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Random Effects Distribution (random + effects_distribution)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Smooth Random Effects Distribution in a Linear Mixed Model

BIOMETRICS, Issue 4 2004
Wendimagegn Ghidey
Summary A linear mixed model with a smooth random effects density is proposed. A similar approach to P -spline smoothing of Eilers and Marx (1996, Statistical Science11, 89,121) is applied to yield a more flexible estimate of the random effects density. Our approach differs from theirs in that the B -spline basis functions are replaced by approximating Gaussian densities. Fitting the model involves maximizing a penalized marginal likelihood. The best penalty parameters minimize Akaike's Information Criterion employing Gray's (1992, Journal of the American Statistical Association87, 942,951) results. Although our method is applicable to any dimensions of the random effects structure, in this article the two-dimensional case is explored. Our methodology is conceptually simple, and it is relatively easy to fit in practice and is applied to the cholesterol data first analyzed by Zhang and Davidian (2001, Biometrics57, 795,802). A simulation study shows that our approach yields almost unbiased estimates of the regression and the smoothing parameters in small sample settings. Consistency of the estimates is shown in a particular case. [source]

Two-part regression models for longitudinal zero-inflated count data

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2010
Marco Alfò
Abstract Two-part models are quite well established in the economic literature, since they resemble accurately a principal-agent type model, where homogeneous, observable, counted outcomes are subject to a (prior, exogenous) selection choice. The first decision can be represented by a binary choice model, modeled using a probit or a logit link; the second can be analyzed through a truncated discrete distribution such as a truncated Poisson, negative binomial, and so on. Only recently, a particular attention has been devoted to the extension of two-part models to handle longitudinal data. The authors discuss a semi-parametric estimation method for dynamic two-part models and propose a comparison with other, well-established alternatives. Heterogeneity sources that influence the first level decision process, that is, the decision to use a certain service, are assumed to influence also the (truncated) distribution of the positive outcomes. Estimation is carried out through an EM algorithm without parametric assumptions on the random effects distribution. Furthermore, the authors investigate the extension of the finite mixture representation to allow for unobservable transition between components in each of these parts. The proposed models are discussed using empirical as well as simulated data. The Canadian Journal of Statistics 38: 197,216; 2010 © 2010 Statistical Society of Canada Les modèles en deux parties sont bien établis dans la littérature économique puisqu'ils sont très similaires à un modèle principal-agent pour lequel les résultats homogènes, observables et dénombrables sont sujets à un critère de sélection (exogène et a priori). La première décision est représentée à l'aide un modèle de choix binaire et une fonction de lien probit ou logit tandis que la seconde peut être analysée à l'aide d'une loi discrète tronquée telle que la loi de Poisson tronquée, la loi binomiale négative, etc. Depuis peu, une attention particulière a été portée à la généralisation du modèle en deux parties pour prendre en compte les données longitudinales. Les auteurs présentent une méthode d'estimation semi-paramétrique pour les modèles en deux parties dynamiques et ils les comparent avec d'autres modèles alternatifs bien connus. Les sources hétérogènes qui influencent le premier niveau du processus de décision, c'est-à-dire la décision d'utiliser un certain service, sont censées influencer aussi la distribution (tronquée) des résultats positifs. L'estimation est faite à l'aide de l'algorithme EM sans présupposés paramétriques sur la distribution des effets aléatoires. De plus, les auteurs considèrent une généralisation à une représentation en mélange fini afin de permettre une transition non observable entre les différentes composantes de chacune des parties. Une discussion est faite sur les modèles présentés en utilisant des données empiriques ou simulées. La revue canadienne de statistique 38: 197,216; 2010 © 2010 Société statistique du Canada [source]

A SEMIPARAMETRIC BAYESIAN APPROACH TO MULTIVARIATE LONGITUDINAL DATA

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2010
Pulak Ghosh
Summary We extend the standard multivariate mixed model by incorporating a smooth time effect and relaxing distributional assumptions. We propose a semiparametric Bayesian approach to multivariate longitudinal data using a mixture of Polya trees prior distribution. Usually, the distribution of random effects in a longitudinal data model is assumed to be Gaussian. However, the normality assumption may be suspect, particularly if the estimated longitudinal trajectory parameters exhibit multi-modality and skewness. In this paper we propose a mixture of Polya trees prior density to address the limitations of the parametric random effects distribution. We illustrate the methodology by analysing data from a recent HIV-AIDS study. [source]

A Semi-Parametric Shared Parameter Model to Handle Nonmonotone Nonignorable Missingness

BIOMETRICS, Issue 1 2009
Roula Tsonaka
Summary Longitudinal studies often generate incomplete response patterns according to a missing not at random mechanism. Shared parameter models provide an appealing framework for the joint modelling of the measurement and missingness processes, especially in the nonmonotone missingness case, and assume a set of random effects to induce the interdependence. Parametric assumptions are typically made for the random effects distribution, violation of which leads to model misspecification with a potential effect on the parameter estimates and standard errors. In this article we avoid any parametric assumption for the random effects distribution and leave it completely unspecified. The estimation of the model is then made using a semi-parametric maximum likelihood method. Our proposal is illustrated on a randomized longitudinal study on patients with rheumatoid arthritis exhibiting nonmonotone missingness. [source]