Simplex regression models with measurement error

Abstract

This paper considers the simplex regression model when there is measurement error in the covariate. We consider a structural approach where the measurement error follows a normal or gamma distribution. We apply a Monte Carlo EM algorithm to estimate the parameters using a pseudo-likelihood function. A simulation study is used to investigate the impact of ignoring the measurement error. Finally, the results are illustrated with a data set.

Keywords:

• Simplex distribution
• Gamma distribution
• Error-in-variables
• Pseudo-likelihood function
• Monte Carlo EM algorithm
• Proportion data

Acknowledgments

The authors are grateful to two anonymous referees and the Editor for very useful comments and suggestions. This work was partially supported by Conselho Nacional de Desenvolvimento Cientco e Tecnolgico (CNPq), Brazil, Programa de Apoio a Pesquisadores Emergentes - UFBA, Brazil and the Department of Statistical Sciences of the University of Toronto, Canada.

Notes

1 https://cran.r-project.org/web/packages/numDeriv/index.html