Bayesian Analysis of Binary and Polychotomous Response Data

Albert, James H.; Chib, Siddhartha

doi:10.2307/2290350

Cited by 1,425 publications

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“…Note that this notation accommodates for the possibility of missing observations in one or more categories [1].…”

Section: Fully Conditional Distributionsmentioning

confidence: 99%

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A bivariate quantitative genetic model for a threshold trait and a survival trait

Damgaard¹,

Korsgaard²

2006

Genet. Sel. Evol.

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-Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.bivariate genetic model / survival trait / ordered categorical trait / Bayesian analysis

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“…Note that this notation accommodates for the possibility of missing observations in one or more categories [1].…”

Section: Fully Conditional Distributionsmentioning

confidence: 99%

“…Records of both traits were generated for 6000 animals after 100 unrelated sires each having 60 offspring (balanced half-sib design) using the bivariate model (1). The number of categories for the threshold character was three with observed frequencies; 1: (32%), 2: (45%) and 3: (23%).…”

Section: Simulation Studymentioning

confidence: 99%

A bivariate quantitative genetic model for a threshold trait and a survival trait

Damgaard¹,

Korsgaard²

2006

Genet. Sel. Evol.

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“…A t-distribution may again be expressed as a scale mixture of normals with λ t ∼ IG(ν/2, ν/2). An approximative logit model is then obtained with ν = 8 (Albert and Chib (1993)). …”

Section: Binary Response Modelsmentioning

confidence: 99%

“…Bayesian inference is based on latent utility representations of binary regression models, see Albert and Chib (1993) for probit models and Holmes and Knorr-Held (2003) for logit models. The advantage of augmenting the data by latent utilities is that the full conditionals of unknown parameters are Gaussian and efficient MCMC sampling schemes developed for Gaussian responses can be exploited.…”

Section: Introductionmentioning

confidence: 99%

Locally Adaptive Function Estimation for Binary Regression Models

Jerak

Lang

2005

Biom. J.

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In this paper we present a nonparametric Bayesian approach for fitting unsmooth or highly oscillating functions in regression models with binary responses. The approach extends previous work by Lang et al. (2002) for Gaussian responses. Nonlinear functions are modelled by first or second order random walk priors with locally varying variances or smoothing parameters. Estimation is fully Bayesian and uses latent utility representations of binary regression models for efficient block sampling from the full conditionals of nonlinear functions.

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“…The joint posterior density of θ, σ 2 s , and σ 2 u , given the true data, was obtained as follows: The joint posterior density in equation (13) was augmented with the liabilities for all observations in the data set. All conditional posterior distributions of model parameters were in closed form as described by Albert and Chib [1] and Sorensen et al [12]. These distributions were normal for the location parameters, truncated normal for each of the liabilities and scaled-inverted chi-square distributions for the dispersion parameters.…”

Section: Application To First Insemination Success In Beef Cattlementioning

confidence: 99%

A simulation study for the analysis of uncertain binary responses: Application to first insemination success in beef cattle

et al. 2005

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-A simulation was carried out to investigate the methods of analyzing uncertain binary responses for success or failure at first insemination. A linear mixed model that included, herd, year, and month of mating as fixed effects; and unrelated service sire, sire and residual as random effects was used to generate binary data. Binary responses were assigned using the difference between days to calving and average gestation length. Females deviating from average gestation length lead to uncertain binary responses. Thus, the methods investigated were the following: (1) a threshold model fitted to certain (no uncertainty) binary data (M1); (2) a threshold model fitted to uncertain binary data ignoring uncertainty (M2); and (3) analysis of uncertain binary data, accounting for uncertainty from day 16 to 26 (M3) or from day 14 to 28 (M4) after introduction of the bull, using a threshold model with fuzzy logic classification. There was virtually no difference between point estimates obtained from M1, M3, and M4 with true values. When uncertain binary data were analyzed ignoring uncertainty (M2), sire variance and heritability were underestimated by 22 and 24%, respectively. Thus, for noisy binary data, a threshold model contemplating uncertainty is needed to avoid bias when estimating genetic parameters.binary data / fertility / fuzzy logic / simulation / threshold model

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Bayesian Analysis of Binary and Polychotomous Response Data

Cited by 1,425 publications

References 0 publications

A bivariate quantitative genetic model for a threshold trait and a survival trait

A bivariate quantitative genetic model for a threshold trait and a survival trait

Locally Adaptive Function Estimation for Binary Regression Models

A simulation study for the analysis of uncertain binary responses: Application to first insemination success in beef cattle

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