Linear Mixed-effects Models for Censored Data with Serial Correlation Errors Using the Multivariate Student’s t-distribution

Zhong, Kelin; Olivari, Rommy C.; Garay, Aldo M.; Lachos, Víctor H.

doi:10.51387/24-NEJSDS68

The New England Journal of Statistics in Data Science

Linear Mixed-effects Models for Censored Data with Serial Correlation Errors Using the Multivariate Student’s t-distribution

Kelin Zhong Rommy C. Olivari Aldo M. Garay All authors (4)

https://doi.org/10.51387/24-NEJSDS68

Pub. online: 30 July 2024 Type: Statistical Methodology

Open Access

Accepted
6 July 2024

Published
30 July 2024

Abstract

The purpose of this paper is to develop a practical framework for the analysis of the linear mixed-effects models for censored or missing data with serial correlation errors, using the multivariate Student’s t-distribution, being a flexible alternative to the use of the corresponding normal distribution. We propose an efficient ECM algorithm for computing the maximum likelihood estimates for these models with standard errors of the fixed effects and likelihood function as a by-product. This algorithm uses closed-form expressions at the E-step, which relies on formulas for the mean and variance of a truncated multivariate Student’s t-distribution. In order to illustrate the usefulness of the proposed new methodology, artificial and a real dataset are analyzed. The proposed algorithm and methods are implemented in the R package ARpLMEC.

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Keywords

AR(p) models Censored data Damped exponential correlation EM algorithm Linear mixed effects models Student’s t-distribution

Funding

The research of Aldo M. Garay was supported by Grant APQ-0950-1.02/22 from Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco FACEPE - Brazil and by Grant 441476/2023-6 from National Council for Scientific and Technological Development – CNPq – Brazil. Victor H. Lachos acknowledges the partial financial support from the Office of the Vice President for Research and UConn - CLAS’s Summer Research Funding Initiative 2023.

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