ABSTRACT The identifiability of a statistical model is an essential and necessary property. When a model is not identifiable, even an infinite number of observations cannot determine the true parameter. Non-identifiablity problem in generalized linear models with and without random effects is very common. Also it can occur in such models when the response variable has non-ignorably missing. Since the structure of the beta regression model is similar to that of the generalized linear models and identifiability of many commonly used models such as the beta regression model has not been investigated in the literature, we establish a study about identifiability of some types of the beta regression models such as beta regression model with non-ignorable missing mechanism, zero and one inflated beta regression model, zero and one inflated beta regression model with non-ignorable missing mechanism, longitudinal beta regression model, longitudinal zero and one inflated beta regression model, longitudinal zero and one inflated beta regression model with non-ignorable missing mechanism, and longitudinal correlated bivariate Poisson and zero and one inflated beta regression model with non-ignorable missing mechanism. We construct estimators for the parameters in all mentioned models based on the EM algorithm and the likelihood-based approach. Simulation results and two applications of the Facebook network and FBI datasets are also presented.

中文翻译：

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具有不可忽略缺失机制的纵向相关泊松和膨胀β回归模型中参数的可识别性

摘要 统计模型的可识别性是一个基本和必要的属性。当模型不可识别时，即使是无限数量的观察也无法确定真实参数。具有和不具有随机效应的广义线性模型中的不可识别性问题非常普遍。当响应变量不可忽视地丢失时，它也可能发生在此类模型中。由于beta回归模型的结构与广义线性模型相似，而且很多常用模型如beta回归模型的可识别性在文献中都没有研究过，我们建立了对某些类型的beta的可识别性研究回归模型，例如具有不可忽略缺失机制的 Beta 回归模型、零和一膨胀 Beta 回归模型，具有不可忽略缺失机制的零一膨胀β回归模型、纵向β回归模型、纵向零一膨胀β回归模型、具有不可忽略缺失机制的纵向零一膨胀β回归模型、纵向相关双变量泊松和零以及一个具有不可忽略缺失机制的膨胀 beta 回归模型。我们基于 EM 算法和基于似然的方法为所有提到的模型中的参数构建估计量。还介绍了 Facebook 网络和 FBI 数据集的模拟结果和两个应用。具有不可忽略缺失机制的纵向零一膨胀β回归模型，以及具有不可忽略缺失机制的纵向相关二元泊松和零一膨胀β回归模型。我们基于 EM 算法和基于似然的方法为所有提到的模型中的参数构建估计量。还介绍了 Facebook 网络和 FBI 数据集的模拟结果和两个应用。具有不可忽略缺失机制的纵向零一膨胀β回归模型，以及具有不可忽略缺失机制的纵向相关二元泊松和零一膨胀β回归模型。我们基于 EM 算法和基于似然的方法为所有提到的模型中的参数构建估计量。还介绍了 Facebook 网络和 FBI 数据集的模拟结果和两个应用。