Journal ArticleDOI
Mixtures of marginal models
TLDR
A mixture model originally developed for regression models with independent data for the more general case of correlated outcome data, which includes longitudinal data as a special case is adapted, and the systematic component of this mixture of marginal models is more flexible than the conventional linear function.Abstract:
SUMMARY In this paper, we adapt a mixture model originally developed for regression models with independent data for the more general case of correlated outcome data, which includes longitudinal data as a special case. The estimation is performed by a generalisation of the EM algorithm which we call the Expectation-Solution (Es) algorithm. In this ES algorithm the M-step of the EM algorithm is replaced by a step requiring the solution of a series of generalised estimating equations. The ES algorithm, a general algorithm for solving generalised estimating equations with incomplete data, is then applied to the present problem of mixtures of marginal models. In addition to allowing for correlation inherent in correlated outcome data, the systematic component of this mixture of marginal models is more flexible than the conventional linear function. The methodology is applied in the contexts of normal and Poisson response data. Some theory regarding the ES algorithm is presented.read more
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References
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Journal ArticleDOI
Longitudinal data analysis using generalized linear models
Kung Yee Liang,Scott L. Zeger +1 more
TL;DR: In this article, an extension of generalized linear models to the analysis of longitudinal data is proposed, which gives consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence.
Book
Analysis of longitudinal data
TL;DR: In this paper, a generalized linear model for longitudinal data and transition models for categorical data are presented. But the model is not suitable for categric data and time dependent covariates are not considered.
Journal ArticleDOI
Longitudinal data analysis for discrete and continuous outcomes.
Scott L. Zeger,Kung-Yee Liang +1 more
TL;DR: A class of generalized estimating equations (GEEs) for the regression parameters is proposed, extensions of those used in quasi-likelihood methods which have solutions which are consistent and asymptotically Gaussian even when the time dependence is misspecified as the authors often expect.
Journal ArticleDOI
Adaptive mixtures of local experts
TL;DR: A new supervised learning procedure for systems composed of many separate networks, each of which learns to handle a subset of the complete set of training cases, which is demonstrated to be able to be solved by a very simple expert network.
Journal ArticleDOI
Approximate inference in generalized linear mixed models
Norman E. Breslow,D. G. Clayton +1 more
TL;DR: In this paper, generalized linear mixed models (GLMM) are used to estimate the marginal quasi-likelihood for the mean parameters and the conditional variance for the variances, and the dispersion matrix is specified in terms of a rank deficient inverse covariance matrix.