Multivariate Measurement Error Models Based on Student-t Distribution under Censored Responses

Larissa A. Matos
Luis M. Castro
Celso R. B. Cabral
Vı́ctor H. Lachos

Measurement error models constitute a wide class of models, that include linear and nonlinear regression models. They are very useful to model many real life phenomena, particularly inthe medical and biological areas. The great advantage of these models is that, in some sense, they can be represented as mixed effects models, allowing to us the implementation of well-known techniques, like the EM-algorithm for the parameter estimation. In this paper, we consider a class of multivariate measurement error models where the observed response and/orcovariate are not fully observed, i.e., the observations are subject to certain threshold values below or above which the measurements are not quantifiable. Consequently, these observationsare considered censored. We assume a Student-t distribution for the unobserved true values of the mismeasured covariate and the error term of the model, providing a robust alternativefor parameter estimation. Our approach relies on a likelihood-based inference using the EM-algorithm. The proposed method is illustrated through simulation studies and the analysis of a real dataset.

Censored responses
EM algorithm
Measurement error models
Student- t distribution