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Bayesian model checking for multivariate outcome data

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  • Crespi, Catherine M.
  • Boscardin, W. John

Abstract

Bayesian models are increasingly used to analyze complex multivariate outcome data. However, diagnostics for such models have not been well developed. We present a diagnostic method of evaluating the fit of Bayesian models for multivariate data based on posterior predictive model checking (PPMC), a technique in which observed data are compared to replicated data generated from model predictions. Most previous work on PPMC has focused on the use of test quantities that are scalar summaries of the data and parameters. However, scalar summaries are unlikely to capture the rich features of multivariate data. We introduce the use of dissimilarity measures for checking Bayesian models for multivariate outcome data. This method has the advantage of checking the fit of the model to the complete data vectors or vector summaries with reduced dimension, providing a comprehensive picture of model fit. An application with longitudinal binary data illustrates the methods.

Suggested Citation

  • Crespi, Catherine M. & Boscardin, W. John, 2009. "Bayesian model checking for multivariate outcome data," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3765-3772, September.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:11:p:3765-3772
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    1. Dipak Dey & Alan Gelfand & Tim Swartz & Pantelis Vlachos, 1998. "A simulation-intensive approach for checking hierarchical models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 325-346, December.
    2. Alex Lewin & Sylvia Richardson & Clare Marshall & Anne Glazier & Tim Aitman, 2006. "Bayesian Modeling of Differential Gene Expression," Biometrics, The International Biometric Society, vol. 62(1), pages 10-18, March.
    3. Catherine M. Crespi & William G. Cumberland & Sally Blower, 2005. "A Queueing Model for Chronic Recurrent Conditions under Panel Observation," Biometrics, The International Biometric Society, vol. 61(1), pages 193-198, March.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    2. Cristina Elisa Orso & Enrico Fabrizi, 2013. "Microcredit and women's empowerment in Bangladesh: a structural equation model for categorical observed variables," DISCE - Quaderni del Dipartimento di Scienze Economiche e Sociali dises1396, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).

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