在制造缺陷、专利申请、道路安全和公共卫生等应用领域, 经常会出现较多的零观测值和一观测值. 采用传统的泊松回归或负二项回归模型往往会过低地估计零观测值和一观测值出现的概率, 数据拟合的效果欠佳. 文章提出了0-1膨胀几何分布回归模型, 巧妙地引入隐变量并进行极大似然估计和贝叶斯估计, 基于数据扩充策略分别采用最大期望(EM)算法和Metropolis-Hastings抽样算法对回归参数向量进行估计. 在不同的样本容量下进行数值模拟, 并对两种估计方法的性能进行评价. 研究表明, 对于博士研究生发表论文数量的数据集, 0-1膨胀几何分布回归模型能够达到更好的拟合效果.

Count data with excess zeros and ones arise frequently in various fields when dealing with manufacturing defects, patent applications, road safety and public health. Conventional models such as Poisson or negative binomial distribution may not fit these data well, and seriously underestimate the zero-count and one-count probability. In this paper, a zero-and-one-inflated geometric distribution (ZOIGE) regression model is proposed. Ingeniously introducing implicit variables, maximum likelihood estimation and Bayesian estimation are investigated. Based on data-augmentation strategy, the regression parameter vectors are obtained by expectation-maximization (EM) algorithm and Metropolis-Hastings sampling respectively. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, a doctoral dissertation data set is analyzed to illustrate the practicability of the proposed method.