Bayesian significance testing and multiple comparisons from MCMC outputs
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Andrews, Donald W K, 1994.
"The Large Sample Correspondence between Classical Hypothesis Tests and Bayesian Posterior Odds Tests,"
Econometric Society, vol. 62(5), pages 1207-32, September.
- Donald W.K. Andrews, 1992. "The Large Sample Correspondence Between Classical Hypothesis Tests and Bayesian Posterior Odds Tests," Cowles Foundation Discussion Papers 1035, Cowles Foundation for Research in Economics, Yale University.
- William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
- Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
- 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, vol. 99, pages 314-324, January.
- 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.
- Hoshino, Takahiro, 2008. "A Bayesian propensity score adjustment for latent variable modeling and MCMC algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1413-1429, January.
- Welsch, Roy E., 1977. "Tables for stepwise multiple comparison procedures," Working papers 949-77., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Takahiro Hoshino & Hiroshi Kurata & Kazuo Shigemasu, 2006. "A Propensity Score Adjustment for Multiple Group Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 691-712, December.
- K. Jöreskog, 1971. "Simultaneous factor analysis in several populations," Psychometrika, Springer;The Psychometric Society, vol. 36(4), pages 409-426, December.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3543-3559. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.