Model fitting for categorical data and handling over-dispersion

在这项研究中，方法的数据，有分类的反应进行了调查。特别是，分析方法来处理过度分散的发展和调查，以评估协变量的影响，这样的数据集。模型的关联指数的关系与/无有序信息，如多项式logits，累积logits，连续比logits，相邻类别logits，互补log-log和立体型模型，和线性预测构建的协变量的方法被认为是。研究的基本方法是基于多项分布的分布扩展的极大似然方法，如Dirichlet-多项分布及其扩展，分布的均值-方差结构的广义估计方程，以及计算机密集型方法，如Jackknife方法，我们开发了这类数据的分析系统，并对几个实际发表的数据进行了分析。通过这些分析，可以清楚地看到过色散和阶次信息建模的影响，以及基于该方法的差异。此外，还发现了Dirichlet多项分布在处理欠分散问题上的局限性。为了研究所提出的方法的性能，还进行了一些模拟研究。通过这些模拟研究，我们得出结论，在数据的基线分布为Dirichlet多项式的情况下，这些方法在平均结构参数的偏差和方差估计方面具有良好的一致性，并且基于Jackknife的方法具有相当的能力来合并过度分散的影响。

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.