Generating Correlated Binary Variables with Complete Specification of the Joint Distribution

Kang, Seung Ho; Jung, Sin Ho

doi:10.1002/1521-4036(200106)43:3<263::aid-bimj263>3.0.co;2-5

Cited by 26 publications

(13 citation statements)

References 18 publications

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“…Alternatively, Kang & Jung (2001) derived a more flexible method. The approach required that the joint distribution of Y 1 , …, Y T be enumerated, which is then used to create a cumulative distribution.…”

Section: Methods For Generating Longitudinally Correlated Binary Datamentioning

confidence: 99%

“…Although this approach allows for unpatterned correlation and non‐stationary sequences, it is computationally inefficient for large T , as it requires that the entire joint distribution be determined. For the case of a stationary exchangeable process, Kang & Jung (2001) also proposed a method that avoids the need to obtain the joint distribution. Initially, they simulate the total number of ones, n = Y 1 +⋯+ Y T using the beta binomial distribution, and then obtain a random permutation of n ones and T − n zeroes.…”

Section: Methods For Generating Longitudinally Correlated Binary Datamentioning

confidence: 99%

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Methods for Generating Longitudinally Correlated Binary Data

Farrell

Rogers‐Stewart

2007

Int Statistical Rev

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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. Copyright 2007 The Authors. Journal compilation (c) 2007 International Statistical Institute.

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Section: Methods For Generating Longitudinally Correlated Binary Datamentioning

confidence: 99%

Section: Methods For Generating Longitudinally Correlated Binary Datamentioning

confidence: 99%

Methods for Generating Longitudinally Correlated Binary Data

Farrell

Rogers‐Stewart

2007

Int Statistical Rev

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“…Using the algorithm of Kang and Jung, 14 we simulate S = 50 data sets such that in each, N observations y = ( y 1 , y 2 , y 3 ) have prior probability 0.5 of belonging to class c i ( i = 1, 2), where

f_{i} false(y_{1}, y_{2}, y_{3} false) = \frac{exp false(\sum_{j = 1}^{3} δ_{i j} y_{j} + \sum_{j < k} γ_{i, j k} y_{j} y_{k} + α_{i} y_{1} y_{2} y_{3} false)}{\sum_{all values of false(y_{1}, y_{2}, y_{3} false)} exp false(\sum_{j = 1}^{3} δ_{i j} y_{j} + \sum_{i < j} γ_{i, j k} y_{j} y_{k} + α_{i} y_{1} y_{2} y_{3} false)} .

In our simulations, we consider the following cases: Case 1: δ 1 = (δ 11 , δ 12 , δ 13 ) = (0.1, 0.2, 0.3), δ 2 = (δ 21 , δ 22 , δ 23 ) = (0.1, 0.2, 0.3); γ 1 = (γ 1,12 , γ 1,13 , γ 1,23 ) = (0, 0, 0), γ 2 = (γ 2,12 , γ 2,13 , γ 2,23 ) = (0.1, 0.2, 0.3); α 1 = 2, α 2 = 1.Case 2: δ 1 = (δ 11 , δ 12 , δ 13 ) = (0.1, 0.2, 0.3), δ 2 = (δ 21 , δ 22 , δ 23 ) = (0.1, 0.2, 0.3); γ 1 = (γ 1,12 , γ 1,13 , γ 1,23 ) = (0.55, 0.66, 0.77), γ 2 = (γ 2,12 , γ 2,13 , γ 2,23 ) = (0.06, 0.05, 0.08); α 1 = −5, α 2 = −1. …”

Section: Simulation Studiesmentioning

confidence: 99%

A Pairwise Naïve Bayes Approach to Bayesian Classification

Asafu‐Adjei

Betensky

2015

Int. J. Patt. Recogn. Artif. Intell.

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Despite the relatively high accuracy of the naïve Bayes (NB) classifier, there may be several instances where it is not optimal, i.e. does not have the same classification performance as the Bayes classifier utilizing the joint distribution of the examined attributes. However, the Bayes classifier can be computationally intractable due to its required knowledge of the joint distribution. Therefore, we introduce a “pairwise naïve” Bayes (PNB) classifier that incorporates all pairwise relationships among the examined attributes, but does not require specification of the joint distribution. In this paper, we first describe the necessary and sufficient conditions under which the PNB classifier is optimal. We then discuss sufficient conditions for which the PNB classifier, and not NB, is optimal for normal attributes. Through simulation and actual studies, we evaluate the performance of our proposed classifier relative to the Bayes and NB classifiers, along with the HNB, AODE, LBR and TAN classifiers, using normal density and empirical estimation methods. Our applications show that the PNB classifier using normal density estimation yields the highest accuracy for data sets containing continuous attributes. We conclude that it offers a useful compromise between the Bayes and NB classifiers.

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“…While the generation of multivariate normal random variables for simulations is standard practice, generating correlated binomial random variables that are additionally nested is not as common, although a few methods exist (Farrell and Rogers-Stewart, 2008;Kang and Jung, 2001;Lunn and Davies, 1998;Oman and Zucker, 2001;Park et al, 1996). To generate the within-study correlated binomial random variables, we used the method provided by Lunn and Davies (1998) and Oman and Zucker (2001).…”

Section: Generating the Sample Values P Cij And P Tijmentioning

confidence: 99%

Robust variance estimation in meta‐regression with binary dependent effects

Tipton

2013

Research Synthesis Methods

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Dependent effect size estimates are a common problem in meta-analysis. Recently, a robust variance estimation method was introduced that can be used whenever effect sizes in a meta-analysis are not independent. This problem arises, for example, when effect sizes are nested or when multiple measures are collected on the same individuals. In this paper, we investigate the robustness of this method in small samples when the effect size of interest is the risk difference, log risk ratio, or log odds ratio. This simulation study examines the accuracy of 95% confidence intervals constructed using the robust variance estimator across a large variety of parameter values. We report results for both estimations of the mean effect (intercept) and of a slope. The results indicate that the robust variance estimator performs well even when the number of studies is as small as 10, although coverage is generally less than nominal in the slope estimation case. Throughout, an example based on a meta-analysis of cognitive behavior therapy is used for motivation. Copyright © 2013 John Wiley & Sons, Ltd.

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Generating Correlated Binary Variables with Complete Specification of the Joint Distribution

Cited by 26 publications

References 18 publications

Methods for Generating Longitudinally Correlated Binary Data

Methods for Generating Longitudinally Correlated Binary Data

A Pairwise Naïve Bayes Approach to Bayesian Classification

Robust variance estimation in meta‐regression with binary dependent effects

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