Model fitting for categorical data and handling over-dispersion

分类数据的模型拟合和处理过度分散

基本信息

批准号：
10680319
负责人：
OCHI Yoshimichi
金额：
$ 1.22万
依托单位：
Oita University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

In this study, methods for data that have categorical responses are investigated. Especially, analytical methods to deal with over-dispersion are developed and investigated in order to evaluate covariate effects for such data sets.To incorporate the over-dispersion that cannot be explained by models based on multinomial distribution, we considered Dirichlet-multinomial distribution. Methods which model the relations of indices of association with/without ordered information, such as multinomial logits, cumulative logits, continuation ratio logits, adjacent category logits, complimentary log-log and stereo type model, and linear predictors constructed from the covariates are considered. Fundamental approaches for the work are the maximum likelihood methods based on the distributional extension of the multinomial distribution, such as Dirichlet-multinomial distribution and its extension, generalized estimation equations for the mean-variance structure of the distribution, and computer intensive methods such as the Jackknife method.We developed analysis systems for such data and analyzed several actual published data. With these analyses, effects of the over-dispersion and modeling of the order information, as wen as differences based on the approach were made clear. The limitations for the Dirichlet-multinomial distribution, especially to handle under-dispersion, were also detected.In order to study performance of the developed methods, some simulation studies were conducted as well. With these simulation studies, we concluded that the methods were in good agreement in terms of biases and variance estimates of the mean structure parameters in the case where the baseline distributions of the data were Dirichlet-multinomial, and that the method based on Jackknife had comparable abilities to incorporate the effects of over-dispersion.

在这项研究中，研究了具有分类响应的数据的方法。特别是，开发和研究了处理过度分散的分析方法，以评估此类数据集的协变量效应。为了结合基于多项式分布的模型无法解释的过度分散，我们认为Dirichlet-Lextiminorial分布。模拟与/没有有序信息相关的指标关系的方法，例如多项式逻辑，累积逻辑，持续比率逻辑，相邻的类别逻辑，免费日志logog和立体声类型模型以及从协变量构建的线性预测指标。这项工作的基本方法是基于多项式分布的分布扩展的最大似然方法，例如Dirichlet-Multinoilsial分布及其扩展，扩展分布的均值差异结构的广义估计方程以及计算机密集型方法，例如折刀方法。我们为此类数据开发了分析系统，并分析了几个实际已发布的数据。通过这些分析，订单信息的过度分散和建模的影响，如基于该方法的差异一样。还检测到了Dirichlet多性分布的局限性，尤其是用于处理不足的局限性。为了研究开发方法的性能，还进行了一些仿真研究。通过这些模拟研究，我们得出结论，在数据基线分布是数据的基线分布中，这些方法在偏差和差异估计方面非常吻合，并且基于Jackknife的方法具有可比性纳入过度分散的影响的能力。