A class of multivariate discrete distributions based on an approximate density in GLMM

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概要

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• It is well known that the generalized linear mixed model is useful for analyzing the overdispersion and correlation structure for multivariate discrete data.In this paper, we derive an approximation of the density function for the generalized linear mixed model. This approximation is found to satisfy the properties of probability density function under some conditions. Therefore, this approximation can be regarded as a class of multivariate distributions. Estimation of the parameters in this class can be carried out by the maximum likelihood method. We give the likelihood ratio criteria for testing several covariance structures. Several simulation studies were also conducted for the Poisson log-normal model when the proposed density function is regarded as an approximate likelihood of the generalized linear mixed model.

• 広島大学の論文

著者

• Tonda Tetsuji

  Department Of Environmetrics And Biometrics Research Institute For Radiation Biology And Medicine Hi

• Tonda Tetsuji

  Department Of Environmentrics And Biometrics Research Institute For Radiation Biology And Medicine H

関連論文

• Asymptotic expansion of the null distribution of the likelihood ratio statistic for testing the equality of variances in a nonnormal one-way ANOVA model
• Asymptotic expansion of the null distribution of the modified normal likelihoodratio criterion for testing $\Sigma=\Sigma_0$ under nonnormality
• A class of multivariate discrete distributions based on an approximate density in GLMM
• Adjustment on an asymptotic expansion of the distribution function with $χ^2$-approximation

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