Moment estimators for the beta-binomial distribution

Yamamoto, Etsuhide; Yanagimoto, Takemi

doi:10.1080/02664769200000023

Cited by 19 publications

(27 citation statements)

References 19 publications

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“…Lately, Yamamoto and Yanagimoto [15] propose the so-called 'unbiased' moment estimator, which is actually equivalent [16] to the above ANOVA estimator. Focusing point estimation on the intraclass correlation, Yamamoto and Yanagimoto compare the performance of the ANOVA estimator with the maximum likelihood estimator (MLE), the moment estimator, and the stabilized moment estimator proposed elsewhere [17] under the beta-binomial model, a special case of the Dirichlet-multinomial model with the number of categories J = 2.…”

Section: Appendixmentioning

confidence: 99%

“…We present the detailed justiÿcation of using the ANOVA estimatorˆ i together with a few relevant publications [7,[14][15][16][17][18] in the Appendix. When m ik = 1 for all i and k, the estimated variance var( [ GOR) simpliÿes to the variance derived elsewhere [1] for the case of a single measurement per subject.…”

Section: Estimation Of Generalized Odds Ratiomentioning

confidence: 99%

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Interval estimation of generalized odds ratio in data with repeated measurements

Lui

2002

Statistics in Medicine

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When the underlying responses are on an ordinal scale, the generalized odds ratio (GOR), defined as the ratio of the proportions of concordant and discordant pairs, is a useful index to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable. We discuss interval estimation of the GOR for ordinal data with repeated measurements. On the basis of the Dirichlet-multinomial model, we develop three asymptotic interval estimators of the GOR using Wald's test statistic, a logarithmic transformation, and a method analogous to Fieller's theorem, respectively. To evaluate and compare the finite-sample performance of these estimators, we apply Monte Carlo simulation. We find that when the number of subjects per group is not large, the coverage probability of interval estimator using Wald's test statistic is likely to be less than the desired confidence level. By contrast, the coverage probability of the other two estimators are approximately equal to or larger than the desired confidence level. When the number of subjects per group is small and the intraclass correlation between repeated measurements within subjects is large, we note that applying the interval estimator derived from a method analogous to Fieller's theorem can lose efficiency. We also note that the interval estimator using the logarithmic transformation is generally preferable to the other two estimators with respect to both the coverage probability and the average length. Finally, on the basis of a few preliminary simulations, we do find some robustness for all the estimators developed here. We include an example comparing the inflammation grade after lung transplant between surgeries to illustrate the use of the proposed interval estimators.

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Section: Appendixmentioning

confidence: 99%

Section: Estimation Of Generalized Odds Ratiomentioning

confidence: 99%

Interval estimation of generalized odds ratio in data with repeated measurements

Lui

2002

Statistics in Medicine

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“…Note that the Dirichlet-multinomial distribution is not an exponential family. Furthermore, as noted by Yamamoto and Yanagimoto (1992), the unimodality of the Dirichlet-multinomial distribution has only been proved under very restricted conditions (Levin & Reeds, 1977). In fact, both Yamamoto & Yanagimoto (1992) and Tamura & Young (1987) consider the beta-binomial model (which is a special case of the Dirichlet-multinomial model) and note that the methods based on moments can be preferable to the maximum likelihood estimator (MLE) in a wide range of parameter space.…”

Section: Introductionmentioning

confidence: 98%

“…Furthermore, as noted by Yamamoto and Yanagimoto (1992), the unimodality of the Dirichlet-multinomial distribution has only been proved under very restricted conditions (Levin & Reeds, 1977). In fact, both Yamamoto & Yanagimoto (1992) and Tamura & Young (1987) consider the beta-binomial model (which is a special case of the Dirichlet-multinomial model) and note that the methods based on moments can be preferable to the maximum likelihood estimator (MLE) in a wide range of parameter space. Given these unfavorable properties, the findings, and the need of employing a sophisticated numerical procedure to calculate the MLE, we focus discussion on development of a closedform interval estimator based on the moments in this paper.…”

Section: Introductionmentioning

confidence: 98%

“…Furthermore, the focus of their paper is different from ours, which is the development of an asymptotic closed-form interval estimator. Other discussions and applications of estimation for the intraclass correlation as a means of assessing the reliability of a measurement tool or investigating the heritability of a certain trait in psychological, biological, and toxicological experiments appear elsewhere (Fleiss, 1981(Fleiss, & 1986Mak, 1988;Yamamoto & Yanagimoto, 1992).…”

Section: Introductionmentioning

confidence: 99%

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Interval estimation for the intraclass correlation in dirichlet-multinomial data

et al. 1999

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Tests for homogeneity of the risk ratio in a series of 2×2 tables

Lui

Kelly

2000

Statist. Med.

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We often apply the risk ratio to measure the strength of a causal relationship between a suspected risk factor and a disease of interest. In this paper we consider testing the homogeneity of risk ratio over a series of 2×2 tables. In addition to the classical weighted least squares (CWLS) test procedure, we consider two test procedures using simple transformations of the CWLS statistic and develop three other asymptotically weighted test procedures. On the basis of Monte Carlo simulation, we conclude that the commonly‐used CWLS test procedure is generally conservative, especially when the number of 2×2 tables is large and the mean group size per table is moderate or small. We further find that two of the test procedures discussed here can not only generally outperform the CWLS test procedure, but also perform well in a variety of situations considered in this paper. Finally, we illustrate the use of these testing procedures with an example of six randomized trials that assess the effects of aspirin on the prevention of death in post‐myocardial infarction patients. Copyright © 2000 John Wiley & Sons, Ltd.

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Moment estimators for the beta-binomial distribution

Cited by 19 publications

References 19 publications

Interval estimation of generalized odds ratio in data with repeated measurements

Interval estimation of generalized odds ratio in data with repeated measurements

Interval estimation for the intraclass correlation in dirichlet-multinomial data

Tests for homogeneity of the risk ratio in a series of 2×2 tables

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