A Study on Non-ignorable Nonresponse Problems in Generalized Linear Models

自1996年以来，Baker, Chen, Clifford, Fitzmaurice, Heath, Ibrahim, Laird, Lipshitz， Zahner等人研究了具有不可忽略缺失响应或协变量的广义线性模型（GLM）。他们提出的估计方法没有考虑模型参数的不可估计性及其标准误差。在下面列出的第五篇论文中，我们揭示了当GLM中的一些协变量不可忽略地缺失时的不可估计模式。在下面列出的第四篇论文中，当GLM中的一些响应不可忽视地缺失时，我们再次揭示了不可估计的模式。在本文中，我们还从理论上表明，如果一些响应是可忽略的缺失，那么对列表中明智删除的数据进行分析将产生与使用Ibrahim等人在1996年生物计量学论文中提出的方法相同的结果。在因变量中存在不可忽略的非响应时，我们将其参数估计方法扩展到比例-赔率模型，并将…More方法应用于美国汽车市场的总拥有量估计。结构方程模型被广泛认为是社会科学的重要工具。近年来，专门研究结构方程建模的统计软件（如LISREL、EQS和AMOS）的进展加速了它的使用。在每项测量都是分类的情况下，模型需要更复杂的方法，而且似乎在如何分析这些分类数据方面没有一个既定的共识。Allison（2003）回顾了处理结构方程模型中缺失值的最新进展，其中指出了更传统的方法（如列表删除或成对删除）的局限性，并探讨了更现代的最大似然估计方法。并对多种插值方法的基本思想和实际实现进行了广泛的讨论。今年，我们彻底回顾了该领域之前的进展，并在下面列出的前两篇论文中使用真实世界的数据探讨了其在估计中的问题

Generalized linear models (GLM) with non-ignorably missing response or covariates has been studied since 1996 by Baker, Chen, Clifford, Fitzmaurice, Heath, Ibrahim, Laird, Lipshitz, Zahner. Their proposed method of estimation does not consider inestimability of the model parameters and their standard errors. In the fifth paper listed below, we uncovered the pattern of inestimability when some of the covariates in GLM are non-ignorably missing. In the fourth paper listed below, we again uncovered the pattern of inestimability when some of the resposes in GLM are non-ignorably missing. In this paper we also theoretically showed that if some of the responses are ignorably missing, then analysis of the listwisely deleted data will yield identical results with those using the method proposed by Ibrahim et al. in 1996 Biometrics paper. We also extended their parameter estimations method when there are non-ignorable non-responses in dependent variable to proportional-odds model and apply the … More method to total cast of ownership estimation in automobile markets in the U.S. in the paper listed third belowStructural equation models are widely recognized as an important tool for social sciences. The recent progresses in statistical software specializing in structural equation modeling such as LISREL, EQS, and AMOS accelerated its usage. In cases where each measurements are categorical, the model requires much more sophisticated approach and there does not seem to be an established consensus in how those categorical data ought to be analyzed. The recent advances in treating missing values in structural equation models are reviewed in Allison (2003) in which the limitations are pointed out of the more traditional methods such as listwise deletion or pairwise deletion and the more modern maximum likelihood estimation methods are explored. Also the underlying ideas and the actual implementation of multiple imputation methods are broadly discussed. This year we thoroughly reviewed the preceding progresses in this field and explore its problems in estimation using the real-world data in the first two papers listed below Less