A new robust parameter estimation approach for multinomial categorical response data with outliers and mismeasured covariates

Being confronted with multinomial categorical response data often occurs in the medical, health, social sciences and other fields. However, the data in practice are subject to measurement error (ME) or outliers due to some unavoidable reasons. There are few studies dealing with problems of ME and outliers in the data with unordered and multi-classified responses <i>simultaneously</i>. To address the effects of ME and outliers in multinomial logistic models, which are most suitable for analyzing categorical outcome variables, we propose novel approaches. Firstly, we develop the extensively weighed corrected score method to estimate parameters in multinomial logistic models with ME. Furthermore, to tackle the problem of that how to obtain parameter estimations when the ME and outliers occur <i>simultaneously</i>, we develop a new robust method, namely the robust extensive weighted corrected score method. Some simulation studies are conducted to evaluate the estimators’ finite sample performance. It has been verified that these estimators are consistent and asymptotically normally distributed under general conditions. They are easy to compute, perform well and stably and are robust against the normality assumption for the ME. The proposed methods are also applied to two real datasets to illustrate the practicability of methods.

在医学、卫生科学、社会科学等诸多领域中，多项分类响应数据的应用场景十分常见。然而，受诸多不可避免的因素影响，实际采集的此类数据往往存在测量误差（measurement error，ME）或异常值问题。目前，针对无序多分类响应数据同时处理测量误差与异常值问题的相关研究仍较为匮乏。鉴于多项逻辑斯蒂模型是分析分类结果变量的适配性最优工具，为解决该模型中测量误差与异常值带来的干扰，本文提出了全新的研究方法。首先，我们构建了广义加权校正得分法，用于对存在测量误差的多项逻辑斯蒂模型开展参数估计。进一步地，针对测量误差与异常值同时出现时的参数估计难题，我们提出了一种鲁棒性新方法——鲁棒广义加权校正得分法。我们通过多组仿真实验对所提估计量的有限样本性能进行了评估。验证结果表明，在一般正则条件下，此类估计量具备一致性且服从渐近正态分布；其计算过程简便、表现优异且稳定性强，同时对测量误差的正态性假设具有鲁棒性。最后，我们将所提方法应用于两个真实数据集，以展示其实际应用可行性。