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Association Parameters (association + parameter)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

AN EVALUATION OF NON-ITERATIVE METHODS FOR ESTIMATING THE LINEAR-BY-LINEAR PARAMETER OF ORDINAL LOG-LINEAR MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2009
Eric J. Beh
Summary Parameter estimation for association and log-linear models is an important aspect of the analysis of cross-classified categorical data. Classically, iterative procedures, including Newton's method and iterative scaling, have typically been used to calculate the maximum likelihood estimates of these parameters. An important special case occurs when the categorical variables are ordinal and this has received a considerable amount of attention for more than 20 years. This is because models for such cases involve the estimation of a parameter that quantifies the linear-by-linear association and is directly linked with the natural logarithm of the common odds ratio. The past five years has seen the development of non-iterative procedures for estimating the linear-by-linear parameter for ordinal log-linear models. Such procedures have been shown to lead to numerically equivalent estimates when compared with iterative, maximum likelihood estimates. Such procedures also enable the researcher to avoid some of the computational difficulties that commonly arise with iterative algorithms. This paper investigates and evaluates the performance of three non-iterative procedures for estimating this parameter by considering 14 contingency tables that have appeared in the statistical and allied literature. The estimation of the standard error of the association parameter is also considered. [source]

Genetic association tests in the presence of epistasis or gene-environment interaction

GENETIC EPIDEMIOLOGY, Issue 7 2008
Kai WangArticle first published online: 24 APR 200
Abstract A genetic variant is very likely to manifest its effect on disease through its main effect as well as through its interaction with other genetic variants or environmental factors. Power to detect genetic variants can be greatly improved by modeling their main effects and their interaction effects through a common set of parameters or "generalized association parameters" (Chatterjee et al. [2006] Am. J. Hum. Genet. 79:1002,1016) because of the reduced number of degrees of freedom. Following this idea, I propose two models that extend the work by Chatterjee and colleagues. Particularly, I consider not only the case of relatively weak interaction effect compared to the main effect but also the case of relatively weak main effect. This latter case is perhaps more relevant to genetic association studies. The proposed methods are invariant to the choice of the allele for scoring genotypes or the choice of the reference genotype score. For each model, the asymptotic distribution of the likelihood ratio statistic is derived. Simulation studies suggest that the proposed methods are more powerful than existing ones under certain circumstances. Genet. Epidemiol. 2008. © 2008 Wiley-Liss, Inc. [source]

Methods for Generating Longitudinally Correlated Binary Data

INTERNATIONAL STATISTICAL REVIEW, Issue 1 2008
Patrick J. Farrell
Summary The analysis of longitudinally correlated binary data has attracted considerable attention of late. Since the estimation of parameters in models for such data is based on asymptotic theory, it is necessary to investigate the small-sample properties of estimators by simulation. In this paper, we review the mechanisms that have been proposed for generating longitudinally correlated binary data. We compare and contrast these models with regard to various features, including computational efficiency, flexibility and the range restrictions that they impose on the longitudinal association parameters. Some extensions to the data generation mechanism originally suggested by Kanter (1975) are proposed. Résumé L'analyse des données longitudinales corrélées fait récemment l'objet d'un grand intérêt. Comme l'estimation des paramètres des modèles pour de telles données est souvent basée sur des études asymptotiques, il est nécessaire de procéder à des simulations pour explorer les propriétés des estimateurs en petits échantillonages. Dans ce papier, nous présentons une revue des méthodes qui ont été proposées pour générer des données binaires longitudinales corrélées. Nous les comparons sous différents aspects, notamment en termes d'efficience, flexibilité, et des restrictions qu'elles peuvent avoir sur les paramètres dits d'association longitudinale. Quelques extensions, de la méthode suggérée par Kanter (1975) pour générer de telles données, sont aussi proposées. [source]

Median Regression Models for Longitudinal Data with Dropouts

BIOMETRICS, Issue 2 2009
Grace Y. Yi
Summary Recently, median regression models have received increasing attention. When continuous responses follow a distribution that is quite different from a normal distribution, usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily. In this article, we discuss using median regression models to deal with longitudinal data with dropouts. Weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data, where the weights are determined by modeling the dropout process. Consistency and the asymptotic distribution of the resultant estimators are established. The proposed method is used to analyze a longitudinal data set arising from a controlled trial of HIV disease (Volberding et al., 1990, The New England Journal of Medicine322, 941,949). Simulation studies are conducted to assess the performance of the proposed method under various situations. An extension to estimation of the association parameters is outlined. [source]