Factor analysis models for structuring covariance matrices of additive genetic effects: a Bayesian implementation

Multivariate linear models are increasingly important in quantitative genetics. In high dimensional specifications, factor analysis (FA) may provide an avenue for structuring (co)variance matrices, thus reducing the number of parameters needed for describing (co)dispersion. We describe how FA can be used to model genetic effects in the context of a multivariate linear mixed model. An orthogonal common factor structure is used to model genetic effects under Gaussian assumption, so that the marginal likelihood is multivariate normal with a structured genetic (co)variance matrix. Under standard prior assumptions, all fully conditional distributions have closed form, and samples from the joint posterior distribution can be obtained via Gibbs sampling. The model and the algorithm developed for its Bayesian implementation were used to describe five repeated records of milk yield in dairy cattle, and a one common FA model was compared with a standard multiple trait model. The Bayesian Information Criterion favored the FA model

Age‑specific rate of severe and critical SARS‑CoV‑2 infections estimated with multi‑country seroprevalence studies

Background: Knowing the age-specific rates at which individuals infected with SARS-CoV-2 develop severe and critical disease is essential for designing public policy, for infectious disease modeling, and for individual risk evaluation. Methods: In this study, we present the first estimates of these rates using multi-country serology studies, and public data on hospital admissions and mortality from early to mid-2020. We combine these under a Bayesian framework that accounts for the high heterogeneity between data sources and their respective uncertainties. We also validate our results using an indirect method based on infection fatality rates and hospital mortality data. Results: Our results show that the risk of severe and critical disease increases exponentially with age, but much less steeply than the risk of fatal illness. We also show that our results are consistent across several robustness checks. Conclusion: A complete evaluation of the risks of SARS-CoV-2 for health must take non-fatal disease outcomes into account, particularly in young populations where they can be 2 orders of magnitude more frequent than deaths

Sparsity-Inducing Categorical Prior Improves Robustness of the Information Bottleneck

The information bottleneck framework provides a systematic approach to learning representations that compress nuisance information in the input and extract semantically meaningful information about predictions. However, the choice of a prior distribution that fixes the dimensionality across all the data can restrict the flexibility of this approach for learning robust representations. We present a novel sparsity-inducing spike-slab categorical prior that uses sparsity as a mechanism to provide the flexibility that allows each data point to learn its own dimension distribution. In addition, it provides a mechanism for learning a joint distribution of the latent variable and the sparsity and hence can account for the complete uncertainty in the latent space. Through a series of experiments using in-distribution and out-of-distribution learning scenarios on the MNIST, CIFAR-10, and ImageNet data, we show that the proposed approach improves accuracy and robustness compared to traditional fixed-dimensional priors, as well as other sparsity induction mechanisms for latent variable models proposed in the literature

Three-step Bayesian factor analysis applied to QTL detection in crosses between outbred pig populations

AbstractMarker assisted selection (MAS) can be used to improve the efficiency of genetic selection of traits for which phenotypic measurements are expensive or cannot be obtained on selection candidates, such as carcass traits. Marker information required for MAS may be acquired through the identification of QTLs. Generally, univariate models are used for QTL detection, although multiple-trait models (MTM) may enhance QTL detection and breeding value estimation. In MTM, however, the number of parameters can be large and, if traits are highly correlated, such as carcass traits, estimates of (co)variance matrices may be close to singular. Because of this, dimension reduction techniques such as Factor Analysis (FA) may be useful. The aim of our project is to evaluate the use of FA for structuring (co)variance matrices in the context of Bayesian models for QTL detection in crosses between outbred populations. In our method, QTL effects are postulated at the level of common factors (CF) rather than the original traits, using a three-step approach. In a first step, a MTM is fitted to arrive at estimates of systematic effects and prediction of breeding values (procedure A) and only systematic effect (procedure B). These estimates/predictions are then used to generate an adjusted phenotype that is further analyzed with a Bayesian FA model. This step yields estimates of factor scores for each animal and CF. In the last step, the scores relative to each CF are analyzed independently using probabilities for the line of origin combination. To illustrate the methodology, data on 416 F2 pigs (Brazilian Piau X commercial) with ten traits (5 fat-related, 2 loin measurements, and 3 carcass classification systems) were analyzed. For each of the three resulting CFs, an independent QTL scan was performed on chromosome 7 considering three models: I) null (i.e., absence of QTL); II) additive effect QTL, and III) additive and dominance effect QTL. The posterior probability (PP) of each model was calculated from Bayes factor for each considered procedures (A and B). A Three-step Bayesian factor analysis allowed us to calculate the probability of QTLs that simultaneously affect a group of carcass traits for each position of SSC 7. The removal of systematic effects in the first step of the evaluation (procedure B) allowed that the factor analysis, which was performed in the second step, identify three distinct factors that explained 85% of the total traits variation. For the common factor that represented fat-related traits (bacon depth, midline lower backfat thickness, higher backfat thickness on the shoulder; midline backfat thickness after the last rib; midline backfat thickness on the last lumbar vertebrae) the third step of the analysis showed that the highest probability of an additive QTL effect at the 65cM position was 86%

Analysis of social interactions in group-housed animals using dyadic linear models

Understanding factors affecting social interactions among animals is important for applied animal behavior research. Thus, there is a need to elicit statistical models to analyze data collected from pairwise behavioral interactions. In this study, we propose treating social interaction data as dyadic observations and propose a statistical model for their analysis. We performed posterior predictive checks of the model through different validation strategies: stratified 5-fold random cross-validation, block-by-social-group cross-validation, and block-by-focal-animals validation. The proposed model was applied to a pig behavior dataset collected from 797 growing pigs freshly remixed into 59 social groups that resulted in 10,032 records of directional dyadic interactions. The response variable was the duration in seconds that each animal spent delivering attacks on another group mate. Generalized linear mixed models were fitted. Fixed effects included sex, individual weight, prior nursery mate experience, and prior littermate experience of the two pigs in the dyad. Random effects included aggression giver, aggression receiver, dyad, and social group. A Bayesian framework was utilized for parameter estimation and posterior predictive model checking. Prior nursery mate experience was the only significant fixed effect. In addition, a weak but significant correlation between the random giver effect and the random receiver effect was obtained when analyzing the attacking duration. The predictive performance of the model varied depending on the validation strategy, with substantially lower performance from the block-by-social-group strategy than other validation strategies. Collectively, this paper demonstrates a statistical model to analyze interactive animal behaviors, particularly dyadic interactions

Diagnosing pregnancy status using infrared spectra and milk composition in dairy cows

Data on Holstein (16,890), Brown Swiss (31,441), Simmental (25,845), and Alpine Grey (12,535) cows reared in northeastern Italy were used to assess the ability of milk components (fat, protein, casein, and lactose) and Fourier transform infrared (FTIR) spectral data to diagnose pregnancy. Pregnancy status was defined as whether a pregnancy was confirmed by a subsequent calving and no other subsequent inseminations within 90 d of the breeding of specific interest. Milk samples were analyzed for components and FTIR full-spectrum data using a MilkoScan FT+ 6000 (Foss Electric, Hiller\uf8d, Denmark). The spectrum covered 1,060 wavenumbers (wn) from 5,010 to 925 cm 121. Pregnancy status was predicted using generalized linear models with fat, protein, lactose, casein, and individual FTIR spectral bands or wavelengths as predictors. We also fitted a generalized linear model as a simultaneous function of all wavelengths (1,060 wn) with a Bayesian variable selection model using the BGLR R-package (https://r-forge.r-project.org/projects/bglr/). Prediction accuracy was determined using the area under a receiver operating characteristic curve based on a 10-fold cross-validation (CV-AUC) assessment based on sensitivities and specificities of phenotypic predictions. Overall, the best prediction accuracies were obtained for the model that included the complete FTIR spectral data. We observed similar patterns across breeds with small differences in prediction accuracy. The highest CV-AUC value was obtained for Alpine Grey cows (CV-AUC = 0.645), whereas Brown Swiss and Simmental cows had similar performance (CV-AUC = 0.630 and 0.628, respectively), followed by Holsteins (CV-AUC = 0.607). For single-wavelength analyses, important peaks were detected at wn 2,973 to 2,872 cm 121 where Fat-B (C-H stretch) is usually filtered, wn 1,773 cm 121 where Fat-A (C=O stretch) is filtered, wn 1,546 cm 121 where protein is filtered, wn 1,468 cm 121 associated with urea and fat, wn 1,399 and 1,245 cm 121 associated with acetone, and wn 1,025 to 1,013 cm 121 where lactose is filtered. In conclusion, this research provides new insight into alternative strategies for pregnancy screening of dairy cows

Threshold Models for Genome-Enabled Prediction of Ordinal Categorical Traits in Plant Breeding

Categorical scores for disease susceptibility or resistance often are recorded in plant breeding. The aim of this study was to introduce genomic models for analyzing ordinal characters and to assess the predictive ability of genomic predictions for ordered categorical phenotypes using a threshold model counterpart of the Genomic Best Linear Unbiased Predictor (i.e., TGBLUP). The threshold model was used to relate a hypothetical underlying scale to the outward categorical response. We present an empirical application where a total of nine models, five without interaction and four with genomic x environment interaction (G·E) and genomic additive x additive x environment interaction (GxGxE), were used. We assessed the proposed models using data consisting of 278 maize lines genotyped with 46,347 single-nucleotide polymorphisms and evaluated for disease resistance [with ordinal scores from 1 (no disease) to 5 (complete infection)] in three environments (Colombia, Zimbabwe, and Mexico). Models with GxE captured a sizeable proportion of the total variability, which indicates the importance of introducing interaction to improve prediction accuracy. Relative to models based on main effects only, the models that included GxE achieved 9–14% gains in prediction accuracy; adding additive x additive interactions did not increase prediction accuracy consistently across locations

Changes in milk characteristics and fatty acid profile during the estrous cycle in dairy cows

The relationship of the estrous cycle to milk composition and milk physical properties was assessed on Holstein (n = 10,696), Brown Swiss (n = 20,501), Simmental (n = 17,837), and Alpine Grey (n = 8,595) cows reared in northeastern Italy. The first insemination after calving for each cow was chosen to be the day of estrus and insemination. Test days surrounding the insemination date (from 10 d before to 10 d after the day of the estrus) were selected and categorized in phases relative to estrus as diestrus high-progesterone, proestrus, estrus, metestrus, and diestrus increasing-progesterone phases. Milk components and physical properties were predicted on the basis of Fourier-transform infrared spectra of milk samples and were analyzed using a linear mixed model, which included the random effects of herd, the fixed classification effects of year-month, parity number, breed, estrous cycle phase, day nested within the estrous cycle phase, conception, partial regressions on linear and quadratic effects of days in milk nested within parity number, as well as the interactions between conception outcome with estrous cycle phase and breed with estrous cycle phase. Milk composition, particularly fat, protein, and lactose, showed clear differences among the estrous cycle phases. Fat increased by 0.14% from diestrus high-progesterone to estrous phase, whereas protein concomitantly decreased by 0.03%. Lactose appeared to remain relatively constant over diestrus high-progesterone, rising 1 d before the day of estrus followed by a gradual reduction over the subsequent phases. Specific fatty acids were also affected across the estrous cycle phases: C14:0 and C16:0 decreased ( 120.34 and 120.48%) from proestrus to estrus with a concomitant increase in C18:0 and C18:1 cis-9 (0.40 and 0.73%). More general categories of fatty acids showed a similar behavior; that is, unsaturated fatty acids, monounsaturated fatty acids, polyunsaturated fatty acids, trans fatty acids, and long-chain fatty acids increased, whereas the saturated fatty acids, mediumchain fatty acids, and short-chain fatty acids decreased during the estrous phase. Finally, urea, somatic cell score, freezing point, pH, and homogenization index were also affected indicating variation associated with the hormonal and behavioral changes of cows in standing estrus. Hence, the variation in milk profiles of cows showing estrus should potentially be taken into account for precision dairy farming management