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Bivariate location–scale models for regression analysis, with applications to lifetime data
Author(s) -
He Wenqing,
Lawless Jerald F.
Publication year - 2005
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00488.x
Subject(s) - bivariate analysis , univariate , multivariate statistics , estimator , statistics , econometrics , regression analysis , scale (ratio) , bivariate data , linear regression , mathematics , computer science , geography , cartography
Summary. The literature on multivariate linear regression includes multivariate normal models, models that are used in survival analysis and a variety of models that are used in other areas such as econometrics. The paper considers the class of location–scale models, which includes a large proportion of the preceding models. It is shown that, for complete data, the maximum likelihood estimators for regression coefficients in a linear location–scale framework are consistent even when the joint distribution is misspecified. In addition, gains in efficiency arising from the use of a bivariate model, as opposed to separate univariate models, are studied. A major area of application for multivariate regression models is to clustered, ‘parallel’ lifetime data, so we also study the case of censored responses. Estimators of regression coefficients are no longer consistent under model misspecification, but we give simulation results that show that the bias is small in many practical situations. Gains in efficiency from bivariate models are also examined in the censored data setting. The methodology in the paper is illustrated by using lifetime data from the Diabetic Retinopathy Study.