Full conjugate analysis of normal multiple traits with missing records using a generalized inverted Wishart distribution

Cantet, Rodolfo Juan Carlos; Birchmeier, A. N.; Steibel, Juan P.

doi:10.1186/1297-9686-36-1-49

Cited by 9 publications

(14 citation statements)

References 14 publications

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“…We now describe the priors for all parameters and the likelihood of the data, and then explain the FCG algorithm for multiple traits. In doing so, we follow closely Cantet et al (2004).…”

Section: Statistical Modelmentioning

confidence: 98%

“…To define this distribution, order the data by trait within tree. This allows missing data patterns to be accommodated by an indicator matrix M k (Dominici et al 2000;Cantet et al 2004) having r k rows and r columns, with k = 1, 2, …, K, where K is the number of patterns of missing data in the data set. For example, suppose r = 3.…”

Section: Statistical Modelmentioning

confidence: 99%

“…The parameters of the covariance matrix of y are the elements of the covariance matrices G 0 and R 0 of additive genetic and error effects, respectively. These dispersion parameters are estimated by a Bayesian approach using the FCG algorithm proposed by Dominici et al (2000), which was adapted to a multiple-trait setting by Cantet et al (2004). The algorithm can handle different patterns of observed and "missing" traits more efficiently than can "data augmentation" (Van Tassell and Van Vleck 1996).…”

Section: Statistical Modelmentioning

confidence: 99%

“…The reason for this correlation is that the sampling of the "missing data" (error terms for nonobserved data) and of the (co)variance components depend on each other. To lessen the effect of this correlation, Cantet et al (2004) proposed an MCMC method for estimating covariance matrices of error effects in multiple-trait normal models: the full conjugate Gibbs (FCG) algorithm. This method reaches faster convergence than do the data augmentation procedures of Van Tassell and Van Vleck (1996) by reducing the correlation between sampled missing errors and their covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

“…The goal of this paper is twofold: (1) to apply the FCG algorithm proposed by Cantet et al (2004) to estimate (co)variance components, or functions of them, from multiple-trait individual-tree models with missing records;…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bayesian inference for normal multiple-trait individual-tree models with missing records via full conjugate Gibbs

Cappa¹,

Cantet²

2006

Can. J. For. Res.

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In forest genetics, restricted maximum likelihood (REML) estimation of (co)variance components from normal multiple-trait individual-tree models is affected by the absence of observations in any trait and individual. Missing records affect the form of the distribution of REML estimates of genetics parameters, or of functions of them, and the estimating equations are computationally involved when several traits are analysed. An alternative to REML estimation is a fully Bayesian approach through Markov chain Monte Carlo. The present research describes the use of the full conjugate Gibbs algorithm proposed by Cantet et al. (R.J.C. Cantet, A.N. Birchmeier, and J.P. Steibel. 2004. Genet. Sel. Evol. 36: 49-64) to estimate (co)variance components in multiple-trait individual-tree models. This algorithm converges faster to the marginal posterior densities of the parameters than regular data augmentation from multivariate normal data with missing records. An expression to calculate the deviance information criterion for the selection of linear parameters in normal multiple-trait models is also given. The developments are illustrated by means of data from different crosses of two species of Pinus.Résumé : En génétique forestière, la méthode d'estimation par le maximum de vraisemblance restreinte (REML) des composantes de la variance et de la covariance à partir de modèles normaux à caractères multiples d'arbres individuels est influencée par les observations manquantes pour un caractère ou un individu. Les données manquantes influencent la forme de la distribution des estimations par REML des paramètres génétiques ou des fonctions mathématiques qui les représentent. De plus, les équations d'estimation sont aussi impliquées dans le calcul lorsque plusieurs caractères sont analysés. Une approche bayésienne complète recourrant aux méthodes de Monte Carlo par chaînes de Markov constitue une alternative à la méthode d'estimation par REML. Les auteurs décrivent une utilisation de l'algorithme de Gibbs dans sa version complètement conjuguée, tel que Cantet et al. (R.J.C. Cantet, A.N. Birchmeier et J.P. Steibel. 2004. Genet. Sel. Evol. 36 : 49-64) l'ont proposé, pour estimer les composantes de la variance et de la covariance pour des modèles à caractères multiples d'arbres individuels. Cet algorithme converge plus rapidement vers les densités marginales a posteriori des paramètres que la méthode traditionnelle d'augmentation des données à partir des données normales multivariées comprenant les observations manquantes. Les auteurs fournissent également une équation permettant de calculer le critère d'information de la déviance pour la sélection des paramètres linéaires dans les modèles normaux à caractères multiples. Les développements mathématiques sont illustrés à partir des données provenant de différents croisements chez deux espèces du genre Pinus.[Traduit par la Rédaction] Cappa and Cantet 1285

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“…We now describe the priors for all parameters and the likelihood of the data, and then explain the FCG algorithm for multiple traits. In doing so, we follow closely Cantet et al (2004).…”

Section: Statistical Modelmentioning

confidence: 98%

Section: Statistical Modelmentioning

confidence: 99%

Section: Statistical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian inference for normal multiple-trait individual-tree models with missing records via full conjugate Gibbs

Cappa¹,

Cantet²

2006

Can. J. For. Res.

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Bayesian inference for multi-environment spatial individual-tree models with additive and full-sib family genetic effects for large forest genetic trials

Cappa

Yanchuk

Cartwright

2012

Annals of Forest Science

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& Context The gain in accuracy of breeding values with the use of single trial spatial analysis is well known in forestry. However, spatial analyses methodology for single forest genetic trials must be adapted for use with combined analyses of forest genetic trials across sites. & Aims This paper extends a methodology for spatial analysis of single forest genetic trial to a multi-environment trial (MET) setting. & Methods A two-stage spatial MET approach using an individual-tree model with additive and full-sib family genetic effects was developed. Dispersion parameters were estimated using Bayesian techniques via Gibbs sampling. The procedure is illustrated using height growth data at age 10 from eight large Tsuga heterophylla (Raf.) Sarg. second-generation full-sib progeny trials from two series established across seven sites in British Columbia (Canada) and on one in Washington (USA). & Results The proposed multi-environment spatial mixed model displayed a consistent reduction of the posterior mean and an increase in the precision of error variances σ 2 e À Á than the model with "sets in replicates" or incomplete block alpha designs. Also, the multi-environment spatial model provided an average increase in the posterior means of the narrow-and broad-sense individual-tree heritabilities h 2 N and h 2 B , respectively). No consistent changes were observed in the posterior means of additive genetic correlations (r Ajj′). & Conclusion Although computationally demanding, all dispersion parameters were successfully estimated from the proposed multi-environment spatial individual-tree model using Bayesian techniques via Gibbs sampling. The proposed twostage spatial MET approach produced better results than the commonly used nonspatial MET analysis.

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Inferring Phenotypic Trait Evolution on Large Trees With Many Incomplete Measurements

Hassler

Tolkoff

Allen

et al. 2020

Journal of the American Statistical Association

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Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the taxa to avoid spurious inference. An additional challenge arises as obtaining a full suite of measurements becomes increasingly difficult with increasing taxa. This generally necessitates data imputation or integration, and existing control techniques typically scale poorly as the number of taxa increases. We propose an inference technique that integrates out missing measurements analytically and scales linearly with the number of taxa by using a post-order traversal algorithm under a multivariate Brownian diffusion (MBD) model to characterize trait evolution. We further exploit this technique to extend the MBD model to account for sampling error or nonheritable residual variance. We test these methods to examine mammalian life history traits, prokaryotic genomic and phenotypic traits, and HIV infection traits. We find computational efficiency increases that top two orders-of-magnitude over current best practices. While we focus on the utility of this algorithm in phylogenetic comparative methods, our approach generalizes to solve long-standing challenges in computing the likelihood for matrix-normal and multivariate normal distributions with missing data at scale.

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Full conjugate analysis of normal multiple traits with missing records using a generalized inverted Wishart distribution

Cited by 9 publications

References 14 publications

Bayesian inference for normal multiple-trait individual-tree models with missing records via full conjugate Gibbs

Bayesian inference for normal multiple-trait individual-tree models with missing records via full conjugate Gibbs

Bayesian inference for multi-environment spatial individual-tree models with additive and full-sib family genetic effects for large forest genetic trials

Inferring Phenotypic Trait Evolution on Large Trees With Many Incomplete Measurements

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