Graphical Diagnostics for Markov Models for Categorical Data
Graphical Diagnostics for Markov Models for Categorical Data
复制标题
分类数据马尔可夫模型的图形诊断
DOI：
10.1198/jcgs.2010.08135
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发表时间：
2011
影响因子：
2.4
通讯作者：
M. Bravington
中科院分区：
文献类型：
--
作者：
S. Foster;M. Bravington
马尔可夫模型被广泛用于描述具有平稳和非平稳自相关的分类数据。然而，马尔可夫模型的诊断方法在很大程度上被忽视了。为此，我们引入了两种类型的残差：一种用于评估状态变化之间的运行长度，另一种用于评估过程从任何给定状态移动到其他状态的频率。提出了计算两种残差抽样分布的方法，通过图形总结实现客观解释。图形摘要是使用适用于离散数据的概率积分变换的修改而形成的。给出了模拟数据集的残差，以证明模型何时适合数据，何时不适合数据。这两种类型的残差用于突出为海洋环境中海底动物群的实际数据所提出的模型的不足之处。补充材料，包括一个R-package RMC，具有对本文中考虑的模型类执行诊断措施的功能，可在该杂志的网站上找到。r包也可在CRAN。
Markov models are widely used as a method for describing categorical data that exhibit stationary and nonstationary autocorrelation. However, diagnostic methods are a largely overlooked topic for Markov models. We introduce two types of residuals for this purpose: one for assessing the length of runs between state changes, and the other for assessing the frequency with which the process moves from any given state to the other states. Methods for calculating the sampling distribution of both types of residuals are presented, enabling objective interpretation through graphical summaries. The graphical summaries are formed using a modification of the probability integral transformation that is applicable for discrete data. Residuals from simulated datasets are presented to demonstrate when the model is, and is not, adequate for the data. The two types of residuals are used to highlight inadequacies of a model posed for real data on seabed fauna from the marine environment. Supplemental materials, including an R-package RMC with functions to perform the diagnostic measures on the class of models considered in this article, are at the journal’s website. The R-package is also available at CRAN.