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The imputation model consisted of three variables X1, X2, and the WLE in a fully conditional specification (see van Buuren [2007]) to account for the process that created the missing data.
Briefly, a fully conditional specification method was automatically chosen to replace missing data.
Five imputed datasets and their pooled estimates were generated using a fully conditional specified model to handle missing values.
Through a fully conditional specification model, applying linear regression as the prediction method for scale variables and two-way interactions for categorical variables, we generated twenty complete datasets for each of the HRQL-scores with 10 iterations per dataset.
Through a fully conditional specification, applying linear regression as prediction method for variables at scale level, and two-way interaction for categorical variables, we generated M=5 complete imputed datasets with 10 iterations per dataset.
The STAR model is fitted by a fully Bayesian influence approach using a Markov Chain Monte Carlo technique carried out by randomly drawing samples from a fully conditional distribution of blocks of parameters given the rest of parameters and data (Musio et al. 2010).
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As all fully conditional posterior distributions had closed forms, a Gibbs sampler, as discussed in [ 15], was applied to obtain a single chain of 300, 000 iterations for each model fitted.
The precision, or inverse of the variance parameter σ j 2, has an inverse-Gaussian fully conditional posterior distribution leading to following fully conditional expectation for the effect variances σ j 2 : = | β j | λ.
During implementation via a Bayesian MCMC approach, threshold levels were sampled using a Metropolis step because their fully conditional posterior distributions do not have a closed form.
Assuming an univariate model, the fully conditional density of the genetic variance is: which is in the form of a scale inverted chi-square distribution with q (dimension of A) degrees of freedom and scale parameter (a'A -1a), where.
Accordingly, under the Bayesian G-BLUP the degrees of freedom ν of the inverse- χ density do not have a substantial contribution to the fully conditional posterior expectation of the additional genetic variance E (σ u 2 | ⋆ ) = (u ′ G − 1 u + ν τ 2 ) / (ν + N − 2 ), and we therefore set permanently ν = 2, while the scale parameter τ may need data specific tuning.
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