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Conditional independence of multivariate binary data with an application in caries research

COMPUTATIONAL STATISTICS & data ANALYSIS 2007年第6期51卷 3223-3234页

作者： Garcia-Zattera, Maria Jose Jara, Alejandro Lesaffre, Emmanuel Declerck, Dominique Catholic Univ Louvain Ctr Biostat B-3000 Louvain Belgium Catholic Univ Louvain Sch Dent B-3000 Louvain Belgium

For the analysis of caries experience in seven-year old children the association between the presence or absence of caries experience among deciduous molars within each child is explored. Some of the high associations have an etiological basis (e.g., between symmetrically opponent molars), while others (diagonally opponent molars) are assumed to be the result of the transitivity of association and to disappear once conditioned on the caries experience status of the other deciduous molars, covariates and random effects. However, using discrete models for multivariate binary data, conditioning does not remove the diagonal association. When the association is explored on a latent scale, e.g., by a multivariate probit model, then conditional independence can be concluded. This contrast is confirmed when using other models on the (observed) binary scale and on the latent scale. Depending on the point of view, the differences in conditional independence might be seen as a consequence of different types of measurements or as a consequence of different models. An example shows that the results and conclusions can be markedly different with important consequences on model building. The explanation for this result is exemplified mathematically and illustrated using dental data from the Signal-Tandmobiel((R)) study. (c) 2006 Elsevier B.V. All rights reserved.

关键词： conditional independence multivariate binary data latent variable representation multivariate probit model

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Variable selection in high-dimensional multivariate binary data with application to the analysis of microbial community DNA fingerprints

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BIOMETRICS 2002年第2期58卷 378-386页

作者： Wilbur, JD Ghosh, JK Nakatsu, CH Brouder, SM Doerge, RW Purdue Univ Dept Stat W Lafayette IN 47907 USA Indian Stat Inst Kolkata 700035 W Bengal India Purdue Univ Dept Agron W Lafayette IN 47907 USA

In order to understand the relevance of microbial communities on crop productivity, the identification and characterization of the rhizosphere soil microbial community is necessary. Characteristic profiles of the microbial communities are obtained by denaturing gradient gel electrophoresis (DGGE) of polymerase chain reaction (PCR) amplified 16S rDNA from soil extracted DNA. These characteristic profiles, commonly called community DNA fingerprints, can be represented in the form of high-dimensional binary vectors. We address the problem of modeling and variable selection in high-dimensional multivariate binary data and present an application of our methodology in the context of a controlled agricultural experiment.

关键词： classification DNA fingerprints high-dimensional data microbial communities multivariate binary data permutation tests variable selection

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MODELING AND INFERENCE FOR multivariate binary data WITH POSITIVE DEPENDENCE

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 1984年第385期79卷 188-193页

作者： BOYLES, RA SAMANIEGO, FJ UNIV CALIF DAVIS DIV STATDAVISCA 95616

A model is proposed for multivariate binary data that incorporates positive dependence among components in a natural way. The model is derived from reliability-theoretic concepts, but is regarded as appropriate for analysis of multivariate binary data in any field when positive dependence is an appropriate assumption. Maximum likelihood estimation by iterative solution of likelihood equations is discussed for the general model, and asymptotically efficient estimates are obtained in closed form for the fully parameterized (saturated) model. The estimation procedures are illustrated on a data set from Martin and Bradley (1972).

关键词： multivariate binary data Positive dependence Shock models Estimation Asymptotic efficiency

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Notes on testing noninferiority in multivariate binary data under the matched-pair design

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STATISTICAL METHODS IN MEDICAL RESEARCH 2016年第4期25卷 1272-1289页

作者： Lui, Kung-Jong Chang, Kuang-Chao San Diego State Univ Coll Sci Dept Math & Stat San Diego CA 92182 USA Fu Jen Catholic Univ Dept Stat & Informat Sci New Taipei Taiwan

Since therapeutic efficacy is often measured by multiple endpoints, it will be of use if one can incorporate the information on various variables of response into procedures for testing noninferiority to improve power of a univariate test procedure for each individual variable. On the basis of the proposed mixed effects logistic regression model for multivariate binary data under the matched-pairs design, we develop procedures for testing noninferiority with respect to the odds ratio in multivariate binary data under the matched-pair design. We discuss use of Bonferroni's and Scheffe's methods to control the inflation in Type I error due to multiple tests. We further employ Monte Carlo simulation to evaluate and compare the performance of these test procedures. Finally, we use the data taken from a crossover clinical trial that monitored several adverse events of an antidepressive drug to illustrate the use of test procedures derived here.

关键词： Odds ratio multivariate binary data matched-pairs noninferiority exact test bootstrapping

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A Note on the Graphical Representation of multivariate binary data

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Journal of the Royal Statistical Society: Series C (Applied Statistics) 1980年第3期29卷 238-245页

作者： C. F. Banfield J. C. Gower Rothamsted Experimental Station Harpenden Herts UK

Various ordination methods for mapping n units characterized by v binary variables are in common use in which the distance between points P i and P j , representing units i and j , approximates some function (a similarity coefficient) of ( a ij , b ij , c ij , d ij ) , the usual cell-counts in a 2 × 2 table. Ordination generally requires (n – 1) dimensions to represent the distances exactly, but the quantities b ij - c ij can always be represented in one dimension. This leads to a simple graphical extension of ordination that helps with interpretation, reveals discrepancies, screens clustering possibilities and permits the recovery of approximations to all the ( a, b, c, d )-values. Two examples illustrate the technique.

关键词： multivariate binary data graphical representation ordination similarity

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Order-Restricted Inference for multivariate binary data With Application to Toxicology

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2011年第496期106卷 1394-1404页

作者： Davidov, Ori Peddada, Shyamal Univ Haifa Dept Stat IL-31905 Haifa Israel Natl Inst Environm Hlth Sci Biostat Branch Res Triangle Pk NC 27709 USA

In many applications, researchers collect multivariate binary response data under two or more naturally ordered experimental conditions. In such situations, one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions. To make such comparisons, we develop a general methodology for testing for the multivariate stochastic order between K >= 2 multivariate binary distributions. Our proposed test uses order-restricted estimators, which, according to our simulation study, are more efficient than the unrestricted estimators in terms of their mean squared error. We compared the power of the proposed test with that of several alternative tests, including procedures that combine individual univariate tests for order, such as union-intersection tests and a Bonferroni-based test. We also compared the proposed test with an unrestricted Hotel ling T-2-type test. Our simulations suggest that the proposed method competes well with these alternatives. The gain in power is often substantial. The proposed methodology is illustrated by applying it to a two-year rodent cancer bioassay data obtained from the U.S. National Toxicology Program. Supplemental materials are available online.

关键词： Dose-response study multivariate binary data Order-restricted statistical inference Stochastic order relation

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Time Series Models for multivariate binary and Categorical data

Time Series Models for Multivariate Binary and Categorical D...

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作者： Reichmann, Lena Christine Universitaet Mannheim (Germany)

学位级别：Dr.rer.nat., Doctor of Natural Science

In the following thesis, we investigate the modeling of time series data with multivariate discrete and especially binary structure. A model for categorical time series data with a nice interpretability which, in addition, is parsimonious, is the New Discrete AutoRe- gressive Moving Average (NDARMA) model of Jacobs and Lewis (1983). However, this model only can capture positive autocorrelation as well as positive parameters. In the first part of the thesis, we propose an extension of the NDARMA model class for the special case of binary data, that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. For this class of processes, we infer statistical properties and compare it in a simulation study with the benchmark model, the Markov Processes and other time series models. In the second part, we adopt the approach of the first part and propose a vector- valued extension of gbAR processes, that enable the joint modeling of serial and cross- sectional dependence of multivariate binary data. The resulting class of generalized binary vector Auto-Regressive (gbVAR) models is parsimonious, nicely interpretable and allows also to model negative dependence. We further extend the gbVAR model to include a moving average part, resulting in turn in the gbVARMA model. In the third and final part we pursue a further extension to vector-valued categorical time series data. For the proposed gbVARMA and NDVARMA models, we provide stationarity conditions and state the stationary solution. Stochastic properties, e.g. Yule-Walker- type equations and classical Yule-Walker equations for the pure autore- gressive case are derived. We show φ- and ψ- mixing properties of the gbVAR and NDVARMA model by proving the strict positivity of the transition probabilities. For the NDVARMA model, we discuss the identification of the distribution of the vector- valued innovation p

关键词： Time series models multivariate binary data Categorical data Markov Processes

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Selection of binary variables and classification by boosting

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2007年第4期36卷 855-869页

作者： Park, Junyong Wilbur, Jayson D. Ghosh, Jayanta K. Nakatsu, Cindy H. Ackerman, Corinne Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA Worcester Polytech Inst Dept Math Sci Worcester MA 01609 USA Purdue Univ Dept Stat W Lafayette IN 47907 USA Purdue Univ Dept Agron W Lafayette IN 47907 USA

We adopt boosting for classification and selection of high-dimensional binary variables for which classical methods based on normality and non singular sample dispersion are inapplicable. Boosting seems particularly well suited for binary variables. We present three methods of which two combine boosting with the relatively classical variable selection methods developed in Wilbur et al. (2002). Our primary interest is variable selection in classification with small misclassification error being used as validation of proposed method for variable selection. Two of the new methods perform uniformly better than Wilbur et al. (2002) in one set of simulated and three real life examples.

关键词： boosting cross validation DNA fingerprints high-dimensional data multivariate binary data thresholding variable selection

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A Simple Distribution for the Sum of Correlated, Exchangeable binary data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2014年第20期43卷 4265-4280页

作者： Witt, Gary Temple Univ Fox Sch Business Philadelphia PA 19122 USA

This article describes a generalization of the binomial distribution. The closed form probability function for the probability of k successes out of n correlated, exchangeable Bernoulli trials depends on the number of trials and its two parameters: the common success probability and the common correlation. The distribution is derived under the assumption that the common correlation between all pairs of Bernoulli trials remains unchanged conditional on successes in all completed trials. The distribution was developed to model bond defaults but may be suited to biostatistical applications involving clusters of binary data encountered in repeated measurements or toxicity studies of families of organisms. Maximum likelihood estimates for the parameters of the distribution are found for a set of binary data from a developmental toxicity study on litters of mice.

关键词： multivariate binary data Correlated Bernoulli trials

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Two-sample tests for sparse high-dimensional binary data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第22期46卷 11181-11193页

作者： Plunkett, Amanda Park, Junyong Dept Def Ft George G Meade MD USA Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA

In this article, we study the methods for two-sample hypothesis testing of high-dimensional data coming from a multivariate binary distribution. We test the random projection method and apply an Edgeworth expansion for improvement. Additionally, we propose new statistics which are especially useful for sparse data. We compare the performance of these tests in various scenarios through simulations run in a parallel computing environment. Additionally, we apply these tests to the 20 Newsgroup data showing that our proposed tests have considerably higher power than the others for differentiating groups of news articles with different topics.

关键词： Dimension reduction High dimension multivariate binary data

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