Mixed Model Methodology and the Box-Cox Theory of Transformations: A Bayesian Approach

Gianola, Daniel; Im, Sungbin; Fernando, Rohan L.; Foulley, JL

doi:10.1007/978-3-642-74487-7_2

Cited by 16 publications

(15 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The correlation of breeding values between transformed and untransformed data was high (BEBES et al 1993;SAVAS et al 1998b). Although the data were normally distributed, the traits evaluated had little biological meaning (BEAUMONT 1992) and were difficult to interpret for most people (GIANOLA et al 1990;SAVAS et al 1999). Retransformation of the data to the raw scale was possible, but it was dangerous to make selection decision on the back-transformed functions of the record (GIANOLA et al 1990).…”

Section: Discussionmentioning

confidence: 99%

Genetic and phenotypic parameters for monthly egg production in White Leghorn hens

Anang

Mielenz

Schüler

2000

J Animal Breeding Genetics

View full text Add to dashboard Cite

This article reports genetic and phenotypic parameters of monthly egg production and the influence of Box-Cox transformation on the parameters from a population of White Leghorns, selected for feed efficiency. A total of 6450 daughters of 180 sires and 1335 dams were analysed by restricted maximum likelihood (REML) using a multivariate animal model. The traits considered were monthly egg productions, cumulative production of the first 5 months (S5), cumulative production of first 10 months (S10), and survivor egg production in the first cycle (S12). Two sets of data were analysed: the original data and with the Box-Cox method transformed data. The results indicated that there were no great differences in the estimates between untransformed and transformed data. The estimates of heritability for monthly egg production were high for the first period, decreased to reach the lowest during peak production, and increased to the end of lay. The estimates of heritability for cumulative records were generally higher than monthly records. Genetic and phenotypic correlations among monthly egg production totals were generally high for contiguous periods and then decreased as the interval between months increased. The highest genetic correlation between monthly records and S5 was for the second month of production, whereas the correlations between monthly production totals and S10 and S12 reached their peak at the sixth and eighth months of production, respectively. Zusammenfassung Genetische und phä notypische Parameter fü r die monatliche Legeleistung der Rasse Weißes LeghornDas Ziel der Untersuchung bestand in der Schätzung genetischer und phänotypischer Parameter fü r die monatliche Legeleistung bei Legehennen. Insgesamt 6450 Hennen der Rasse Weißes Leghorn, selektiert auf Futterverzehr, welche von 180 Vätern und 1335 Mü ttern abstammen, wurden mit einem Tiermodell unter Verwendung der REML-Methode analysiert. In die Auswertung gingen folgende Merkmale ein: monatliche Legeleistungen, akkumulierte Legeleistungen vom ersten bis fü nften Monat (S5), vom ersten bis zehnten Monat (S10), und eine Gesamtleistung (S12) im ersten Zyklus der Legephase. Zwei Datensätze wurden analysiert: die Originaldaten und die mit der Box-Cox-Methode transformierten Daten. Die Ergebnisse zeigten nur geringfü gige Differenzen zwischen den Schätzungen mit untransformierten und transformierten Daten. Die Heritabilität war im ersten Monat hoch, verringerte sich bis zum dritten Monat und stieg zum Ende der Eiproduktion wieder an. Die Heritabilitäten der kumulativen Leistungen waren hö her als die der monatlichen Leistungen. Die genetischen und phänotypischen Korrelationen zwischen benachbarten monatlichen Legeleistungen waren generell hoch. Die hö chsten genetischen Korrelationen zwischen den monatlichen und den kumulativen Legeleistungen S5, S10 bzw. S12 ergaben sich im zweiten, im siebenten bzw. im achten Monat. U.S.

show abstract

Section: Discussionmentioning

confidence: 99%

Genetic and phenotypic parameters for monthly egg production in White Leghorn hens

Anang

Mielenz

Schüler

2000

J Animal Breeding Genetics

View full text Add to dashboard Cite

show abstract

“…Andrews et al (1971) extended the transformation theory to multivariate models by introducing a vector of parameters, one for each of the response variables. Sakia (1990), Gianola et al (1990) and Solomon and Taylor (1999) studied approaches to transformations for simple variance component models. Oberg and Davidian (2000) extended the methods for estimating transformations to non-linear mixed effects models for repeated measurement data, employing the transform-both-sides model that was proposed by Carroll and Ruppert (1984).…”

Section: Literature Reviewmentioning

confidence: 99%

Extending the Box–Cox Transformation to the Linear Mixed Model

Gurka

Edwards

Muller

et al. 2005

Journal of the Royal Statistical Society Series A: Statistics in Society

108

View full text Add to dashboard Cite

For a univariate linear model, the Box-Cox method helps to choose a response transformation to ensure the validity of a Gaussian distribution and related assumptions. The desire to extend the method to a linear mixed model raises many vexing questions. Most importantly, how do the distributions of the "two" sources of randomness (pure error and random effects) interact in determining the validity of assumptions? For an otherwise valid model, we prove that the success of a transformation may be judged solely in terms of how closely the "total error" follows a Gaussian distribution. Hence the approach avoids the complexity of separately evaluating pure errors and random effects. The extension of the transformation to the mixed model requires an exploration of its potential effect on estimation and inference of the model parameters. Analysis of longitudinal pulmonary function data and Monte Carlo simulations illustrate the methodology discussed. Copyright 2005 Royal Statistical Society.

show abstract

“…Os efeitos residuais foram assumidos como sendo normalmente distribuídos. Usando essas pressuposições, a equação de modelo mistos produz soluções BLUE e BLUP para efeitos fixos e aleatórios, respectivamente, considerando que as variâncias são conhecidas (Gianola & Fernando, 1986;Gianola et al, 1990).…”

Section: Methodsunclassified

Estimação de parâmetros genéticos em suínos usando Amostrador de Gibbs

Barbosa¹,

Lopes²,

Regazzi³

et al. 2008

R. Bras. Zootec.

View full text Add to dashboard Cite

RESUMO -Um total de 38.865 registros de animais da raça Large White foi usado para estimar componentes de co-variância e parâmetros genéticos das características idade ao atingir 100 kg de peso vivo (IDA) e espessura de toucinho ajustada para 100 kg de peso vivo (ET), em análises bicaracterísticas. Para obtenção dos componentes de co-variância, foi utilizado o Amostrador de Gibbs por meio do programa MTGSAM. O modelo misto utilizado continha efeito fixo de grupo contemporâneo e os seguintes efeitos aleatórios: efeito genético aditivo direto, efeito genético aditivo materno, efeito comum de leitegada e efeito residual. As médias das estimativas de herdabilidade aditivas diretas foram 0,33 e 0,44 para IDA e ET, respectivamente. As médias das estimativas do efeito comum de leitegada foram 0,09 e 0,02 para IDA e ET, respectivamente. A estimativa de correlação genética aditiva entre as características foi próxima de zero (-0,015). As herdabilidades obtidas para as características de desempenho avaliadas indicam que ganhos genéticos satisfatórios podem ser obtidos no melhoramento de suínos da raça Large White para essas características e que a seleção simultânea para ambas as características pode ser realizada, uma vez que é baixa a correlação genética aditiva direta.Palavras-chave: análise bayesiana, desempenho, espessura de toucinho, herdabilidade, idade, intervalo de alta densidade Estimation of genetic parameters for growth and backfat thickness of LargeWhite pigs using the Gibbs Sampler ABSTRACT -Data consisting of 38,865 records of Large White pigs were used to estimate genetic parameters for days to 100 kg (DAYS) and backfat thickness adjusted to 100 kg (BF). Covariance components were estimated by a bivariate mixed model including the fixed effect of contemporary group and the direct and maternal additive genetic, common litter and residual random effects using the Gibbs Sampling algorithm of the MTGSAM program. Estimates of direct and common litter effects for DAYS and BF were 0.33 and 0.44 and 0.09 and 0.02, respectively. Additive genetic correlation between DAYS and BF was close to zero (-0.015). The heritability estimates indicate that genetic gains may be obtained by selection and that both traits should be considered in a breeding program for the Large White breed.Key Words: age, backfat thickness, Bayesian analysis, heritability, high density interval, performance IntroduçãoEm um programa de melhoramento genético, a seleção é o principal método utilizado para a escolha dos melhores animais para reprodução. A eficiência desta seleção, intimamente relacionada ao progresso genético a ser obtido, baseia-se na utilização de critérios adequados de avaliação dos animais que aproxime o máximo possível do resultado obtido com os verdadeiros valores genéticos dos animais (Costa et al., 2001).A avaliação genética depende da disponibilidade de estimativas de parâmetros genéticos acuradas para as características de maior interesse. A acurácia da estimativa desses parâmetros depende de um conjunto de fatores, entre e...

show abstract

Mixed Model Methodology and the Box-Cox Theory of Transformations: A Bayesian Approach

Cited by 16 publications

References 29 publications

Genetic and phenotypic parameters for monthly egg production in White Leghorn hens

Genetic and phenotypic parameters for monthly egg production in White Leghorn hens

Extending the Box–Cox Transformation to the Linear Mixed Model

Estimação de parâmetros genéticos em suínos usando Amostrador de Gibbs

Contact Info

Product

Resources

About