Bayesyen yaklaşımında Genelleştirilmiş Linear Karışık Etkili Model ile Transformasyonun Karşılaştırılması

Linear karışık etkili modeler (LKM), hayvan ıslahı verilerinin neredeyse tüm analizlerinde yaygın olarak kulanılmaktadır. Varyans bileşenleri ile genetik parametrelerin tahmini ve hayvanların genetik değerini belirlemek için çok güçlü araçlardır. Bu modeler normallik varsayımı ve varyansların sabitliği gibi bazı varsayımlar sağlandığında kullanılabilen modellerdir. Ancak bu varsayımlar sağlanmazsa veriler transforme edilip analize transforme edilmiş verilerle devam edilir. Genelleştirilmiş linear karışık etkili modeller (GLKM) transformasyon olmaksızın normallik varsayımını iligili problemler için çözüm sağlar. Bu, araştırmacıların teorik bağlamda en uygun verileri kullanarak hayvanların uygun şekilde değerlendirilmesini sağlar. Bu çalışmanın amacı; Bayesyen yaklaşımı ile hayvan ıslahında önemli ekonomik değere sahip doğum ağırlığı (DA) ve sütten kesim ağırlığına (SKA) ait verileri transformasyon uygulanmış (LKM_t), transformasyon uygulanmamış (LKM_ut) haliyle LKM ve transforme edilmemiş haliyle GKLM modelleri kullanarak varyans unsurlarını ve genetik parameterini tahminlemektir. Bu çalışma aynı zamanda hem modelleri hem de LKM_t ve GLKM ile elde edilen tahmini parametre değerlerini karşılaştırmayı amaçlamıştır. Analizde kullanılan veri 2012- 2016 yılları arasında doğan 4972 İvesi kuzularından elde edilmiş DA ve SKA’ dan meydana gelmiştir. Sonuç olarak; GLKM model seçme kriteri DIC’ye göre DA ve SKA için en uygun model olarak belirlenmiştir. DA’na ait kalıtım derecesi tahminleri tüm modelerde değişmemesine rağmen SKA’na ait kalıtım derecesi tahminlerinde önemli farklılıklar vardır.

Generalized Linear Mixed Model versus Transformation on Bayesian Approach

Linear mixed effects models (LMM) have been widely used for nearly all analysis of animal breedingdata. They are very powerful tools for the estimation of variance components and genetic parameters, and forthe prediction of genetic merit of animals. These models can only be used when some specific assumptions areprovided such as normality and constant of variances. However, if these assumptions are not provided, the datashould be transformed and the statistical analysis is carried out with the transformed data. Generalized linearmixed-effect models (GLMM) provide a solution for this problem by satisfying normality assumptions withouttransformation. This allows differences among animals to be assessed properly using the data most appropriateto the researcher's theoretical context. The aim of this study is to estimate variance components, geneticparameter of birth weight (BW), weaning weight (WW) which have economic values in animal breeding withLMM_t (with transformed data), LMM_ut (with untransformed data) and GLMM based on Bayesian approach.The present study also intended to compare the both models and the estimated parameters values obtained withLMM_t and GLMM. The data is obtained from BW and WW of 4972 Awassi lambs were born between theyears of 2012-2016. As a result, GLMM is the most suitable model for BW and WW according to DIC values.Although estimation of BW heritabilities does not change in all models, there are significant differences inestimation of WW heritabilities.

PDF

___

Aparicio A G, Zuki S M, Azpilicueta M M, Barbero F Á, Pastorino M J (2015). Genetic versus environmental contributions to variation in seedling resprouting in Nothofagusobliqua. Tree genetics and genomes. 11(2): 23-28.
Apiolaza L A, Chauhan S S, Walker J C (2011). Genetic control of very early compression and opposite wood in Pinusradiata and its implications for selection. Tree genetics and genomes. 7(3): 563-571.
Barbosa L T, Santos G D B, Muniz E N, Azevedo H C, Fagundes J L (2015). Genetic parameters for growth traits of Santa Inês sheep using Gibbs sampling. Revista Caatinga. 28(4): 211-216.
Cappa E P, Yanchuk A D, Cartwright C V (2012). Bayesian inference for multi-environment spatial individualtree models with additive and full-sib family genetic effects for large forest genetic trials. Annals of forest science. 69(5): 627-640.
Conover W J, Iman R L (1980). The rank transformation as a method of discrimination with some examples. Communications in Statistics, Series A. 9: 465–487.
Conover W J, Iman R L (1981). Rank transformations as a bridge between parametric and nonparametric statistics. The American Statistician. 35(3): 124-129.
Crouse C F (1968). A distribution-free method of analyzing a 2m factorial experiment. South African Statistics Journal. 2: 101–108.
deVillemereuil P (2012). Estimation of a biological trait heritability using the animal model. How to use the MCMCglmm R package. http://devillemereuil.legtux.org/wpcontent/uploads/2012/12/ tuto_en.pdf. (Erişim tarihi: 01 Mart, 2018)
deVillemereuil P, Gimenez O, Doligez B (2013). Comparing parent–offspring regression with frequentist and Bayesian animal models to estimate heritability in wild populations: a simulation study for Gaussian and binary traits. Methods in Ecology and Evolution. 4(3): 260-275.
Hadfield J D (2010). MCMC methods for multi-response generalized linear mixed models: the MCMCglmm R package. J Stat Softw. 33:1–22.
Hamilton B L (1976). A Monte Carlo test of the robustness of parametric and nonparametric analysis of covariance against unequal regression slopes. Journal of the American Statistical Association. 71: 864– 869.
Henderson H V, McCulloch C E (1990). Transfom or Link? https://core.ac.uk/download/pdf /79036775.pdf. (Erişim tarihi: 01 Mart, 2018)
Iman R L, Conover W J (1979). The use of the rank transform in regression. Technometrics. 21: 499–509. Koç T (2012). Genelleştirilmiş Lineer Karma Modeller. Ondokuz Mayıs Ünv., Fen Bil. Enst., YL Tezi. 56 s.
Lemmer H H, Stoker D J (1967). A distribution-free analysis of variance for the two-way classification. South African Statistics Journal. 1: 67–74.
Leys C, Schumann S (2010). A nonparametric method to analyze interactions: The adjusted rank transform test. Journal of Experimental Social Psychology. 46: 684–688.
MacDonald B J, Thompson W A (1967). Rank sum multiple comparisons in one- and two-way classifications. Biometrika. 54: 487–498.
Nelder J A, Wedderburn R W M (1972). Generalized Linear Models. Journal of the Royal Statistical Society. Series A (General). 135 (3): 370-384.
Nordstokke D W, Zumbo B D (2010). A new nonparametric Levene test for equal variances. Psicologica. 31: 401–430.
Quade D (1967). Rank analysis of covariance. Journal of the American Statistical Association. 62: 1187–1200. R development Core Team 2012. A Language and Environment for Statistical Computing. Foundation for Statistical Computing, Vienna, Austria.
Robert C P, Casella G (2004). Monte Carlo statistical methods, 2nd ed., New York: Springer.
Sawilowsky S S (1990). Nonparametric tests of interaction in experimental design. Review of Educational Research. 60: 91–126.
Scheirer C J, Ray W S, Hare N (1976). The analysis of rank data derived from completely randomized factorial designs. Biometrics. 32: 429–434.
Waldmann P, Ericsson T (2006). Comparison of REML and Gibbs sampling estimates of multi-trait genetic parameters in Scots pine. Theoretical and Applied Genetics. 112(8): 1441-1451.
Waldmann P, Hallander J, Hoti F, Sillanpää M J (2008). Efficient Markov chain Monte Carlo implementation of Bayesian analysis of additive and dominance genetic variances in noninbred pedigrees. Genetics. 179(2): 1101-1112.
Willham R L (1972). The Role of Maternal Effects in Animal Breeding: III. Biometrical Aspects of Maternal Effects in Animals. Journal of Animal Science. 35(6): 1288-1293.
Williams D A (1982). Extra-Binomial Variation in Logistic Linear Models. Applied Statistics. 31: 144-148.
Zimmerman D W (1994). Simplified interaction tests for non-normal data in psychological research. British Journal of Mathematical and Statistical Psychology. 47: 327–335.