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Bayesian significance testing and multiple comparisons from MCMC outputs

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  • Hoshino, Takahiro
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    Abstract

    This article proposes a Bayesian method to directly evaluate and test hypotheses in multiple comparisons. Transformation and integration over the coordinates relevant to the hypothesis are shown to enable us to directly test the hypotheses expressed as a linear equation of a parameter vector, given a linear constraint. When the conditional posterior distribution of the parameter vector we are interested in is the multivariate normal distribution, the proposed method can be applied to calculate the p-value of hypotheses pertaining to the parameters in any complex model such as generalized linear mixed effect models with latent variables, by using outputs from Markov chain Monte Carlo (MCMC) methods. Further, the proposed testing can be implemented without prior information. Some applications are presented, and the simulation results are provided to compare the powers of this method with those of other methods of conventional multiple comparisons. Simulation studies have shown that the proposed method is valid for multiple comparisons under nonequivalent variances and mean comparisons in latent variable modeling with categorical variables.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 52 (2008)
    Issue (Month): 7 (March)
    Pages: 3543-3559

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    Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3543-3559

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    Web page: http://www.elsevier.com/locate/csda

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    1. Welsch, Roy E., 1977. "Tables for stepwise multiple comparison procedures," Working papers 949-77., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer, vol. 58(4), pages 525-543, December.
    3. Takahiro Hoshino & Hiroshi Kurata & Kazuo Shigemasu, 2006. "A Propensity Score Adjustment for Multiple Group Structural Equation Modeling," Psychometrika, Springer, vol. 71(4), pages 691-712, December.
    4. Andrews, Donald W K, 1994. "The Large Sample Correspondence between Classical Hypothesis Tests and Bayesian Posterior Odds Tests," Econometrica, Econometric Society, Econometric Society, vol. 62(5), pages 1207-32, September.
    5. Hoshino, Takahiro, 2008. "A Bayesian propensity score adjustment for latent variable modeling and MCMC algorithm," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(3), pages 1413-1429, January.
    6. Hogan J.W. & Tchernis R., 2004. "Bayesian Factor Analysis for Spatially Correlated Data, With Application to Summarizing Area-Level Material Deprivation From Census Data," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 99, pages 314-324, January.
    7. K. Jöreskog, 1971. "Simultaneous factor analysis in several populations," Psychometrika, Springer, vol. 36(4), pages 409-426, December.
    8. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, Elsevier, vol. 49(1-2), pages 195-238.
    9. D. B. Dunson, 2000. "Bayesian latent variable models for clustered mixed outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 355-366.
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    Cited by:
    1. Marín, J.M. & Rodríguez-Bernal, M.T., 2012. "Multiple hypothesis testing and clustering with mixtures of non-central t-distributions applied in microarray data analysis," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(6), pages 1898-1907.

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