Estimation for zero-inflated beta-binomial regression model with missing response data

Discrete data in the form of proportions with overdispersion and zero inflation can arise in toxicology and other similar fields. In regression analysis of such data, another problem that also may arise in practice is that some responses may be missing. In this paper, we develop estimation procedure for the parameters of a zero-inflated overdispersed binomial model in the presence of missing responses under three different missing data mechanisms. A weighted expectation maximization algorithm is used for the maximum likelihood estimation of the parameters involved. Extensive simulations are conducted to study the properties of the estimates in terms of average of estimates, relative bias, variance, mean squared error, and coverage probability of estimates. Simulations show much superior properties of the estimates obtained using the weighted expectation maximization algorithm. Some illustrative examples and a discussion are given.

在毒理学及其他类似领域中，可能会出现具有过度离散和零膨胀的比例形式的离散数据。在对这类数据进行回归分析时，实践中可能出现的另一个问题是某些响应可能缺失。在本文中，我们针对三种不同缺失数据机制下存在缺失响应的零膨胀过度离散二项式模型的参数，开发了估计程序。采用加权期望最大化算法对相关参数进行最大似然估计。进行了大量模拟，以从估计均值、相对偏差、方差、均方误差和估计的覆盖概率等方面研究估计值的性质。模拟结果表明，使用加权期望最大化算法得到的估计值具有更优的性质。文中给出了一些示例和讨论。