Maximum Likelihood, Profile Likelihood, and Penalized Likelihood: A Primer
Maximum Likelihood, Profile Likelihood, and Penalized Likelihood: A Primer
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DOI：
10.1093/aje/kwt245
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发表时间：
2014-01-15
影响因子：
5
通讯作者：
Greenland, Sander
中科院分区：
文献类型：
--
作者：
Cole, Stephen R.;Chu, Haitao;Greenland, Sander
最大似然法广泛应用于流行病学，但许多流行病学家很少或根本没有接受过该方法概念基础的教育。在这里，我们提供了最大似然和一些重要扩展的入门知识，这些扩展已被证明在流行病学研究中有用，并揭示了最大似然和贝叶斯方法之间的联系。对于给定的数据集和概率模型，最大似然查找为观测数据提供最高概率的模型参数值。与所有推论统计方法一样，最大似然基于假设的模型，无法解释不受模型或研究设计控制的偏差来源。尽管如此，最大似然仍然很受欢迎，因为它在计算上简单且直观，并且因为最大似然估计器在正确指定模型的（很大程度上是虚构的）情况下具有理想的大样本属性。在这里，我们通过一个示例来说明最大似然估计的机制，并说明如何使用商业软件轻松进行改进。然后，我们描述了最近的扩展和概括，它们更适合观察健康研究，并且可以说应该取代标准最大似然法作为默认方法。
The method of maximum likelihood is widely used in epidemiology, yet many epidemiologists receive little or no education in the conceptual underpinnings of the approach. Here we provide a primer on maximum likelihood and some important extensions which have proven useful in epidemiologic research, and which reveal connections between maximum likelihood and Bayesian methods. For a given data set and probability model, maximum likelihood finds values of the model parameters that give the observed data the highest probability. As with all inferential statistical methods, maximum likelihood is based on an assumed model and cannot account for bias sources that are not controlled by the model or the study design. Maximum likelihood is nonetheless popular, because it is computationally straightforward and intuitive and because maximum likelihood estimators have desirable large-sample properties in the (largely fictitious) case in which the model has been correctly specified. Here, we work through an example to illustrate the mechanics of maximum likelihood estimation and indicate how improvements can be made easily with commercial software. We then describe recent extensions and generalizations which are better suited to observational health research and which should arguably replace standard maximum likelihood as the default method.