Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers
The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is v...
Saved in:
| Published in | Journal of multivariate analysis Vol. 105; no. 1; pp. 300 - 310 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Elsevier Inc
01.02.2012
Elsevier Taylor & Francis LLC |
| Series | Journal of Multivariate Analysis |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0047-259X 1095-7243 |
| DOI | 10.1016/j.jmva.2011.10.006 |
Cover
| Abstract | The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is vulnerable to potential atypical observations. We present a fully Bayesian approach to the multivariate t linear mixed model (MtLMM), which is a robust extension of MLMM with the random effects and errors jointly distributed as a multivariate t distribution. Owing to the introduction of too many hidden variables in the model, the conventional Markov chain Monte Carlo (MCMC) method may converge painfully slowly and thus fails to provide valid inference. To alleviate this problem, a computationally efficient inverse Bayes formulas (IBF) sampler coupled with the Gibbs scheme, called the IBF-Gibbs sampler, is developed and shown to be effective in drawing samples from the target distributions. The issues related to model determination and Bayesian predictive inference for future values are also investigated. The proposed methodologies are illustrated with a real example from an AIDS clinical trial and a careful simulation study. |
|---|---|
| AbstractList | The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is vulnerable to potential atypical observations. We present a fully Bayesian approach to the multivariate t linear mixed model (MtLMM), which is a robust extension of MLMM with the random effects and errors jointly distributed as a multivariate t distribution. Owing to the introduction of too many hidden variables in the model, the conventional Markov chain Monte Carlo (MCMC) method may converge painfully slowly and thus fails to provide valid inference. To alleviate this problem, a computationally efficient inverse Bayes formulas (IBF) sampler coupled with the Gibbs scheme, called the IBF-Gibbs sampler, is developed and shown to be effective in drawing samples from the target distributions. The issues related to model determination and Bayesian predictive inference for future values are also investigated. The proposed methodologies are illustrated with a real example from an AIDS clinical trial and a careful simulation study. The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is vulnerable to potential atypical observations. We present a fully Bayesian approach to the multivariate t linear mixed model (MtLMM), which is a robust extension of MLMM with the random effects and errors jointly distributed as a multivariate t distribution. Owing to the introduction of too many hidden variables in the model, the conventional Markov chain Monte Carlo (MCMC) method may converge painfully slowly and thus fails to provide valid inference. To alleviate this problem, a computationally efficient inverse Bayes formulas (IBF) sampler coupled with the Gibbs scheme, called the IBF-Gibbs sampler, is developed and shown to be effective in drawing samples from the target distributions. The issues related to model determination and Bayesian predictive inference for future values are also investigated. The proposed methodologies are illustrated with a real example from an AIDS clinical trial and a careful simulation study. [PUBLICATION ABSTRACT] |
| Author | Wang, Wan-Lun Fan, Tsai-Hung |
| Author_xml | – sequence: 1 givenname: Wan-Lun surname: Wang fullname: Wang, Wan-Lun email: wlunwang@fcu.edu.tw organization: Department of Statistics, Feng Chia University, Taichung 40724, Taiwan – sequence: 2 givenname: Tsai-Hung surname: Fan fullname: Fan, Tsai-Hung organization: Graduate Institute of Statistics, National Central University, Jhongli 32001, Taiwan |
| BackLink | http://econpapers.repec.org/article/eeejmvana/v_3a105_3ay_3a2012_3ai_3a1_3ap_3a300-310.htm$$DView record in RePEc |
| BookMark | eNp9UU1v1DAUtKoidVv4A5ws7lme42SdSFxoRT9EJS5U6s16sV_AUeIE27ti_z0OWy4cehg_aTQzen5zyc797Imx9wK2AsTu47AdpgNuSxAiE1uA3RnbCGjrQpWVPGcbgEoVZd0-X7DLGAfIwlpVG0bXeKTo0HP0OB6ji3zu-bQfkztgcJiIJz46Txj45H6T5dNsaYx8H53_wZGbeeqcx-Rmvzofrm9zkuV3rusijzgtI4X4lr3pcYz07mVesafbL99v7ovHb3cPN58fCyPbOhV10_UoKoBG2gobC8JKoYypVW9p10rVqKa3lQKjUKI1YEog1XfYNUQIRl6xD6fcJcy_9hSTHuZ9yB-LuhVlW5WilFn09SQKtJDRS3AThqMmovWGHvVBSxRQ5_eYkW9a5uFWMmPJkABaCtA_05TTmlOaCXOMgXptXPp7jhTQjTrL1ob0oNd0vTa0crmhbC3_s_7b5VXTp5Mpl0AHR0FH48gbsi6QSdrO7jX7H30yrOM |
| CODEN | JMVAAI |
| CitedBy_id | crossref_primary_10_1080_02664763_2015_1014895 crossref_primary_10_3390_e17085353 crossref_primary_10_1007_s00180_015_0620_8 crossref_primary_10_1080_03610918_2019_1694153 crossref_primary_10_1186_s13063_022_06983_6 crossref_primary_10_1002_sim_6788 crossref_primary_10_1111_anzs_12229 crossref_primary_10_1111_rssc_12405 crossref_primary_10_1111_biom_12201 crossref_primary_10_1002_bimj_202000015 crossref_primary_10_1002_bimj_201200001 crossref_primary_10_1002_sim_8554 crossref_primary_10_1002_sim_6144 crossref_primary_10_1177_1471082X13480283 crossref_primary_10_3390_e17096481 crossref_primary_10_1080_00949655_2020_1812608 crossref_primary_10_1080_10543406_2014_920660 crossref_primary_10_1080_10543406_2020_1852246 crossref_primary_10_1002_cjs_11338 crossref_primary_10_1007_s00180_022_01280_x |
| Cites_doi | 10.1002/sim.1885 10.1016/0047-259X(73)90030-4 10.1016/j.jspi.2005.12.010 10.1109/TPAMI.1984.4767596 10.1080/00031305.1995.10476177 10.2307/2986121 10.1080/10618600.1998.10474787 10.1080/01621459.1990.10476213 10.1016/j.csda.2009.11.021 10.1080/01621459.1990.10474968 10.1002/(SICI)1097-0258(19970215)16:3<259::AID-SIM484>3.0.CO;2-S 10.1002/sim.2384 10.1016/j.csda.2004.12.006 10.1093/biomet/57.1.97 10.1080/01621459.1997.10474030 10.1111/j.0006-341X.2002.00742.x 10.1198/106186002760180608 10.1002/bimj.200900184 10.1111/j.1467-9574.2007.00345.x 10.1056/NEJM199610103351501 10.5705/ss.2009.306 10.2307/2529876 10.1186/1297-9686-35-6-489 10.1198/10618600152628059 10.1002/sim.3026 10.1111/1467-9868.00353 10.1023/A:1008853808677 10.1002/bimj.200510192 10.1016/S0167-7152(03)00044-0 |
| ContentType | Journal Article |
| Copyright | 2011 Elsevier Inc. Copyright Taylor & Francis Group Feb 2012 |
| Copyright_xml | – notice: 2011 Elsevier Inc. – notice: Copyright Taylor & Francis Group Feb 2012 |
| DBID | 6I. AAFTH AAYXX CITATION DKI X2L JQ2 |
| DOI | 10.1016/j.jmva.2011.10.006 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef RePEc IDEAS RePEc ProQuest Computer Science Collection |
| DatabaseTitle | CrossRef ProQuest Computer Science Collection |
| DatabaseTitleList | ProQuest Computer Science Collection |
| Database_xml | – sequence: 1 dbid: DKI name: RePEc IDEAS url: http://ideas.repec.org/ sourceTypes: Index Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1095-7243 |
| EndPage | 310 |
| ExternalDocumentID | 2549313361 eeejmvana_v_3a105_3ay_3a2012_3ai_3a1_3ap_3a300_310_htm 10_1016_j_jmva_2011_10_006 S0047259X11002016 |
| Genre | Feature |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 0SF 1B1 1RT 1~. 1~5 29L 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN 9JO AAAKF AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO AAYJJ ABAOU ABEFU ABFNM ABIVO ABJNI ABMAC ABUCO ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACIWK ACNCT ACRLP ADBBV ADEZE ADFGL ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ APLSM ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CAG COF CS3 DM4 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HAMUX HVGLF HZ~ IHE IXB J1W KOM LG5 M25 M41 MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. PQQKQ Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSB SSD SSW SSZ T5K TN5 UHS WUQ XFK XOL XPP YHZ ZGI ZMT ZU3 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD 0R 1 8P ABFLS ABPTK ADALY DKI EFJIC G- HZ IPNFZ K M OHM OVS PQEST X X2L Z AGCQF JQ2 |
| ID | FETCH-LOGICAL-c395t-58bfa140083d4a8d01d317cc57fde6937878fd470c7a3adc0c20e7fbab8eea0c3 |
| IEDL.DBID | .~1 |
| ISSN | 0047-259X |
| IngestDate | Wed Aug 13 08:36:18 EDT 2025 Wed Aug 18 03:51:20 EDT 2021 Thu Apr 24 23:06:18 EDT 2025 Wed Oct 01 06:41:28 EDT 2025 Fri Feb 23 02:27:55 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | 91-08 Conditional conjugate priors MCMC 62H12 Hierarchical models Inverse Bayes formulas 62F15 Multivariate longitudinal data |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c395t-58bfa140083d4a8d01d317cc57fde6937878fd470c7a3adc0c20e7fbab8eea0c3 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| OpenAccessLink | https://www.sciencedirect.com/science/article/pii/S0047259X11002016 |
| PQID | 912942123 |
| PQPubID | 27957 |
| PageCount | 11 |
| ParticipantIDs | proquest_journals_912942123 repec_primary_eeejmvana_v_3a105_3ay_3a2012_3ai_3a1_3ap_3a300_310_htm crossref_citationtrail_10_1016_j_jmva_2011_10_006 crossref_primary_10_1016_j_jmva_2011_10_006 elsevier_sciencedirect_doi_10_1016_j_jmva_2011_10_006 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2012-02-01 |
| PublicationDateYYYYMMDD | 2012-02-01 |
| PublicationDate_xml | – month: 02 year: 2012 text: 2012-02-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationSeriesTitle | Journal of Multivariate Analysis |
| PublicationTitle | Journal of multivariate analysis |
| PublicationYear | 2012 |
| Publisher | Elsevier Inc Elsevier Taylor & Francis LLC |
| Publisher_xml | – name: Elsevier Inc – name: Elsevier – name: Taylor & Francis LLC |
| References | Ng (br000115) 1997 Tan, Tian, Ng (br000160) 2003; 13 Chib, Greenberg (br000030) 1995; 49 Kotz, Nadarajah (br000085) 2004 Gelfand, Hills, Racine-Poon, Smith (br000040) 1990; 85 Tian, Tan, Ng (br000180) 2007; 61 Box, Jenkins, Reinsel (br000010) 1994 Hammer, Katzenstein, Hughes, Gundacker, Schooley, Haubrich, Henry, Lederman, Phair, Niu, Hirsch, Merigan (br000060) 1996; 335 Wang, Fan (br000190) 2010; 54 Roy (br000125) 2006; 48 Rubin (br000130) 1987; 82 Song, Zhang, Qu (br000150) 2007; 17 Lin, Lee (br000105) 2008; 27 Tan, Tian, Ng (br000170) 2010 Kizilkaya, Carnier, Albera, Bittante (br000080) 2003; 35 Tian, Tan (br000175) 2003; 62 BarndorR-Nielsen, Schou (br000005) 1973; 3 Pinheiro, Liu, Wu (br000120) 2001; 10 Tan, Tian, Ng (br000165) 2006; 50 Wakefield, Smith, Racine-Poon, Gelfand (br000185) 1994; 43 Brooks, Gelman (br000015) 1998; 7 Hogan, Laird (br000070) 1997; 16 Laird, Ware (br000090) 1982; 38 Lin, Lee (br000095) 2006; 25 Ho, Lin (br000075) 2010; 52 Spiegelhalter, Best, Carlin, Linde (br000155) 2002; 64 Lin, Lee (br000100) 2007; 137 Gelfand, Smith (br000045) 1990; 85 Carlin, Louis (br000020) 2000 Geman, Geman (br000050) 1984; 6 Shah, Laird, Schoenfeld (br000140) 1997; 92 Hastings (br000065) 1970; 57 Song, Davidian, Tsiatis (br000145) 2002; 58 Ljung, Box (br000110) 1980; 7 Wang, Fan (br000195) 2011; 21 Chib, Carlin (br000025) 1999; 9 Fieuws, Verbeke (br000035) 2004; 23 Schafer, Yucel (br000135) 2002; 11 Golub, Van Loan (br000055) 1989 Kotz (10.1016/j.jmva.2011.10.006_br000085) 2004 Laird (10.1016/j.jmva.2011.10.006_br000090) 1982; 38 Gelfand (10.1016/j.jmva.2011.10.006_br000040) 1990; 85 Ho (10.1016/j.jmva.2011.10.006_br000075) 2010; 52 Kizilkaya (10.1016/j.jmva.2011.10.006_br000080) 2003; 35 BarndorR-Nielsen (10.1016/j.jmva.2011.10.006_br000005) 1973; 3 Song (10.1016/j.jmva.2011.10.006_br000150) 2007; 17 Hastings (10.1016/j.jmva.2011.10.006_br000065) 1970; 57 Ljung (10.1016/j.jmva.2011.10.006_br000110) 1980; 7 Shah (10.1016/j.jmva.2011.10.006_br000140) 1997; 92 Rubin (10.1016/j.jmva.2011.10.006_br000130) 1987; 82 Hammer (10.1016/j.jmva.2011.10.006_br000060) 1996; 335 Tian (10.1016/j.jmva.2011.10.006_br000175) 2003; 62 Chib (10.1016/j.jmva.2011.10.006_br000025) 1999; 9 Box (10.1016/j.jmva.2011.10.006_br000010) 1994 Lin (10.1016/j.jmva.2011.10.006_br000100) 2007; 137 Tan (10.1016/j.jmva.2011.10.006_br000165) 2006; 50 Pinheiro (10.1016/j.jmva.2011.10.006_br000120) 2001; 10 Lin (10.1016/j.jmva.2011.10.006_br000105) 2008; 27 Roy (10.1016/j.jmva.2011.10.006_br000125) 2006; 48 Chib (10.1016/j.jmva.2011.10.006_br000030) 1995; 49 Tan (10.1016/j.jmva.2011.10.006_br000170) 2010 Schafer (10.1016/j.jmva.2011.10.006_br000135) 2002; 11 Hogan (10.1016/j.jmva.2011.10.006_br000070) 1997; 16 Song (10.1016/j.jmva.2011.10.006_br000145) 2002; 58 Ng (10.1016/j.jmva.2011.10.006_br000115) 1997 Tian (10.1016/j.jmva.2011.10.006_br000180) 2007; 61 Brooks (10.1016/j.jmva.2011.10.006_br000015) 1998; 7 Lin (10.1016/j.jmva.2011.10.006_br000095) 2006; 25 Wang (10.1016/j.jmva.2011.10.006_br000190) 2010; 54 Spiegelhalter (10.1016/j.jmva.2011.10.006_br000155) 2002; 64 Tan (10.1016/j.jmva.2011.10.006_br000160) 2003; 13 Geman (10.1016/j.jmva.2011.10.006_br000050) 1984; 6 Golub (10.1016/j.jmva.2011.10.006_br000055) 1989 Gelfand (10.1016/j.jmva.2011.10.006_br000045) 1990; 85 Fieuws (10.1016/j.jmva.2011.10.006_br000035) 2004; 23 Wang (10.1016/j.jmva.2011.10.006_br000195) 2011; 21 Carlin (10.1016/j.jmva.2011.10.006_br000020) 2000 Wakefield (10.1016/j.jmva.2011.10.006_br000185) 1994; 43 |
| References_xml | – volume: 13 start-page: 625 year: 2003 end-page: 639 ident: br000160 article-title: A noniterative sampling method for computing posteriors in the structure of publication-title: Statist. Sinica – volume: 49 start-page: 327 year: 1995 end-page: 335 ident: br000030 article-title: Understanding the Metropolis–Hastings algorithm publication-title: Amer. Statist. – volume: 3 start-page: 408 year: 1973 end-page: 419 ident: br000005 article-title: On the parameterization of autoregressive models by partial autocorrelations publication-title: J. Multivariate Anal. – volume: 85 start-page: 972 year: 1990 end-page: 985 ident: br000040 article-title: Illustration of Bayesian inference in normal data models using Gibbs sampling publication-title: J. Amer. Statist. Assoc. – volume: 6 start-page: 721 year: 1984 end-page: 741 ident: br000050 article-title: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 35 start-page: 489 year: 2003 end-page: 512 ident: br000080 article-title: Tempelman R: cumulative publication-title: Genet. Sel. Evol. – volume: 137 start-page: 484 year: 2007 end-page: 495 ident: br000100 article-title: Bayesian analysis of hierarchical linear mixed modeling using the multivariate publication-title: J. Statist. Plann. Inference – volume: 61 start-page: 232 year: 2007 end-page: 242 ident: br000180 article-title: An exact noniterative sampling procedure for discrete missing data problem publication-title: Statistica Neerlandica – volume: 43 start-page: 201 year: 1994 end-page: 221 ident: br000185 article-title: Bayesian analysis of linear and non-linear model by using Gibbs sampler publication-title: Appl. Statist. – start-page: 571 year: 1997 end-page: 584 ident: br000115 article-title: Inversion of Bayes formula: exact formulae for unconditional pdf publication-title: Advances in the Theory and Practice in Statistics—A Volume in Honor of Samuel Kotz – volume: 21 start-page: 1857 year: 2011 end-page: 1880 ident: br000195 article-title: Estimation in multivariate publication-title: Statist. Sinica – volume: 38 start-page: 963 year: 1982 end-page: 974 ident: br000090 article-title: Random effects models for longitudinal data publication-title: Biometrics – volume: 82 start-page: 543 year: 1987 end-page: 546 ident: br000130 article-title: A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest: the SIR algorithm, discussion of Tanner and Wong publication-title: J. Amer. Statist. Assoc. – volume: 17 start-page: 929 year: 2007 end-page: 943 ident: br000150 article-title: Maximum likelihood inference in robust linear mixed-effects models using multivariate publication-title: Statist. Sinica – volume: 25 start-page: 1397 year: 2006 end-page: 1412 ident: br000095 article-title: A robust approach to publication-title: Statist. Med. – volume: 48 start-page: 286 year: 2006 end-page: 301 ident: br000125 article-title: Estimating correlation coefficient between two variables with repeated observations using mixed effects model publication-title: Biom. J. – volume: 58 start-page: 742 year: 2002 end-page: 753 ident: br000145 article-title: A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data publication-title: Biometrics – volume: 7 start-page: 434 year: 1998 end-page: 455 ident: br000015 article-title: General methods for monitoring convergence of iterative simulations publication-title: J. Comput. Graph. Statist. – year: 1994 ident: br000010 article-title: Time Series Analysis Forecasting and Control – volume: 23 start-page: 3093 year: 2004 end-page: 3104 ident: br000035 article-title: Joint modelling of multivariate longitudinal profiles: pitfalls of the random-effects approach publication-title: Statist. Med. – volume: 16 start-page: 259 year: 1997 end-page: 272 ident: br000070 article-title: Model-based approaches to analysing incomplete longitudinal and failure time data publication-title: Statist. Med. – volume: 9 start-page: 17 year: 1999 end-page: 26 ident: br000025 article-title: On MCMC sampling in hierarchical models publication-title: Statist. Comput. – year: 2004 ident: br000085 article-title: Multivariate – volume: 7 start-page: 172 year: 1980 end-page: 180 ident: br000110 article-title: Analysis of variance with autocorrelated observations publication-title: Scandinavian J. Statist. – volume: 10 start-page: 249 year: 2001 end-page: 276 ident: br000120 article-title: Efficient algorithms for robust estimation in linear mixed-effects model using the multivariate publication-title: J. Comput. Graph. Statist. – volume: 52 start-page: 449 year: 2010 end-page: 469 ident: br000075 article-title: Robust linear mixed models using the skew publication-title: Biom. J. – volume: 64 start-page: 583 year: 2002 end-page: 639 ident: br000155 article-title: Bayesian measures of model complexity and fit publication-title: J. Roy. Statist. Soc. Ser. B – volume: 62 start-page: 305 year: 2003 end-page: 315 ident: br000175 article-title: Exact statistical solutions using the inverse Bayes formulae publication-title: Statist. Probab. Lett. – volume: 85 start-page: 398 year: 1990 end-page: 409 ident: br000045 article-title: Sampling based approaches to calculate marginal densities publication-title: J. Amer. Statist. Assoc. – volume: 27 start-page: 1490 year: 2008 end-page: 1507 ident: br000105 article-title: Estimation and prediction in linear mixed models with skew normal random effects for longitudinal data publication-title: Statist. Med. – volume: 335 start-page: 1081 year: 1996 end-page: 1090 ident: br000060 article-title: A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 mm publication-title: The New Engl. J. Med. – volume: 50 start-page: 1272 year: 2006 end-page: 1286 ident: br000165 article-title: Hierarchical models for repeated binary data using the IBF sampler publication-title: Comput. Statist. Data. Anal. – year: 2010 ident: br000170 article-title: Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation – year: 2000 ident: br000020 article-title: Bayes and Empirical Bayes Methods for Data Analysis – volume: 57 start-page: 97 year: 1970 end-page: 109 ident: br000065 article-title: Monte Carlo sampling methods using Markov chains and their applications publication-title: Biometrika – volume: 92 start-page: 775 year: 1997 end-page: 779 ident: br000140 article-title: A random-effects model for multiple characteristics with possibly missing data publication-title: J. Amer. Statist. Assoc. – volume: 54 start-page: 1328 year: 2010 end-page: 1341 ident: br000190 article-title: ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors publication-title: Comput. Statist. Data Anal. – volume: 11 start-page: 437 year: 2002 end-page: 457 ident: br000135 article-title: Computational strategies for multivariate linear mixed-effects models with missing values publication-title: J. Comput. Graph. Statist. – year: 1989 ident: br000055 article-title: Matrix Computations – volume: 23 start-page: 3093 year: 2004 ident: 10.1016/j.jmva.2011.10.006_br000035 article-title: Joint modelling of multivariate longitudinal profiles: pitfalls of the random-effects approach publication-title: Statist. Med. doi: 10.1002/sim.1885 – year: 1994 ident: 10.1016/j.jmva.2011.10.006_br000010 – volume: 17 start-page: 929 year: 2007 ident: 10.1016/j.jmva.2011.10.006_br000150 article-title: Maximum likelihood inference in robust linear mixed-effects models using multivariate t distributions publication-title: Statist. Sinica – year: 2010 ident: 10.1016/j.jmva.2011.10.006_br000170 – volume: 7 start-page: 172 year: 1980 ident: 10.1016/j.jmva.2011.10.006_br000110 article-title: Analysis of variance with autocorrelated observations publication-title: Scandinavian J. Statist. – volume: 3 start-page: 408 year: 1973 ident: 10.1016/j.jmva.2011.10.006_br000005 article-title: On the parameterization of autoregressive models by partial autocorrelations publication-title: J. Multivariate Anal. doi: 10.1016/0047-259X(73)90030-4 – volume: 137 start-page: 484 year: 2007 ident: 10.1016/j.jmva.2011.10.006_br000100 article-title: Bayesian analysis of hierarchical linear mixed modeling using the multivariate t distribution publication-title: J. Statist. Plann. Inference doi: 10.1016/j.jspi.2005.12.010 – volume: 6 start-page: 721 year: 1984 ident: 10.1016/j.jmva.2011.10.006_br000050 article-title: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.1984.4767596 – year: 2000 ident: 10.1016/j.jmva.2011.10.006_br000020 – volume: 49 start-page: 327 year: 1995 ident: 10.1016/j.jmva.2011.10.006_br000030 article-title: Understanding the Metropolis–Hastings algorithm publication-title: Amer. Statist. doi: 10.1080/00031305.1995.10476177 – volume: 43 start-page: 201 year: 1994 ident: 10.1016/j.jmva.2011.10.006_br000185 article-title: Bayesian analysis of linear and non-linear model by using Gibbs sampler publication-title: Appl. Statist. doi: 10.2307/2986121 – volume: 7 start-page: 434 year: 1998 ident: 10.1016/j.jmva.2011.10.006_br000015 article-title: General methods for monitoring convergence of iterative simulations publication-title: J. Comput. Graph. Statist. doi: 10.1080/10618600.1998.10474787 – volume: 13 start-page: 625 year: 2003 ident: 10.1016/j.jmva.2011.10.006_br000160 article-title: A noniterative sampling method for computing posteriors in the structure of EM-type algorithms publication-title: Statist. Sinica – volume: 85 start-page: 398 year: 1990 ident: 10.1016/j.jmva.2011.10.006_br000045 article-title: Sampling based approaches to calculate marginal densities publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1990.10476213 – volume: 54 start-page: 1328 year: 2010 ident: 10.1016/j.jmva.2011.10.006_br000190 article-title: ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors publication-title: Comput. Statist. Data Anal. doi: 10.1016/j.csda.2009.11.021 – volume: 85 start-page: 972 year: 1990 ident: 10.1016/j.jmva.2011.10.006_br000040 article-title: Illustration of Bayesian inference in normal data models using Gibbs sampling publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1990.10474968 – year: 1989 ident: 10.1016/j.jmva.2011.10.006_br000055 – volume: 16 start-page: 259 year: 1997 ident: 10.1016/j.jmva.2011.10.006_br000070 article-title: Model-based approaches to analysing incomplete longitudinal and failure time data publication-title: Statist. Med. doi: 10.1002/(SICI)1097-0258(19970215)16:3<259::AID-SIM484>3.0.CO;2-S – volume: 25 start-page: 1397 year: 2006 ident: 10.1016/j.jmva.2011.10.006_br000095 article-title: A robust approach to t linear mixed models applied to multiple sclerosis data publication-title: Statist. Med. doi: 10.1002/sim.2384 – volume: 50 start-page: 1272 year: 2006 ident: 10.1016/j.jmva.2011.10.006_br000165 article-title: Hierarchical models for repeated binary data using the IBF sampler publication-title: Comput. Statist. Data. Anal. doi: 10.1016/j.csda.2004.12.006 – volume: 57 start-page: 97 year: 1970 ident: 10.1016/j.jmva.2011.10.006_br000065 article-title: Monte Carlo sampling methods using Markov chains and their applications publication-title: Biometrika doi: 10.1093/biomet/57.1.97 – volume: 82 start-page: 543 year: 1987 ident: 10.1016/j.jmva.2011.10.006_br000130 article-title: A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest: the SIR algorithm, discussion of Tanner and Wong publication-title: J. Amer. Statist. Assoc. – year: 2004 ident: 10.1016/j.jmva.2011.10.006_br000085 – volume: 92 start-page: 775 year: 1997 ident: 10.1016/j.jmva.2011.10.006_br000140 article-title: A random-effects model for multiple characteristics with possibly missing data publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1997.10474030 – volume: 58 start-page: 742 year: 2002 ident: 10.1016/j.jmva.2011.10.006_br000145 article-title: A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data publication-title: Biometrics doi: 10.1111/j.0006-341X.2002.00742.x – volume: 11 start-page: 437 year: 2002 ident: 10.1016/j.jmva.2011.10.006_br000135 article-title: Computational strategies for multivariate linear mixed-effects models with missing values publication-title: J. Comput. Graph. Statist. doi: 10.1198/106186002760180608 – volume: 52 start-page: 449 year: 2010 ident: 10.1016/j.jmva.2011.10.006_br000075 article-title: Robust linear mixed models using the skew t distribution with application to schizophrenia data publication-title: Biom. J. doi: 10.1002/bimj.200900184 – volume: 61 start-page: 232 year: 2007 ident: 10.1016/j.jmva.2011.10.006_br000180 article-title: An exact noniterative sampling procedure for discrete missing data problem publication-title: Statistica Neerlandica doi: 10.1111/j.1467-9574.2007.00345.x – volume: 335 start-page: 1081 year: 1996 ident: 10.1016/j.jmva.2011.10.006_br000060 article-title: A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 mm−3 publication-title: The New Engl. J. Med. doi: 10.1056/NEJM199610103351501 – volume: 21 start-page: 1857 year: 2011 ident: 10.1016/j.jmva.2011.10.006_br000195 article-title: Estimation in multivariate t linear mixed models for multiple longitudinal data publication-title: Statist. Sinica doi: 10.5705/ss.2009.306 – start-page: 571 year: 1997 ident: 10.1016/j.jmva.2011.10.006_br000115 article-title: Inversion of Bayes formula: exact formulae for unconditional pdf – volume: 38 start-page: 963 year: 1982 ident: 10.1016/j.jmva.2011.10.006_br000090 article-title: Random effects models for longitudinal data publication-title: Biometrics doi: 10.2307/2529876 – volume: 35 start-page: 489 year: 2003 ident: 10.1016/j.jmva.2011.10.006_br000080 article-title: Tempelman R: cumulative t-link threshold models for the genetic analysis of calving ease scores publication-title: Genet. Sel. Evol. doi: 10.1186/1297-9686-35-6-489 – volume: 10 start-page: 249 year: 2001 ident: 10.1016/j.jmva.2011.10.006_br000120 article-title: Efficient algorithms for robust estimation in linear mixed-effects model using the multivariate t distribution publication-title: J. Comput. Graph. Statist. doi: 10.1198/10618600152628059 – volume: 27 start-page: 1490 year: 2008 ident: 10.1016/j.jmva.2011.10.006_br000105 article-title: Estimation and prediction in linear mixed models with skew normal random effects for longitudinal data publication-title: Statist. Med. doi: 10.1002/sim.3026 – volume: 64 start-page: 583 year: 2002 ident: 10.1016/j.jmva.2011.10.006_br000155 article-title: Bayesian measures of model complexity and fit publication-title: J. Roy. Statist. Soc. Ser. B doi: 10.1111/1467-9868.00353 – volume: 9 start-page: 17 year: 1999 ident: 10.1016/j.jmva.2011.10.006_br000025 article-title: On MCMC sampling in hierarchical models publication-title: Statist. Comput. doi: 10.1023/A:1008853808677 – volume: 48 start-page: 286 year: 2006 ident: 10.1016/j.jmva.2011.10.006_br000125 article-title: Estimating correlation coefficient between two variables with repeated observations using mixed effects model publication-title: Biom. J. doi: 10.1002/bimj.200510192 – volume: 62 start-page: 305 year: 2003 ident: 10.1016/j.jmva.2011.10.006_br000175 article-title: Exact statistical solutions using the inverse Bayes formulae publication-title: Statist. Probab. Lett. doi: 10.1016/S0167-7152(03)00044-0 |
| SSID | ssj0011574 |
| Score | 2.0837722 |
| Snippet | The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great... |
| SourceID | proquest repec crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 300 |
| SubjectTerms | Bayesian analysis Conditional conjugate priors Conditional conjugate priors Hierarchical models Inverse Bayes formulas MCMC Multivariate longitudinal data Hierarchical models Inverse Bayes formulas Markov analysis MCMC Monte Carlo simulation Multivariate analysis Multivariate longitudinal data Studies |
| Title | Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers |
| URI | https://dx.doi.org/10.1016/j.jmva.2011.10.006 http://econpapers.repec.org/article/eeejmvana/v_3a105_3ay_3a2012_3ai_3a1_3ap_3a300-310.htm https://www.proquest.com/docview/912942123 |
| Volume | 105 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Baden-Württemberg Complete Freedom Collection (Elsevier) customDbUrl: eissn: 1095-7243 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0011574 issn: 0047-259X databaseCode: GBLVA dateStart: 20110101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals [SCFCJ] customDbUrl: eissn: 1095-7243 dateEnd: 20210930 omitProxy: true ssIdentifier: ssj0011574 issn: 0047-259X databaseCode: AIKHN dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Science Direct customDbUrl: eissn: 1095-7243 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0011574 issn: 0047-259X databaseCode: .~1 dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: ScienceDirect customDbUrl: eissn: 1095-7243 dateEnd: 20211105 omitProxy: true ssIdentifier: ssj0011574 issn: 0047-259X databaseCode: IXB dateStart: 19710401 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: ScienceDirect (Elsevier) customDbUrl: eissn: 1095-7243 dateEnd: 20211105 omitProxy: true ssIdentifier: ssj0011574 issn: 0047-259X databaseCode: ACRLP dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1095-7243 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0011574 issn: 0047-259X databaseCode: AKRWK dateStart: 19710401 isFulltext: true providerName: Library Specific Holdings |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Nb9QwELWq9gIHxKdYCpUP3FBodmPXybHbsuxStScq5WaN7QmkYrerTVjRC7-dmcRZlQM9cLCjWLFlzTgzz_LMsxDvyQMUhOQhMZgXiYKM7GDldOJNQXh87CFHzh2-vDqZX6svpS73xNmQC8NhldH29za9s9ax5ThK83hd15zjqwyB95JJz8iNMe22ohZa0x9_78I8mEumZ2LuGAmKMibO9DFeN8st9DSefYTXv5zTPfB5sME1-ns-aPZUPIngUZ7283sm9nD1XDy-3DGvNi8ETuEOOTFSQqQbkbeV7MIGt7QtJmQpW8nQEjZyWf_CILu7cBrJAfDfJEgSBG2WO31xz8V0RiMF-bl2rpENMJnwpnkprmefvp7Nk3iVQuKzQreJzl0FtJciwBUU5CEdBwIO3mtTBTwhiJKbvArKpN5ABsGnfpKiqRy4HBFSn70S-6vbFb4WkinpUTk18RNmevHgM0JlhTZOg9IYRmI8yND6yDPO1138sENA2Y1luVuWO7eR3Efiw67PumfZePBrPajG_rVWLLmBB_sdDnq08U9tbEGAh0_Fs5E471S7mwAi8ggrsFubAeFQqu-o0IgTetTcSGVNhY8ECSfb7-3yzX9O7lA84oH7gPC3Yr_d_MR3hHdad9Qt6CNxcLq4mF_R2_nFgupFOf0DKJQAuQ |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Nb9QwELVKewAOqHyJpbT4wA2FZhN7nRxpYdlCt6dW2ps1sSeQit2uNumqvfDbmUmcVTnQQw9OJCt2rJlk5o088yzEB_IAOSF5iAxmeaQgJTtYFjpyJic8PnSQIdcOT89Gkwv1faZnW-K4r4XhtMpg-zub3lrr0HMYpHm4rCqu8VWGwPuMSc_IjY0eiR2lE8MR2Kc_mzwPJpPpqJhbSoJ8FipnuiSvy_kaOh7PLsXrf97pDvrcWeES3R0nNN4VzwJ6lJ-7BT4XW7h4IZ5ON9Sr9UuBR3CLXBkpIfCNyKtStnmDa4qLCVrKRjK2hJWcVzfoZXsYTi05A_6nBEmSoGi5VRiPPDka00xefquKopY1MJvwqn4lLsZfz48nUThLIXJprptIZ0UJFEwR4vIKMh8PPSEH57QpPY4Io2QmK70ysTOQgnexS2I0ZQFFhgixS1-L7cXVAt8IyZz0qAqVuISpXhy4lGBZrk2hQWn0AzHsZWhdIBrn8y5-2z6j7NKy3C3LnftI7gPxcTNm2dFs3Pu07lVj__lYLPmBe8ft9Xq04VetbU6Ih7fF04H40qp2swBE5BkWYNc2BQKidL2lRjMmdKu4k9qSGu8JElC2v5r52wcu7r14PDmfntrTk7Mfe-IJv6TLDn8ntpvVNe4T-GmKg_bj_gsGPgBR |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Bayesian+analysis+of+multivariate+t+linear+mixed+models+using+a+combination+of+IBF+and+Gibbs+samplers&rft.jtitle=Journal+of+multivariate+analysis&rft.au=Wang%2C+Wan-Lun&rft.au=Fan%2C+Tsai-Hung&rft.date=2012-02-01&rft.issn=0047-259X&rft.volume=105&rft.issue=1&rft.spage=300&rft.epage=310&rft_id=info:doi/10.1016%2Fj.jmva.2011.10.006&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jmva_2011_10_006 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0047-259X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0047-259X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0047-259X&client=summon |