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Tekrarlanan ölçümlerde farklı kovaryans yapılarının Bayes yöntemi ile modellenmesi

Year 2023, , 611 - 626, 05.01.2024
https://doi.org/10.20289/zfdergi.1341393

Abstract

Amaç: Bu çalışma, tekrarlı ölçümlerde farklı kovaryans yapılarını Bayes analiz yöntemleriyle modelleyerek çözümler elde etmeyi ve bunun hayvan bilimindeki verilere uygulanabilirliğini göstermeyi amaçlamaktadır.
Materyal ve Yöntem: Bu makalede sütten kesilmiş 8 aylık 4154 kuzunun canlı ağırlık verileri analiz edilmiştir. Karma etki modeline dayalı tekrarlı ölçüm analizleri Bayes yöntemleri ile değerlendirilmiştir. 12 farklı kovaryans yapısı için modeller oluşturulmuştur. Model karşılaştırma kriteri olarak, verilerin modele uyumu ile modelin karmaşıklığı arasındaki ilişkiye dayalı Sapma Bilgi Kriterleri kullanılmıştır.
Araştırma Bulguları: 12 farklı kovaryans yapısı arasından yapılandırılmamış kovaryans yapısının bu çalışmanın verilerine uygun yapı olduğu belirlendi.
Sonuç: Tekrarlanan ölçüm verilerinde vücut ağırlığı gibi çeşitli varyans-kovaryans yapılarının kolaylıkla modellenebileceği gösterilmiştir. Karmaşık ve hesaplama zorlukları ve derin kodlama bilgisi gerektiren PROC MCMC yöntemleri yerine, nispeten kullanıcı dostu ve hızlı bir prosedür, teorik yapısıyla birlikte sunuldu ve uygulanabilirliği gösterildi. Literatür taraması sonucunda bu, Bayes yöntemlerin çok çeşitli varyans-kovaryans yapı modellerini çözdüğü ilk çalışmadır.

Thanks

Şekilsel düzenlemeler ve format ayarlarında verdiği desteğinden dolayı yüksek makine mühendisi Erkan Yardibi'ye teşekkür ederiz.

References

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  • Başar, E.K. & M.Z. Fırat, 2016. Comparison of Methods of Estimating Variance Components In Nested Designs. Anadolu University Journal of Science and Technology B-Theoretical Sciences, 4 (1): 1-10.
  • Blasco, A. & P.D.A. Blasco, 2017. Bayesian Data Analysis for Animal Scientists (Vol. 265). Springer, New York NY, USA, 293 pp.
  • Calus, M.P.L., M.E. Goddard, Y.C.J. Wientjes, P.J. Bowman & B.J. Hayes, 2018. Multibreed genomic prediction using multitrait genomic residual maximum likelihood and multitask Bayesian variable selection. Journal of Dairy Science, 101 (5): 4279-4294.
  • Chen, F., G. Brown & M. Stokes, 2016. “Fitting your favorite mixed models with PROC MCMC”. Proceedings of the SAS Global Forum 2016 Conference. Cary, NC: SAS Institute, Inc., 27 pp.
  • Cnaan, A., N.M. Laird, & P. Slasor, 1997. Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. Statistics in Medicine, 16 (20): 2349-2380.
  • de Villemereuil, P., 2019. On the relevance of Bayesian statistics and MCMC for animal models. Journal of Animal Breeding and Genetics, 136 (5): 339-340.
  • Eyduran, E. & Y. Akbaş, 2010. Comparison of different covariance structure used for experimental design with repeated measurement. The Journal of Animal & Plant Sciences, 20 (1): 44-51.
  • Fikse, W.F., R. Rekaya & K.A. Weigel, 2003. Genotype× environment interaction for milk production in Guernsey cattle. Journal of Dairy Science, 86 (5): 1821-1827.
  • Fitzmaurice, G.M., N.M. Laird & J.H. Ware, 2012. Applied Longitudinal Analysis. 2nd Ed. John Wiley & Sons, Boston, MA, 752 pp.
  • François, O. & G. Laval, 2011. Deviance information criteria for model selection in approximate Bayesian computation. Statistical Applications in Genetics and Molecular Biology, 10 (1): 33.
  • Gevrekçi, Y. & Y. Akbaş, 2014. Calving ease analysis as a threshold trait. Ege Üniversitesi Ziraat Fakültesi Dergisi, 51 (3): 237-241.
  • Gomez, E.V., G.B. Schaalje & G.W. Fellingham, 2005. Performance of the Kenward-Roger method when the covariance structure is selected using AIC and BIC. Communications in Statistics-Simulation and Computation®, 34 (2): 377-392.
  • Holand, A.M., I. Steinsland, S. Martino & H. Jensen, 2013. Animal models and integrated nested Laplace approximations. G3: Genes, Genomes, Genetics, 3 (8): 1241-1251.
  • Legarra, A., P. López-Romero & E. Ugarte, 2005. Bayesian model selection of contemporary groups for BLUP genetic evaluation in Latxa dairy sheep. Livestock Production Science, 93 (3): 205-212.
  • Lemoine, N.P., 2019. Moving beyond noninformative priors: Why and how to choose weakly informative priors in Bayesian analyses. Oikos, 128 (7): 912-928.
  • Littell, R.C., P.R. Henry & C.B. Ammerman, 1998. Statistical analysis of repeated measures data using SAS procedures. Journal of Animal Science, 76 (4): 1216-1231.
  • Lunn, D., C. Jackson, N. Best, A. Thomas & D. Spiegelhalter, 2012. The BUGS book: A practical introduction to Bayesian analysis. CRC press, FL, 381 pp.
  • McNeish, D., 2016. On using Bayesian methods to address small sample problems. Structural Equation Modeling: A Multidisciplinary Journal, 23 (5): 750-773.
  • McNeish, D., 2017. Fitting residual error structures for growth models in SAS PROC MCMC. Educational and Psychological Measurement, 77 (4): 587-612.
  • Milkevych, V., P. Madsen, H. Gao & J. Jensen, 2021. The relative effect of genomic information on efficiency of Bayesian analysis of the mixed linear model with unknown variance. Journal of Animal Breeding and Genetics, 138 (1): 14-22.
  • Rekaya, R., K.A. Weigel & D. Gianola, 2003. Bayesian estimation of parameters of a structural model for genetic covariances between milk yield in five regions of the United States. Journal of Dairy Science, 86 (5): 1837-1844.
  • SAS Institute, 2019. The BGLIMM procedure. SAS/STAT 15.2User’s Guide file online. SAS Institute. (Web page: https://support.sas.com/documentation/onlinedoc/stat/151/bglimm.pdf) (Date accessed: June, 2023)
  • Schuurman, N.K., R. Grasman &E.L. Hamaker, 2016. A comparison of inverse-wishart prior specifications for covariance matrices in multilevel autoregressive models. Multivariate Behavioral Research, 51 (2-3): 185-206.
  • Schwarz, G.,1978. Estimating the dimension of a model. The Annals of Statistics, 6 (2): 461-464.
  • Shi, A. & F. Chen, 2019. SAS 3042-2019 Introducing the BGLIMM Procedure for Bayesian Generalized Linear Mixed Models. SAS Institute. (Web page: https://api.semanticscholar.org/CorpusID:164212666) (Date accessed: June, 2023)
  • Sorensen, D., D. Gianola & D. Gianola, 2002. Likelihood, Bayesian and MCMC Methods In Quantitative Genetics. Springer, New York. NY, 740 pp.
  • Spiegelhalter, D.J., N.G. Best, B.P. Carlin & A. Van Der Linde, 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series b (Statistical Methodology), 64 (4): 583-639.
  • Theobald, C.M., M.Z. Firat & R. Thompson, 1997. Gibbs sampling, adaptive rejection sampling and robustness to prior specification for a mixed linear model. Genetics Selection Evolution, 29 (1): 57-72.
  • Verbeke, G. & G. Molenberghs, 2012. Linear Mixed Models in Practice: A SAS-Oriented Approach (Vol. 126). Springer Science & Business Media, NY, 63 pp
  • Verbeke, G., G. Molenberghs & G. Verbeke, 1997. Linear Mixed Models for Longitudinal Data. Springer, New York, NY, 570 pp.
  • Yomi-Owojori, T.O., N.O. Afolabi, A.H. Ekong & B.N. Okafor, 2020. Bayesian Approach on the Effect of Different Covariance Structures on Repeated Measures Data. Benin Journal of Statistics, 3: 101-115.

Modeling of different covariance structures with the Bayesian method in repeated measurements

Year 2023, , 611 - 626, 05.01.2024
https://doi.org/10.20289/zfdergi.1341393

Abstract

Objective: The objective of this study was to obtain solutions by modeling different covariance structures with Bayesian analysis methods in repeated measurement and to show its applicability to data in animal science.
Materials and Methods: This article focused on the analysis of the body weight data of 4154 weaned 8-month-old lambs. Repeated measurement analyses based on the mixed effect model were evaluated with Bayesian methods. Models were created for 12 different covariance structures. As the model comparison criterion, Deviation Information Criteria based on the relationship between the fit of the data to the model and the complexity of the model were used.
Result: Among 12 different covariance structures, the unstructured covariance structure was determined as a suitable structure for the data of this study.
Conclusions: It was concluded that various variance-covariance structures, such as body weight, can be easily modeled in repeated measurement data. Instead of PROC MCMC methods that require complex and computational difficulties and profound coding knowledge, it was presented a relatively user-friendly and fast procedure with its theoretical structure and demonstrated its feasibility. As a result of the literature review, this is the first study in which Bayesian methods solved a wide variety of variance-covariance structure models.

References

  • Akaike, H., 1973. “Information theory and an extension of the maximum-likelihood principle, 267-281”. Proceedings of the Second International Symposium on Information Theory (Eds. B. N. Petrov & F. Caski), Akademiai Kiado, Budapest, Hungary.
  • Başar, E.K. & M.Z. Fırat, 2016. Comparison of Methods of Estimating Variance Components In Nested Designs. Anadolu University Journal of Science and Technology B-Theoretical Sciences, 4 (1): 1-10.
  • Blasco, A. & P.D.A. Blasco, 2017. Bayesian Data Analysis for Animal Scientists (Vol. 265). Springer, New York NY, USA, 293 pp.
  • Calus, M.P.L., M.E. Goddard, Y.C.J. Wientjes, P.J. Bowman & B.J. Hayes, 2018. Multibreed genomic prediction using multitrait genomic residual maximum likelihood and multitask Bayesian variable selection. Journal of Dairy Science, 101 (5): 4279-4294.
  • Chen, F., G. Brown & M. Stokes, 2016. “Fitting your favorite mixed models with PROC MCMC”. Proceedings of the SAS Global Forum 2016 Conference. Cary, NC: SAS Institute, Inc., 27 pp.
  • Cnaan, A., N.M. Laird, & P. Slasor, 1997. Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. Statistics in Medicine, 16 (20): 2349-2380.
  • de Villemereuil, P., 2019. On the relevance of Bayesian statistics and MCMC for animal models. Journal of Animal Breeding and Genetics, 136 (5): 339-340.
  • Eyduran, E. & Y. Akbaş, 2010. Comparison of different covariance structure used for experimental design with repeated measurement. The Journal of Animal & Plant Sciences, 20 (1): 44-51.
  • Fikse, W.F., R. Rekaya & K.A. Weigel, 2003. Genotype× environment interaction for milk production in Guernsey cattle. Journal of Dairy Science, 86 (5): 1821-1827.
  • Fitzmaurice, G.M., N.M. Laird & J.H. Ware, 2012. Applied Longitudinal Analysis. 2nd Ed. John Wiley & Sons, Boston, MA, 752 pp.
  • François, O. & G. Laval, 2011. Deviance information criteria for model selection in approximate Bayesian computation. Statistical Applications in Genetics and Molecular Biology, 10 (1): 33.
  • Gevrekçi, Y. & Y. Akbaş, 2014. Calving ease analysis as a threshold trait. Ege Üniversitesi Ziraat Fakültesi Dergisi, 51 (3): 237-241.
  • Gomez, E.V., G.B. Schaalje & G.W. Fellingham, 2005. Performance of the Kenward-Roger method when the covariance structure is selected using AIC and BIC. Communications in Statistics-Simulation and Computation®, 34 (2): 377-392.
  • Holand, A.M., I. Steinsland, S. Martino & H. Jensen, 2013. Animal models and integrated nested Laplace approximations. G3: Genes, Genomes, Genetics, 3 (8): 1241-1251.
  • Legarra, A., P. López-Romero & E. Ugarte, 2005. Bayesian model selection of contemporary groups for BLUP genetic evaluation in Latxa dairy sheep. Livestock Production Science, 93 (3): 205-212.
  • Lemoine, N.P., 2019. Moving beyond noninformative priors: Why and how to choose weakly informative priors in Bayesian analyses. Oikos, 128 (7): 912-928.
  • Littell, R.C., P.R. Henry & C.B. Ammerman, 1998. Statistical analysis of repeated measures data using SAS procedures. Journal of Animal Science, 76 (4): 1216-1231.
  • Lunn, D., C. Jackson, N. Best, A. Thomas & D. Spiegelhalter, 2012. The BUGS book: A practical introduction to Bayesian analysis. CRC press, FL, 381 pp.
  • McNeish, D., 2016. On using Bayesian methods to address small sample problems. Structural Equation Modeling: A Multidisciplinary Journal, 23 (5): 750-773.
  • McNeish, D., 2017. Fitting residual error structures for growth models in SAS PROC MCMC. Educational and Psychological Measurement, 77 (4): 587-612.
  • Milkevych, V., P. Madsen, H. Gao & J. Jensen, 2021. The relative effect of genomic information on efficiency of Bayesian analysis of the mixed linear model with unknown variance. Journal of Animal Breeding and Genetics, 138 (1): 14-22.
  • Rekaya, R., K.A. Weigel & D. Gianola, 2003. Bayesian estimation of parameters of a structural model for genetic covariances between milk yield in five regions of the United States. Journal of Dairy Science, 86 (5): 1837-1844.
  • SAS Institute, 2019. The BGLIMM procedure. SAS/STAT 15.2User’s Guide file online. SAS Institute. (Web page: https://support.sas.com/documentation/onlinedoc/stat/151/bglimm.pdf) (Date accessed: June, 2023)
  • Schuurman, N.K., R. Grasman &E.L. Hamaker, 2016. A comparison of inverse-wishart prior specifications for covariance matrices in multilevel autoregressive models. Multivariate Behavioral Research, 51 (2-3): 185-206.
  • Schwarz, G.,1978. Estimating the dimension of a model. The Annals of Statistics, 6 (2): 461-464.
  • Shi, A. & F. Chen, 2019. SAS 3042-2019 Introducing the BGLIMM Procedure for Bayesian Generalized Linear Mixed Models. SAS Institute. (Web page: https://api.semanticscholar.org/CorpusID:164212666) (Date accessed: June, 2023)
  • Sorensen, D., D. Gianola & D. Gianola, 2002. Likelihood, Bayesian and MCMC Methods In Quantitative Genetics. Springer, New York. NY, 740 pp.
  • Spiegelhalter, D.J., N.G. Best, B.P. Carlin & A. Van Der Linde, 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series b (Statistical Methodology), 64 (4): 583-639.
  • Theobald, C.M., M.Z. Firat & R. Thompson, 1997. Gibbs sampling, adaptive rejection sampling and robustness to prior specification for a mixed linear model. Genetics Selection Evolution, 29 (1): 57-72.
  • Verbeke, G. & G. Molenberghs, 2012. Linear Mixed Models in Practice: A SAS-Oriented Approach (Vol. 126). Springer Science & Business Media, NY, 63 pp
  • Verbeke, G., G. Molenberghs & G. Verbeke, 1997. Linear Mixed Models for Longitudinal Data. Springer, New York, NY, 570 pp.
  • Yomi-Owojori, T.O., N.O. Afolabi, A.H. Ekong & B.N. Okafor, 2020. Bayesian Approach on the Effect of Different Covariance Structures on Repeated Measures Data. Benin Journal of Statistics, 3: 101-115.
There are 32 citations in total.

Details

Primary Language English
Subjects Agricultural Engineering (Other), Sheep and Goat Breeding and Treatment, Zootechny (Other)
Journal Section Articles
Authors

Fatma Yardibi 0000-0001-8852-2708

Mehmet Fırat 0000-0002-0091-4713

Early Pub Date December 28, 2023
Publication Date January 5, 2024
Submission Date August 11, 2023
Acceptance Date December 5, 2023
Published in Issue Year 2023

Cite

APA Yardibi, F., & Fırat, M. (2024). Modeling of different covariance structures with the Bayesian method in repeated measurements. Journal of Agriculture Faculty of Ege University, 60(4), 611-626. https://doi.org/10.20289/zfdergi.1341393

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