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Experiences With Markov Chain Monte Carlo Convergence Assessment in Two Psychometric Examples

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  • Sandip Sinharay

Abstract

There is an increasing use of Markov chain Monte Carlo (MCMC) algorithms for fitting statistical models in psychometrics, especially in situations where the traditional estimation techniques are very difficult to apply. One of the disadvantages of using an MCMC algorithm is that it is not straightforward to determine the convergence of the algorithm. Using the output of an MCMC algorithm that has not converged may lead to incorrect inferences on the problem at hand. The convergence is not one to a point, but that of the distribution of a sequence of generated values to another distribution, and hence is not easy to assess; there is no guaranteed diagnostic tool to determine convergence of an MCMC algorithm in general. This article examines the convergence of MCMC algorithms using a number of convergence diagnostics for two real data examples from psychometrics. Findings from this research have the potential to be useful to researchers using the algorithms. For both the examples, the number of iterations required (suggested by the diagnostics) to be reasonably confident that the MCMC algorithm has converged may be larger than what many practitioners consider to be safe.

Suggested Citation

  • Sandip Sinharay, 2004. "Experiences With Markov Chain Monte Carlo Convergence Assessment in Two Psychometric Examples," Journal of Educational and Behavioral Statistics, , vol. 29(4), pages 461-488, December.
    • Handle: RePEc:sae:jedbes:v:29:y:2004:i:4:p:461-488
    DOI: 10.3102/10769986029004461
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    Cited by:

    1. Federico ANDREIS & Pier Alda FERRARI, 2015. "Customer Satisfaction Evaluation Using Multidimensional Item Response Theory Models," Departmental Working Papers 2015-25, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. Jingguo Wang & Nan Xiao & H. Raghav Rao, 2015. "Research Note—An Exploration of Risk Characteristics of Information Security Threats and Related Public Information Search Behavior," Information Systems Research, INFORMS, vol. 26(3), pages 619-633, September.
    3. Eric F. Lock & Nidhi Kohli & Maitreyee Bose, 2018. "Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 733-750, September.
    4. Federico Andreis & Pier Alda Ferrari, 2014. "Multidimensional item response theory models for dichotomous data in customer satisfaction evaluation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 2044-2055, September.

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