Analysis of correlated count data using generalised linear mixed models exemplified by field data on aggressive behaviour of boars

Population-averaged and subject-specific models are available to evaluate count data when repeated observations per subject are present. The latter are also known in the literature as generalised linear mixed models (GLMM). In GLMM repeated measures are taken into account explicitly through random animal effects in the linear predictor. In this paper the relevant GLMMs are presented based on conditional Poisson or negative binomial distribution of the response variable for given random animal effects. Equations for the repeatability of count data are derived assuming normal distribution and logarithmic gamma distribution for the random animal effects. Using count data on aggressive behaviour events of pigs (barrows, sows and boars) in mixed-sex housing, we demonstrate the use of the Poisson »log-gamma intercept«, the Poisson »normal intercept« and the »normal intercept« model with negative binomial distribution. Since not all count data can definitely be seen as Poisson or negative-binomially distributed, questions of model selection and model checking are examined. Emanating from the example, we also interpret the least squares means, estimated on the link as well as the response scale. Options provided by the SAS procedure NLMIXED for estimating model parameters and for estimating marginal expected values are presented.

Analysis of correlated count data using generalised linear mixed models exemplified by field data on aggressive behaviour of boars

Population-averaged and subject-specific models are available to evaluate count data when repeated observations per subject are present. The latter are also known in the literature as generalised linear mixed models (GLMM). In GLMM repeated measures are taken into account explicitly through random animal effects in the linear predictor. In this paper the relevant GLMMs are presented based on conditional Poisson or negative binomial distribution of the response variable for given random animal effects. Equations for the repeatability of count data are derived assuming normal distribution and logarithmic gamma distribution for the random animal effects. Using count data on aggressive behaviour events of pigs (barrows, sows and boars) in mixed-sex housing, we demonstrate the use of the Poisson »log-gamma intercept«, the Poisson »normal intercept« and the »normal intercept« model with negative binomial distribution. Since not all count data can definitely be seen as Poisson or negative-binomially distributed, questions of model selection and model checking are examined. Emanating from the example, we also interpret the least squares means, estimated on the link as well as the response scale. Options provided by the SAS procedure NLMIXED for estimating model parameters and for estimating marginal expected values are presented.

Adjustment of Animal Growth Rate Responses in Repeat Measurement Grazing Trials

In animal-response grazing trials there are sources of uncertainty in one-period one-off measurements, which as partial factorisation over time, become traceable and quantifiable sources of variation in repeat measurement trials. This is illustrated for a trial comparing sheep and goat live-weight gains under two stocking rates on mixed species pastures established by three contrasting sowing methods. It used variable plot size to give uniform animal numbers and tracked changes in individual animal performance and pasture growth in different periods. It was repeated on the same plots and animals over 17 grazing cycles. The variation explainable was greater with growth rates expressed as percent live-weight increase per day, than as weight or metabolic weight increase per day. The base data sets were adjusted for specific weighing-day effects of estimated gut-fill using moving averages, and for calibration for individual animal effects by genotype/environment analysis. Collectively these significantly increased the proportion explainable by 3.1-3.8% in variance analyses using qualitative treatment variables, and 2.7-3.7% in response function analyses relative to measured climate, pasture, plot and collective animal covariates. Simulation studies, to allow for variability in the independent variables as well as the dependent variables, indicated that the proportion explainable could increase by a further 0-1.2% and 1.1-1.9% respectively for the variance or response function approaches.

Relationships between external and internal udder measurements and the linear scores for udder morphology traits in dairy sheep

Udder morphology traits were measured and subjectively assessed by the use of linear scores in 266 ewes of Tsigai (T), Improved Walachian (IW) and Lacaune (LC) dairy breeds. Animals were recorded repeatedly within and between lactations, therefore 772 sets of measurements and linear scores were collected in total. Udder measurements included: udder length, udder width, rear udder depth, cistern depth, teat length, teat angle, sum of cistern cross-section areas scanned by the ultrasound technique from the side and from the bottom in a water bath. Linear scores were assessed for: udder depth, cistern depth, teat placement, teat length, udder attachment, udder cleft, and udder shape from the aspect of machine milking. Analysis of variance was conducted by the mixed procedure of SAS statistical package. The model included effects of experimental day, parity, days in milk, random effect of animal and residual error. Subsequently, correlations between random animal effects for udder measurements and linear scores were computed for individual examined breeds separately. Subjectively assessed linear scores for udder depth, cistern depth, teat position and teat size showed high correlations with actual measurements of the respective traits on udder in all examined breeds (r_p = 0.65–0.80). Linear scores for cistern depth and teat position were highly correlated (r_p = 0.84; 0.77 and 0.90 for T; IW and LC ewes), suggesting that they are nearly identical traits. Linear score for udder shape was significantly correlated with the linear score for udder attachment in all examined breeds (r_p = 0.79; 0.80 and 0.78 for T; IW and LC). In T and IW assessments of the udder shape were also highly correlated with linear score for udder height (r_p = 0.84 resp. r_p = 0.79) while in LC this correlation was close to zero. In LC assessment of the udder shape was more dependent on teat position (r_p = –0.37) and cistern depth (r_p = –0.30).  

Variation of mohair staple length across Angora goat fleeces: implications for animal selection and fleece evaluation

SUMMARYThe present study aimed to determine how the average mohair staple length (SL) differences between nine sampling sites vary between sex and flock, to identify differences in SL variability between sampling sites as a result of between-animal and between-sire variability and to determine SL correlations between sampling sites in between-animal and between-sire variability. Australian Angora goats (n=301) from two farms in southern Australia were sampled at 12 and 18 months of age at nine sites (mid side, belly, brisket, hind flank, hip, hock, mid back, neck and shoulder). Staples were taken prior to shearing at skin level and stretched SL determined. For each shearing, differences in SL between sampling sites, how these differences were affected by farm, sex and sire, and the covariance between sites for sire and individual animal effects were investigated by restricted maximum likelihood (REML) analyses. The median mid-side SL at 12 and 18 months of age was 110 and 130 mm, respectively, but the actual range in mid-side SL was 65–165 mm. There was an anterior–posterior decline in SL with the hock being particularly short. There was no evidence that the between-site correlation of the sire effects differed from 1, indicating that genetic selection for SL at one site will be reflected in SL over the whole fleece. However, low heritabilities of SL at the hock, belly and brisket or at any site at 12 months of age were obtained. There was more variability between sites than between sires, but the between-animal variation was greater. The hip and mid-back sites can be recommended for within-flock (culling) and genetic selection for SL due to their low sampling variability, moderate heritability and ease of location.

Limitations of conventional models and a conceptual framework for a nutrient flow representation of energy utilization by animals

Conventional models of energy utilization by animals, based on partitioning metabolizable energy (ME) intake or net energy (NE), are reviewed. The limitations of these methods are discussed, including various experimental, analytical and conceptual problems. Variation in the marginal efficiency of utilizing energy can be attributed to various factors: diet nutrient composition; animal effects on diet ME content; diet and animal effects on ME for maintenance (MEm); experimental methodology; and important statistical issues. ME partitioning can account for some of the variation due to animal factors, but not that related to nutrient source. In addition to many of the problems associated with ME, problems with NE pertain to: estimation of NE for maintenance (NEm); experimental and analytical methodology; and an inability to reflect variation in the metabolic use of NE. A conceptual framework is described for a new model of energy utilization by animals, based on representing explicit flows of the main nutrients and the important biochemical and biological transformations associated with their utilization. Differences in energetic efficiency from either dietary or animal factors can be predicted with this model.