A robust multivariate Birnbaum–Saunders regression model

This work presents a log-linear model for multivariate Birnbaum–Saunders distribution that can be used in survival analysis to investigate correlated log-lifetimes of two or more units. This model is studied through the use of a generalized multivariate sinh-normal distribution, which is built from the multivariate mixture scale of normal distributions. The marginal and conditional linear regression models of the proposed multivariate Birnbaum–Saunders linear regression model are generalizations of the Birnbaum–Saunders linear regression models of Rieck and Nedelman [A log-linear model for the Birnbaum-Saunders distribution. Technometrics. 1991;33:51–60], which have been used effectively to model lifetime and reliability data. We exploit a nice hierarchical representation of the regression model to propose a fast and accurate EM algorithm to compute the maximum likelihood estimates of the model parameters. Hypothesis testing is also performed by the use of the asymptotic normality of the maximum likelihood estimators. Finally, the results of simulation studies as well as an application to a real dataset are displayed, where we also is include a robustness feature of the estimation procedure developed here.