Hierarchical Bayesian modeling of heterogeneous variances in average daily weight gain of commercial feedlot cattle

Modeling the effects of standardized ileal digestible valine to lysine ratio on growth performance of nursery pigs. Transl Anim Sci 2017;1:448-457. [PMID: 32704668 PMCID: PMC7204984 DOI: 10.2527/tas2017.0049]

Two experiments evaluated the effects of increasing Lys and Val on growth performance of nursery pigs. In Exp. 1,300 nursery pigs (PIC 327 × 1,050, initially 6.7 ± 1.4 kg BW) were randomly allotted to 1 of 6 diets containing 1.10, 1.20, 1.30, 1.40, 1.50, or 1.60% standardized ileal digestible (SID) Lys, with 10 pens per dietary treatment and 5 pigs per pen. Linear and nonlinear mixed models were fitted to estimate dose responses. From d 0 to 14, and for the overall 28 d period, ADG and G:F increased (linear, P < 0.001) as SID Lys increased, with no evidence of differences in ADFI. Dose response modeling indicated the SID Lys requirement for ADG and G:F was at 1.45% using a broken line linear (BLL) and greater than 1.60% using a quadratic polynomial (QP) model. In Exp. 2, 280 nursery pigs (PIC 327 × 1,050, initially 6.5 ± 1.3 kg BW) were allotted to 1 of 7 diets containing SID Val:Lys ratios of 50, 57, 63, 68, 73, 78, or 85%. The dietary SID Lys concentration 1.24% SID Lys which was below the estimated requirement from Exp. 1 and ensured the Val:Lys ratio was not underestimated. From d 0 to 14, ADG, ADFI, and G:F increased (quadratic, P < 0.039) with increasing SID Val:Lys. For ADG, the best fitting model was a BLL, with a breakpoint estimate of 62.9% SID Val:Lys [52.2, 73.7] ratio while for G:F the best fit model was a quadratic polynomial with a maximum G:F at 71.7% SID Val:Lys (95%CI:[58, > 85]). Average daily feed intake was also modeled with a quadratic polynomial and maximized at 73.7% Val:Lys (95% CI: [61, > 85]). In conclusion, the Val requirement ranged from approximately 63 to 74% of Lys depending on the response criteria modeled.

Genomic Prediction Accounting for Residual Heteroskedasticity

Whole-genome prediction (WGP) models that use single-nucleotide polymorphism marker information to predict genetic merit of animals and plants typically assume homogeneous residual variance. However, variability is often heterogeneous across agricultural production systems and may subsequently bias WGP-based inferences. This study extends classical WGP models based on normality, heavy-tailed specifications and variable selection to explicitly account for environmentally-driven residual heteroskedasticity under a hierarchical Bayesian mixed-models framework. WGP models assuming homogeneous or heterogeneous residual variances were fitted to training data generated under simulation scenarios reflecting a gradient of increasing heteroskedasticity. Model fit was based on pseudo-Bayes factors and also on prediction accuracy of genomic breeding values computed on a validation data subset one generation removed from the simulated training dataset. Homogeneous vs. heterogeneous residual variance WGP models were also fitted to two quantitative traits, namely 45-min postmortem carcass temperature and loin muscle pH, recorded in a swine resource population dataset prescreened for high and mild residual heteroskedasticity, respectively. Fit of competing WGP models was compared using pseudo-Bayes factors. Predictive ability, defined as the correlation between predicted and observed phenotypes in validation sets of a five-fold cross-validation was also computed. Heteroskedastic error WGP models showed improved model fit and enhanced prediction accuracy compared to homoskedastic error WGP models although the magnitude of the improvement was small (less than two percentage points net gain in prediction accuracy). Nevertheless, accounting for residual heteroskedasticity did improve accuracy of selection, especially on individuals of extreme genetic merit.

A practical guide and power analysis for GLMMs: detecting among treatment variation in random effects

In ecology and evolution generalized linear mixed models (GLMMs) are becoming increasingly used to test for differences in variation by treatment at multiple hierarchical levels. Yet, the specific sampling schemes that optimize the power of an experiment to detect differences in random effects by treatment/group remain unknown. In this paper we develop a blueprint for conducting power analyses for GLMMs focusing on detecting differences in variance by treatment. We present parameterization and power analyses for random-intercepts and random-slopes GLMMs because of their generality as focal parameters for most applications and because of their immediate applicability to emerging questions in the field of behavioral ecology. We focus on the extreme case of hierarchically structured binomial data, though the framework presented here generalizes easily to any error distribution model. First, we determine the optimal ratio of individuals to repeated measures within individuals that maximizes power to detect differences by treatment in among-individual variation in intercept, among-individual variation in slope, and within-individual variation in intercept. Second, we explore how power to detect differences in target variance parameters is affected by total variation. Our results indicate heterogeneity in power across ratios of individuals to repeated measures with an optimal ratio determined by both the target variance parameter and total sample size. Additionally, power to detect each variance parameter was low overall (in most cases >1,000 total observations per treatment needed to achieve 80% power) and decreased with increasing variance in non-target random effects. With growing interest in variance as the parameter of inquiry, these power analyses provide a crucial component for designing experiments focused on detecting differences in variance. We hope to inspire novel experimental designs in ecology and evolution investigating the causes and implications of individual-level phenotypic variance, such as the adaptive significance of within-individual variation.