Model Checking for Hidden Markov Models

Abstract

Residual analysis is a useful tool for checking lack of fit and for providing insight into model improvement. However, literature on residual analysis and the goodness of fit for hidden Markov models (HMMs) is limited. As HMMs with complex structures are increasingly used to accommodate different types of data, there is a need for further tools to check the validity of models applied to real world data. We review model checking methods for HMMs and develop new methods motivated by a particular case study involving a two-dimensional HMM developed for time series with many null events. We propose new residual analysis and stochastic reconstruction methods, which are adapted from model checking techniques for point process models. We apply the new methods to the case study model and discuss their adequacy. We find that there is not one “best” test for diagnostics but that our new methods have some advantages over previously developed tools. The importance of multiple tests for complex HMMs is highlighted and we use the results of our model checking to provide suggestions for possible improvements to the case study model. Supplementary materials for this article are available online.

Keywords:

• Goodness of fit
• Residual analysis
• Stochastic reconstruction
• Viterbi path
• Zero-inflation

Supplementary Materials

The supplementary materials include contour plots of standardized presence residuals and stochastic reconstruction heatmaps for states 3 and 6–17 in the 17 state HMM to complement those in Figures 8 and 13.

Acknowledgments

We would like to thank the associate editor and two anonymous referees for their insightful comments leading to significant improvements in this article.

Additional information

Funding

This work was supported by the Royal Society of New Zealand Marsden Fund (contract UOO1419). Jiancang Zhuang is partially funded by Grants-in-Aid no. 19H04073 for Scientific Research from the Japan Society for the Promotion of Science.