ D $-optimal designs are only locally optimal in theparameter space. This dependence renders the optimization problem verydifficult, as standard theory encodes $ D $-optimality in systems of highlynonlinear equations and inequalities. In this work, we connect design theoryfor discrete choice experiments with Laplacian matrices of connected graphs. Werewrite the $ D $-optimality criterion in terms of Laplacians via Kirchhoff'smatrix tree theorem, and show that its dual has a simple description via theCayley--Menger determinant of the Farris transform of the Laplacian matrix.This results in a drastic reduction of complexity and allows us to implement agradient descent algorithm to find locally $ D $-optimal designs. For thesubclass of Bradley--Terry paired comparison models, we find a direct link tomaximum likelihood estimation for Laplacian-constrained Gaussian graphicalmodels. This implies that every locally $ D $-optimal design is a rationalfunction in the parameter when the design is supported on a chordal graph.Finally, we study the performance of our algorithm and demonstrate itsapplication on real and simulated data.

Optimal designs for discrete choice models via graph Laplacians