Space-time areal mixture model: relabeling algorithm and model selection issues
With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label‐switching problem is often inherent in Bayesian implementation of mixture models, and a variety of relabeling algorithms...
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| Published in | Environmetrics (London, Ont.) Vol. 25; no. 2; pp. 84 - 96 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
England
Blackwell Publishing Ltd
01.03.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1180-4009 1099-095X 1099-095X |
| DOI | 10.1002/env.2265 |
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| Abstract | With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label‐switching problem is often inherent in Bayesian implementation of mixture models, and a variety of relabeling algorithms have been proposed. We use a space‐time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling. Copyright © 2014 John Wiley & Sons, Ltd. |
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| AbstractList | With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label-switching problem is often inherent in Bayesian implementation of mixture models and a variety of relabeling algorithms have been proposed. We use a space-time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling. With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label-switching problem is often inherent in Bayesian implementation of mixture models, and a variety of relabeling algorithms have been proposed. We use a space-time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling. Copyright copyright 2014 John Wiley & Sons, Ltd. With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label-switching problem is often inherent in Bayesian implementation of mixture models and a variety of relabeling algorithms have been proposed. We use a space-time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling.With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label-switching problem is often inherent in Bayesian implementation of mixture models and a variety of relabeling algorithms have been proposed. We use a space-time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling. With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label‐switching problem is often inherent in Bayesian implementation of mixture models, and a variety of relabeling algorithms have been proposed. We use a space‐time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling. Copyright © 2014 John Wiley & Sons, Ltd. |
| Author | Cai, B. Choi, J. Liu, J. Kirby, R. S. Hossain, M. M. Lawson, A. B. |
| AuthorAffiliation | 2 Division of Biostatistics, Bioinformatics and Epidemiology, Medical University of South Carolina, Charleston, SC, USA 1 Division of Biostatistics and Epidemiology, Cincinnati Children’s Hospital Medical Center, Cincinnati, OH, USA 5 Department of Community and Family Health, University of South Florida, Tampa, FL, USA 3 Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA 4 Department of Mathematics, Hanyang University, South Korea |
| AuthorAffiliation_xml | – name: 3 Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA – name: 5 Department of Community and Family Health, University of South Florida, Tampa, FL, USA – name: 1 Division of Biostatistics and Epidemiology, Cincinnati Children’s Hospital Medical Center, Cincinnati, OH, USA – name: 2 Division of Biostatistics, Bioinformatics and Epidemiology, Medical University of South Carolina, Charleston, SC, USA – name: 4 Department of Mathematics, Hanyang University, South Korea |
| Author_xml | – sequence: 1 givenname: M. M. surname: Hossain fullname: Hossain, M. M. email: md.hossain@cchmc.org organization: Division of Biostatistics and Epidemiology, Cincinnati Children's Hospital Medical Center, OH, Cincinnati, U.S.A – sequence: 2 givenname: A. B. surname: Lawson fullname: Lawson, A. B. organization: Division of Biostatistics, Bioinformatics and Epidemiology, Medical University of South Carolina, SC, Charleston, U.S.A – sequence: 3 givenname: B. surname: Cai fullname: Cai, B. organization: Department of Epidemiology and Biostatistics, University of South Carolina, SC, Columbia, U.S.A – sequence: 4 givenname: J. surname: Choi fullname: Choi, J. organization: Department of Mathematics, Hanyang University, South Korea – sequence: 5 givenname: J. surname: Liu fullname: Liu, J. organization: Department of Epidemiology and Biostatistics, University of South Carolina, SC, Columbia, U.S.A – sequence: 6 givenname: R. S. surname: Kirby fullname: Kirby, R. S. organization: Department of Community and Family Health, University of South Florida, FL, Tampa, U.S.A |
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| Cites_doi | 10.1214/06-BA122 10.1214/aos/1016120364 10.1016/S0169-7161(05)25016-2 10.1111/1467-9469.00242 10.1093/biostatistics/4.1.11 10.1198/106186007X238855 10.1080/01621459.1997.10474013 10.1002/env.599 10.1080/10485250211383 10.1007/s10651-008-0102-z 10.1017/CBO9780511584589.011 10.1007/s10651‐012‐0209‐0 10.1093/biomet/65.1.31 10.1111/1467-9868.00362 10.1111/1467-9868.00095 10.1111/j.1467-9574.2012.00516.x 10.1111/1467-9868.00353 10.1080/01966324.2011.10737798 10.1007/s11222-010-9226-8 10.1214/09-BA414 10.1093/biostatistics/kxm049 10.1016/j.csda.2006.07.020 10.1007/s11222-006-9008-5 10.1093/biomet/85.1.1 10.1002/env.613 10.1214/088342305000000016 10.1214/09-BA403 10.1111/j.1467-9868.2008.00700.x 10.1111/1467-9868.00265 10.1198/016214504000001565 10.1002/sim.3917 10.1080/01621459.1997.10474012 10.1093/biomet/93.4.877 10.1002/1097-0258(20000915/30)19:17/18<2555::AID-SIM587>3.0.CO;2-# 10.1007/BF00116466 10.1191/0962280205sm388oa |
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| References_xml | – reference: Assunção RM. 2003. Space varying coefficient models for small area data. Environmetrics 14: 453-473. – reference: Knorr-Held L. 2000. Bayesian modelling of inseparable space-time variation in disease risk. Statistics in Medicine 19: 2555-2567. – reference: Binder DA. 1981. Approximations to Bayesian clustering rules. The Annals of Statistics 68: 275-285. – reference: McGrory CA, Titterington DM. 2007. Variational approximations in Bayesian model selection for finite mixture distributions. Computational Statistics and Data Analysis 51: 5352-5367. – reference: Rue H, Martino S, Chopin N. 2009. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B 71: 319-392. – reference: Celeux G, Forbes F, Robert C, Titterington M. 2006. Deviance information criteria for missing data models. Bayesian Analysis 1: 651-674. – reference: Best N, Richardson S, Thomson A. 2005. A comparison of Bayesian spatial models for Disease mapping. Statistical Methods in Medical Research 14: 35-59. – reference: Gelman A, Carlin JB, Stern HS, Rubin DB. 2004. Bayesian Data Analysis. Chapmann & hall/CRC: Boca Raton. – reference: Binder DA. 1978. Bayesian cluster analysis. Biometrika 65: 31-38. – reference: Waller LA, Carlin BP, Xia H, Gelfand AE. 1997. Hierarchical spatio temporal-mapping of disease rates. Journal of the American Statistical Association 92: 607-617. – reference: Viallefont V, Richardson S, Green PJ. 2002. Bayesian analysis of Poisson mixtures. Journal of Nonparametric Statistics 14: 181-202. – reference: Plummer M. 2008. Penalized loss functions for Bayesian model comparison. Biostatistics 9: 523-539. – reference: Hastie DI, Green PJ. 2012. Model choice using reversible jump Markov chain Monte Carlo. Statistica Neerlandica 66: 309-338. – reference: Gelfand A, Vounatsou P. 2003. Proper multivariate conditional autoregressive models for spatial data analysis. Biostatistics 4: 11-25. – reference: Ando T. 2012. Predictive Bayesian model selection. American Journal of Mathematical and Management Sciences 31: 13-38. – reference: Fritsch A, Ickstadt K. 2009. Improved criteria for clustering based on the posterior similarity matrix. Bayesian Analysis 4: 367-392. – reference: Hossain MM, Lawson AB. 2010. Space-time Bayesian small area disease risk models: development and evaluation with a focus on cluster detection. Environmental and Ecological Statistics 17: 73-95. – reference: Hossain MM, Lawson AB, Cai B, Choi J, Liu J, Kirby RS. 2012. Space-time stick-breaking processes for small area disease cluster estimation. Environmental and Ecological Statistics. DOI: 10.1007/s10651-012-0209-0 – reference: Fernandez C, Green PJ. 2002. 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| Title | Space-time areal mixture model: relabeling algorithm and model selection issues |
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