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Dynamic Conditionally Linear Mixed Models for Longitudinal Data
Author(s) -
Pourahmadi M.,
Daniels M. J.
Publication year - 2002
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2002.00225.x
Subject(s) - cholesky decomposition , linear model , covariance , generalized linear mixed model , random effects model , autoregressive model , mixed model , covariate , linearization , mathematics , conditional independence , covariance matrix , computer science , inference , nonlinear system , algorithm , econometrics , statistics , artificial intelligence , eigenvalues and eigenvectors , medicine , physics , meta analysis , quantum mechanics
Summary. We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within‐subject covariance matrix using a special Cholesky decomposition. Here ‘dynamic’ means using past responses as covariates and ‘conditional linearity’ means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first‐order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh‐Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited.