Inference in multivariate regression models with measurement errors

Abstract

Multivariate regression models are helpful in many fields. However, independent variables (covariates or predictors) could be measured with error. That implies the necessity of considering a new kind of model called Multivariate Regression Models with Measurement Error (MRMMEs). This paper aims to carry out a statistical analysis of these models. We include estimation, hypothesis testing, model assessment, and influence diagnostics. Furthermore, besides considering the classical assumption of the normal distribution, we use maximum likelihood for the whole inference process. Finally, we study the developed approach's performance through simulation experiments and re-analyze the human lung function dataset presented in the literature to illustrate the methodology.

Keywords:

• EM algorithm
• information matrix
• hypothesis testing
• influence diagnostics
• measurement errors

Disclosure statement

The authors report there are no competing interests to declare.

Additional information

Funding

The first author was funded by Agencia Nacional de Investigación y Desarrollo - ANID, under Doctorado Nacional grant 2018/21181064.