Estimation in a multiplicative mixed model involving a genetic relationship matrix

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.     

Mixed-model analysis of a censored normal distribution with reference to animal breeding

A mixed-model procedure for analysis of censored data assuming a multivariate normal distribution is described. A Bayesian framework is adopted which allows for estimation of fixed effects and variance components and prediction of random effects when records are left-censored. The procedure can be extended to right- and two-tailed censoring. The model employed is a generalized linear model, and the estimation equations resemble those arising in analysis of multivariate normal or categorical data with threshold models. Estimates of variance components are obtained using expressions similar to those employed in the EM algorithm for restricted maximum likelihood (REML) estimation under normality.     

Nonparametric methods for incorporating genomic information into genetic evaluations: an application to mortality in broilers

Four approaches using single-nucleotide polymorphism (SNP) information (F(infinity)-metric model, kernel regression, reproducing kernel Hilbert spaces (RKHS) regression, and a Bayesian regression) were compared with a standard procedure of genetic evaluation (E-BLUP) of sires using mortality rates in broilers as a response variable, working in a Bayesian framework. Late mortality (14-42 days of age) records on 12,167 progeny of 200 sires were precorrected for fixed and random (nongenetic) effects used in the model for genetic evaluation and for the mate effect. The average of the corrected records was computed for each sire. Twenty-four SNPs seemingly associated with late mortality were included in three methods used for genomic assisted evaluations. One thousand SNPs were included in the Bayesian regression, to account for markers along the whole genome. The posterior mean of heritability of mortality was 0.02 in the E-BLUP approach, suggesting that genetic evaluation could be improved if suitable molecular markers were available. Estimates of posterior means and standard deviations of the residual variance were 24.38 (3.88), 29.97 (3.22), 17.07 (3.02), and 20.74 (2.87) for E-BLUP, the linear model on SNPs, RKHS regression, and the Bayesian regression, respectively, suggesting that RKHS accounted for more variance in the data. The two nonparametric methods (kernel and RKHS regression) fitted the data better, having a lower residual sum of squares. Predictive ability, assessed by cross-validation, indicated advantages of the RKHS approach, where accuracy was increased from 25 to 150%, relative to other methods.     

Estimation of (co)variances for genomic regions of flexible sizes: application to complex infectious udder diseases in dairy cattle

Background

Multi-trait genomic models in a Bayesian context can be used to estimate genomic (co)variances, either for a complete genome or for genomic regions (e.g. per chromosome) for the purpose of multi-trait genomic selection or to gain further insight into the genomic architecture of related traits such as mammary disease traits in dairy cattle.

Methods

Data on progeny means of six traits related to mastitis resistance in dairy cattle (general mastitis resistance and five pathogen-specific mastitis resistance traits) were analyzed using a bivariate Bayesian SNP-based genomic model with a common prior distribution for the marker allele substitution effects and estimation of the hyperparameters in this prior distribution from the progeny means data. From the Markov chain Monte Carlo samples of the allele substitution effects, genomic (co)variances were calculated on a whole-genome level, per chromosome, and in regions of 100 SNP on a chromosome.

Results

Genomic proportions of the total variance differed between traits. Genomic correlations were lower than pedigree-based genetic correlations and they were highest between general mastitis and pathogen-specific traits because of the part-whole relationship between these traits. The chromosome-wise genomic proportions of the total variance differed between traits, with some chromosomes explaining higher or lower values than expected in relation to chromosome size. Few chromosomes showed pleiotropic effects and only chromosome 19 had a clear effect on all traits, indicating the presence of QTL with a general effect on mastitis resistance. The region-wise patterns of genomic variances differed between traits. Peaks indicating QTL were identified but were not very distinctive because a common prior for the marker effects was used. There was a clear difference in the region-wise patterns of genomic correlation among combinations of traits, with distinctive peaks indicating the presence of pleiotropic QTL.

Conclusions

The results show that it is possible to estimate, genome-wide and region-wise genomic (co)variances of mastitis resistance traits in dairy cattle using multivariate genomic models.     

Principal component and factor analytic models in international sire evaluation

Background

Interbull is a non-profit organization that provides internationally comparable breeding values for globalized dairy cattle breeding programmes. Due to different trait definitions and models for genetic evaluation between countries, each biological trait is treated as a different trait in each of the participating countries. This yields a genetic covariance matrix of dimension equal to the number of countries which typically involves high genetic correlations between countries. This gives rise to several problems such as over-parameterized models and increased sampling variances, if genetic (co)variance matrices are considered to be unstructured.

Methods

Principal component (PC) and factor analytic (FA) models allow highly parsimonious representations of the (co)variance matrix compared to the standard multi-trait model and have, therefore, attracted considerable interest for their potential to ease the burden of the estimation process for multiple-trait across country evaluation (MACE). This study evaluated the utility of PC and FA models to estimate variance components and to predict breeding values for MACE for protein yield. This was tested using a dataset comprising Holstein bull evaluations obtained in 2007 from 25 countries.

Results

In total, 19 principal components or nine factors were needed to explain the genetic variation in the test dataset. Estimates of the genetic parameters under the optimal fit were almost identical for the two approaches. Furthermore, the results were in a good agreement with those obtained from the full rank model and with those provided by Interbull. The estimation time was shortest for models fitting the optimal number of parameters and prolonged when under- or over-parameterized models were applied. Correlations between estimated breeding values (EBV) from the PC19 and PC25 were unity. With few exceptions, correlations between EBV obtained using FA and PC approaches under the optimal fit were ≥ 0.99. For both approaches, EBV correlations decreased when the optimal model and models fitting too few parameters were compared.

Conclusions

Genetic parameters from the PC and FA approaches were very similar when the optimal number of principal components or factors was fitted. Over-fitting increased estimation time and standard errors of the estimates but did not affect the estimates of genetic correlations or the predictions of breeding values, whereas fitting too few parameters affected bull rankings in different countries.     

Genetic heterogeneity of residual variance - estimation of variance components using double hierarchical generalized linear models

Background

The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms.

Results

We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model.

Conclusions

We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.     

Genomic-assisted prediction of genetic value with semiparametric procedures

Semiparametric procedures for prediction of total genetic value for quantitative traits, which make use of phenotypic and genomic data simultaneously, are presented. The methods focus on the treatment of massive information provided by, e.g., single-nucleotide polymorphisms. It is argued that standard parametric methods for quantitative genetic analysis cannot handle the multiplicity of potential interactions arising in models with, e.g., hundreds of thousands of markers, and that most of the assumptions required for an orthogonal decomposition of variance are violated in artificial and natural populations. This makes nonparametric procedures attractive. Kernel regression and reproducing kernel Hilbert spaces regression procedures are embedded into standard mixed-effects linear models, retaining additive genetic effects under multivariate normality for operational reasons. Inferential procedures are presented, and some extensions are suggested. An example is presented, illustrating the potential of the methodology. Implementations can be carried out after modification of standard software developed by animal breeders for likelihood-based or Bayesian analysis.     

Multivariate selection and intersexual genetic constraints in a wild bird population

When selection differs between the sexes for traits that are genetically correlated between the sexes, there is potential for the effect of selection in one sex to be altered by indirect selection in the other sex, a situation commonly referred to as intralocus sexual conflict (ISC). While potentially common, ISC has rarely been studied in wild populations. Here, we studied ISC over a set of morphological traits (wing length, tarsus length, bill depth and bill length) in a wild population of great tits (Parus major) from Wytham Woods, UK. Specifically, we quantified the microevolutionary impacts of ISC by combining intra‐ and intersex additive genetic (co)variances and sex‐specific selection estimates in a multivariate framework. Large genetic correlations between homologous male and female traits combined with evidence for sex‐specific multivariate survival selection suggested that ISC could play an appreciable role in the evolution of this population. Together, multivariate sex‐specific selection and additive genetic (co)variance for the traits considered accounted for additive genetic variance in fitness that was uncorrelated between the sexes (cross‐sex genetic correlation = ?0.003, 95% CI = ?0.83, 0.83). Gender load, defined as the reduction in a population's rate of adaptation due to sex‐specific effects, was estimated at 50% (95% CI = 13%, 86%). This study provides novel insights into the evolution of sexual dimorphism in wild populations and illustrates how quantitative genetics and selection analyses can be combined in a multivariate framework to quantify the microevolutionary impacts of ISC.     

Multicollinearity in spatial genetics: separating the wheat from the chaff using commonality analyses

Direct gradient analyses in spatial genetics provide unique opportunities to describe the inherent complexity of genetic variation in wildlife species and are the object of many methodological developments. However, multicollinearity among explanatory variables is a systemic issue in multivariate regression analyses and is likely to cause serious difficulties in properly interpreting results of direct gradient analyses, with the risk of erroneous conclusions, misdirected research and inefficient or counterproductive conservation measures. Using simulated data sets along with linear and logistic regressions on distance matrices, we illustrate how commonality analysis (CA), a detailed variance‐partitioning procedure that was recently introduced in the field of ecology, can be used to deal with nonindependence among spatial predictors. By decomposing model fit indices into unique and common (or shared) variance components, CA allows identifying the location and magnitude of multicollinearity, revealing spurious correlations and thus thoroughly improving the interpretation of multivariate regressions. Despite a few inherent limitations, especially in the case of resistance model optimization, this review highlights the great potential of CA to account for complex multicollinearity patterns in spatial genetics and identifies future applications and lines of research. We strongly urge spatial geneticists to systematically investigate commonalities when performing direct gradient analyses.     

Estimating variance components and predicting breeding values for eventing disciplines and grades in sport horses

Eventing competitions in Great Britain (GB) comprise three disciplines, each split into four grades, yielding 12 discipline-grade traits. As there is a demand for tools to estimate (co)variance matrices with a large number of traits, the aim of this work was to investigate different methods to produce large (co)variance matrices using GB eventing data. Data from 1999 to 2008 were used and penalty points were converted to normal scores. A sire model was utilised to estimate fixed effects of gender, age and class, and random effects of sire, horse and rider. Three methods were used to estimate (co)variance matrices. Method 1 used a method based on Gibbs sampling and data augmentation and imputation. Methods 2a and 2b combined sub-matrices from bivariate analyses; one took samples from a multivariate Normal distribution defined by the covariance matrix from each bivariate analysis, then analysed these data in a 12-trait multivariate analysis; the other replaced negative eigenvalues in the matrix with positive values to obtain a positive definite (co)variance matrix. A formal comparison of models could not be conducted; however, estimates from all methods, particularly Methods 2a/2b, were in reasonable agreement. The computational requirements of Method 1 were much less compared with Methods 2a or 2b. Method 2a heritability estimates were as follows: for dressage 7.2% to 9.0%, for show jumping 8.9% to 16.2% and for cross-country 1.3% to 1.4%. Method 1 heritability estimates were higher for the advanced grades, particularly for dressage (17.1%) and show jumping (22.6%). Irrespective of the model, genetic correlations between grades, for dressage and show jumping, were positive, high and significant, ranging from 0.59 to 0.99 for Method 2a and 0.78 to 0.95 for Method 1. For cross-country, using Method 2a, genetic correlations were only significant between novice and pre-novice (0.75); however, using Method 1 estimates were all significant and low to moderate (0.36 to 0.70). Between-discipline correlations were all low and of mixed sign. All methods produced positive definite 12 × 12 (co)variance matrices, suitable for the prediction of breeding values. Method 1 benefits from much reduced computational requirements, and by performing a true multivariate analysis.     

Heterosis and epistasis for teat number and fluctuating asymmetry in crosses between Jiaxing and Iberian pigs

In the framework of Wright's view of evolution, long-separate breeds of domestic animals could establish different adaptive epistatic genetic complexes that could be destroyed in crossbred animals by recombination. The objective of this study was to evaluate heterosis and recombination effects in a crossing experiment involving two distinct European and Asian breeds (Iberian and Jiaxing) in the F1 and two successive backcrosses to the Iberian line. Teat number (TN) was recorded in the right and left sides of piglets and analysed by fitting a mixed linear model including the Dickerson's crossbreeding parameters. TN in pigs is a discontinuous and often canalised trait presenting bilateral symmetry. The minor differences between sides make this trait a good candidate to evaluate fluctuating asymmetry (FA) and developmental instability. For TN, the posterior means and standard deviations (SD) of the heritability and of the relative contribution of common litter environmental effect to variance were 0.248 (0.028) and 0.057 (0.019), respectively. The respective values of the difference between breeds, heterosis and recombination effect were 9.990 (0.411), -0.506 (0.196) and 0.684 (0.232). For FA, the posterior means and SDs of the heritability and of the relative contribution of common litter environmental effect to variance were 0.023 (0.005) and 0.014 (0.005), respectively. Another significant genetic effect was a recombination effect of 0.773 (0.117). These results confirm that the rupture by recombination of coadapted genomes decreases developmental stability in domestic pigs.     

Comparing G: multivariate analysis of genetic variation in multiple populations

The additive genetic variance–covariance matrix (G) summarizes the multivariate genetic relationships among a set of traits. The geometry of G describes the distribution of multivariate genetic variance, and generates genetic constraints that bias the direction of evolution. Determining if and how the multivariate genetic variance evolves has been limited by a number of analytical challenges in comparing G-matrices. Current methods for the comparison of G typically share several drawbacks: metrics that lack a direct relationship to evolutionary theory, the inability to be applied in conjunction with complex experimental designs, difficulties with determining statistical confidence in inferred differences and an inherently pair-wise focus. Here, we present a cohesive and general analytical framework for the comparative analysis of G that addresses these issues, and that incorporates and extends current methods with a strong geometrical basis. We describe the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation, all within a Bayesian framework. We illustrate these methods using data from an artificial selection experiment on eight traits in Drosophila serrata, where a multi-generational pedigree was available to estimate G in each of six populations. One method, the tensor, elegantly captures all of the variation in genetic variance among populations, and allows the identification of the trait combinations that differ most in genetic variance. The tensor approach is likely to be the most generally applicable method to the comparison of G-matrices from any sampling or experimental design.     

Genetic structure of phenotypic robustness in the collaborative cross mouse diallel panel

Developmental stability and canalization describe the ability of developmental systems to minimize phenotypic variation in the face of stochastic micro‐environmental effects, genetic variation and environmental influences. Canalization is the ability to minimize the effects of genetic or environmental effects, whereas developmental stability is the ability to minimize the effects of micro‐environmental effects within individuals. Despite much attention, the mechanisms that underlie these two components of phenotypic robustness remain unknown. We investigated the genetic structure of phenotypic robustness in the collaborative cross (CC) mouse reference population. We analysed the magnitude of fluctuating asymmetry (FA) and among‐individual variation of cranial shape in reciprocal crosses among the eight parental strains, using geometric morphometrics and a diallel analysis based on a Bayesian approach. Significant differences among genotypes were found for both measures, although they were poorly correlated at the level of individuals. An overall positive effect of inbreeding was found for both components of variation. The strain CAST/EiJ exerted a positive additive effect on FA and, to a lesser extent, among‐individual variance. Sex‐ and other strain‐specific effects were not significant. Neither FA nor among‐individual variation was associated with phenotypic extremeness. Our results support the existence of genetic variation for both developmental stability and canalization. This finding is important because robustness is a key feature of developmental systems. Our finding that robustness is not related to phenotypic extremeness is consistent with theoretical work that suggests that its relationship to stabilizing selection is not straightforward.     

A primary role of developmental instability in sexual selection

In evolutionary biology, fluctuating asymmetry (FA) is thought to reveal developmental instability (DI, inability to buffer development against perturbations), but its adaptive and genetic bases are being debated. In other fields, such as human clinical genetics, DI is being assessed as incidence of minor morphological abnormalities (MMAs) and used to predict certain fitness outcomes. Here, for the first time, we combine these complementary measures of DI in sexual selection and quantitative genetic studies of a natural population. Comprehensive multivariate analyses demonstrate that FA and MMAs in a condition-dependent sexual ornament, the male Drosophila bipectinata sex comb used in courtship, are sole significant targets of selection favouring their reduced expression in New Caledonia. Comb FA and MMAs are positively correlated, confirming that each are linked to a common buffering system. Ornament size and DI (as FA and MMAs) are positively correlated, genetically and phenotypically, contrary to theoretical expectation of negative size-FA scaling under the assumption that FA reveals overall genetic quality. There exists significant additive genetic variance for MMAs, demonstrating their evolutionary potential. Ornament DI in New Caledonia is markedly elevated compared with populations where such selection was not detected, suggesting that the increased population-level DI is capacitating adaptive evolution.     

Inference of Cross-Level Interaction between Genes and Contextual Factors in a Matched Case-Control Metabolic Syndrome Study: A Bayesian Approach

Genes, environment, and the interaction between them are each known to play an important role in the risk for developing complex diseases such as metabolic syndrome. For environmental factors, most studies focused on the measurements observed at the individual level, and therefore can only consider the gene-environment interaction at the same individual scale. Indeed the group-level (called contextual) environmental variables, such as community factors and the degree of local area development, may modify the genetic effect as well. To examine such cross-level interaction between genes and contextual factors, a flexible statistical model quantifying the variability of the genetic effects across different categories of the contextual variable is in need. With a Bayesian generalized linear mixed-effects model with an unconditional likelihood, we investigate whether the individual genetic effect is modified by the group-level residential environment factor in a matched case-control metabolic syndrome study. Such cross-level interaction is evaluated by examining the heterogeneity in allelic effects under various contextual categories, based on posterior samples from Markov chain Monte Carlo methods. The Bayesian analysis indicates that the effect of rs1801282 on metabolic syndrome development is modified by the contextual environmental factor. That is, even among individuals with the same genetic component of PPARG_Pro12Ala, living in a residential area with low availability of exercise facilities may result in higher risk. The modification of the group-level environment factors on the individual genetic attributes can be essential, and this Bayesian model is able to provide a quantitative assessment for such cross-level interaction. The Bayesian inference based on the full likelihood is flexible with any phenotype, and easy to implement computationally. This model has a wide applicability and may help unravel the complexity in development of complex diseases.     

Accounting for competition in genetic analysis, with particular emphasis on forest genetic trials

Available experimental evidence suggests that there are genetic differences in the abilities of trees to compete for resources, in addition to non-genetic differences due to micro-site variation. The use of indirect genetic effects within the framework of linear mixed model methodology has been proposed for estimating genetic parameters and responses to selection in the presence of genetic competition. In this context, an individual’s total breeding value reflects the effects of its direct breeding value on its own phenotype and its competitive breeding value on the phenotype of its neighbours. The present study used simulated data to investigate the relevance of accounting for competitive effects at the genetic and non-genetic levels in terms of the estimation of (co)variance components and selection response. Different experimental designs that resulted in different genetic relatedness levels within a neighbourhood and survival were other key issues examined. Variances estimated for additive genetic and residual effects tended to be biased under models that ignored genetic competition. Models that fitted competition at the genetic level only also resulted in biased (co)variance estimates for direct additive, competitive additive and residual effects. The ability to detect the correct model was reduced when relatedness within a neighbourhood was very low and survival decreased. Selection responses changed considerably between selecting on breeding value estimates from a model ignoring genetic competition and total breeding estimates using the correct model. Our results suggest that considering a genetic basis to competitive ability will be important to optimise selection programmes for genetic improvement of tree species.     

Analysis of melanoma onset: assessing familial aggregation by using estimating equations and fitting variance components via Bayesian random effects models.

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.     

The use of linear mixed models to estimate variance components from data on twin pairs by maximum likelihood.

It is shown that maximum likelihood estimation of variance components from twin data can be parameterized in the framework of linear mixed models. Standard statistical packages can be used to analyze univariate or multivariate data for simple models such as the ACE and CE models. Furthermore, specialized variance component estimation software that can handle pedigree data and user-defined covariance structures can be used to analyze multivariate data for simple and complex models, including those where dominance and/or QTL effects are fitted. The linear mixed model framework is particularly useful for analyzing multiple traits in extended (twin) families with a large number of random effects.     

Equivalence of multibreed animal models and hierarchical Bayes analysis for maternally influenced traits

Background

It has been argued that multibreed animal models should include a heterogeneous covariance structure. However, the estimation of the (co)variance components is not an easy task, because these parameters can not be factored out from the inverse of the additive genetic covariance matrix. An alternative model, based on the decomposition of the genetic covariance matrix by source of variability, provides a much simpler formulation. In this study, we formalize the equivalence between this alternative model and the one derived from the quantitative genetic theory. Further, we extend the model to include maternal effects and, in order to estimate the (co)variance components, we describe a hierarchical Bayes implementation. Finally, we implement the model to weaning weight data from an Angus × Hereford crossbred experiment.

Methods

Our argument is based on redefining the vectors of breeding values by breed origin such that they do not include individuals with null contributions. Next, we define matrices that retrieve the null-row and the null-column pattern and, by means of appropriate algebraic operations, we demonstrate the equivalence. The extension to include maternal effects and the estimation of the (co)variance components through the hierarchical Bayes analysis are then straightforward. A FORTRAN 90 Gibbs sampler was specifically programmed and executed to estimate the (co)variance components of the Angus × Hereford population.

Results

In general, genetic (co)variance components showed marginal posterior densities with a high degree of symmetry, except for the segregation components. Angus and Hereford breeds contributed with 50.26% and 41.73% of the total direct additive variance, and with 23.59% and 59.65% of the total maternal additive variance. In turn, the contribution of the segregation variance was not significant in either case, which suggests that the allelic frequencies in the two parental breeds were similar.

Conclusion

The multibreed maternal animal model introduced in this study simplifies the problem of estimating (co)variance components in the framework of a hierarchical Bayes analysis. Using this approach, we obtained for the first time estimates of the full set of genetic (co)variance components. It would be interesting to assess the performance of the procedure with field data, especially when interbreed information is limited.     

Hierarchical Bayesian modeling of heterogeneous cluster‐ and subject‐level associations between continuous and binary outcomes in dairy production

The augmentation of categorical outcomes with underlying Gaussian variables in bivariate generalized mixed effects models has facilitated the joint modeling of continuous and binary response variables. These models typically assume that random effects and residual effects (co)variances are homogeneous across all clusters and subjects, respectively. Motivated by conflicting evidence about the association between performance outcomes in dairy production systems, we consider the situation where these (co)variance parameters may themselves be functions of systematic and/or random effects. We present a hierarchical Bayesian extension of bivariate generalized linear models whereby functions of the (co)variance matrices are specified as linear combinations of fixed and random effects following a square‐root‐free Cholesky reparameterization that ensures necessary positive semidefinite constraints. We test the proposed model by simulation and apply it to the analysis of a dairy cattle data set in which the random herd‐level and residual cow‐level effects (co)variances between a continuous production trait and binary reproduction trait are modeled as functions of fixed management effects and random cluster effects.