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Graphical diagnostics for Markov models for categorical data


Foster, S and Bravington, M, Graphical diagnostics for Markov models for categorical data, Journal of Computational and Graphical Statistics, 20, (2) pp. 355-374. ISSN 1061-8600 (2012) [Refereed Article]

Copyright Statement

2011 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

DOI: doi:10.1198/jcgs.2010.08135


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.

Item Details

Item Type:Refereed Article
Keywords:autocorrelation, goodness of fit, nonstationary, probability integral transformation, residuals
Research Division:Agricultural, Veterinary and Food Sciences
Research Group:Agricultural biotechnology
Research Field:Agricultural biotechnology not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Foster, S (Dr Scott Foster)
UTAS Author:Bravington, M (Dr Mark Bravington)
ID Code:119803
Year Published:2012
Web of Science® Times Cited:2
Deposited By:Ecology and Biodiversity
Deposited On:2017-08-04
Last Modified:2017-10-27

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