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Tweedie family of generalized linear models with distribution‐free random effects for skewed longitudinal data
Author(s) -
Ma Renjun,
Yan Guohua,
Hasan M. Tariqul
Publication year - 2018
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7841
Subject(s) - random effects model , skewness , generalized linear mixed model , covariance , mathematics , econometrics , linear model , mixed model , statistics , flexibility (engineering) , population , computer science , medicine , meta analysis , environmental health
Generalized linear mixed models have played an important role in the analysis of longitudinal data; however, traditional approaches have limited flexibility in accommodating skewness and complex correlation structures. In addition, the existing estimation approaches generally rely heavily on the specifications of random effects distributions; therefore, the corresponding inferences are sometimes sensitive to the choice of random effect distributions under certain circumstance. In this paper, we incorporate serially dependent distribution‐free random effects into Tweedie generalized linear models to accommodate a wide range of skewness and covariance structures for discrete and continuous longitudinal data. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects. Our approach unifies population‐averaged and subject‐specific inferences. Our method is illustrated through the analyses of patient‐controlled analgesia data and Framingham cholesterol data.