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Graphical diagnostics for Markov models for categorical data

journal contribution
posted on 2023-05-19, 09:18 authored by Scott FosterScott Foster, Bravington, M
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.

History

Publication title

Journal of Computational and Graphical Statistics

Volume

20

Pagination

355-374

ISSN

1061-8600

Department/School

Institute for Marine and Antarctic Studies

Publisher

Amer Statistical Assoc

Place of publication

1429 Duke St, Alexandria, USA, Va, 22314

Rights statement

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

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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