Detecting Major Genes Controlling Robustness of Chicken Body Weight Using Double Generalized Linear Models

Detecting both the majors genes that control the phenotypic mean and those controlling phenotypic variance has been raised in quantitative trait loci analysis. In order to mapping both kinds of genes, we applied the idea of the classic Haley-Knott regression to double generalized linear models. We performed both kinds of quantitative trait loci detection for a Red Jungle Fowl x White Leghorn F2 intercross using double generalized linear models. It is shown that double generalized linear model is a proper and efficient approach for localizing variance-controlling genes. We compared two models with or without fixed sex effect and prefer including the sex effect in order to reduce the residual variances. We found that different genes might take effect on the body weight at different time as the chicken grows.

A study of slag corrosion of oxides and oxide-carbon refractories during steel refining

The use of ceramic material as refractories in the manufacturing industry is a common practice worldwide. During usage, for example in the production of steel, these materials do experience severe working conditions including high temperatures, low pressures and corrosive environments. This results in lowered service lives and high consumptions of these materials. This, in turn, affects the productivity of the whole steel plant and thereby the cost. In order to investigate how the service life can be improved, studies have been carried out for refractories used in the inner lining of the steel ladles. More specifically, from the slag zone, where the corrosion is most severe. By combining thermodynamic simulations, plant trails and post-mortem studies of the refractories after service, vital information about the behaviour of the slagline refractories during steel refining and the causes of the accelerated wear in this ladle area has been achieved. The results from these studies show that the wear of the slagline refractories of the ladle is initiated at the preheating station, through reduction-oxidation reactions. The degree of the decarburization process is mostly dependent on the preheating fuel or the environment. For refractories without antioxidants, refractory decarburization is slower when coal gas is used in ladle preheating than when a mixture of oil and air is used. In addition, ladle preheating of the refractories without antioxidants leads to direct wear of the slagline refractories. This is due to the total loss of the matrix strength, which results in a sand-like product. Thermal chemical changes that take place in the slagline refractories are due to the MgO-C reaction as well as the formation of liquid phases from impurity oxides. In addition, the decrease in the system pressure during steel refining makes the MgO-C reaction take place at the steel refining temperatures. This reduces the refractory’s resistance to corrosion. This is a serious problem for both the magnesia-carbon and dolomite-carbon refractories. The studies of the reactions between the slagline refractories and the different slag compositions showed that slags rich in iron oxide lead mostly to the oxidation of carbon/graphite in the carbon-containing refractories. This leads to an increased porosity and wettability and therefore an enhanced penetration of slag into the refractory structure. If the slag contains high contents of alumina and or silica (such as the steel refining slag), reactions between the slag components and the dolomite-carbon refractory are promoted. This leads to the formation of low-temperature melting phases such as calcium-aluminates and silicates. The state of these reaction products during steel refining leads to an accelerated wear of the dolomite-carbon refractory. The main products of the reactions between the magnesia-carbon refractory and the steel refining slag are MgAl2O4 spinels, and calcium-aluminates, and silicates. Due to the good refractory properties of MgAl2O4 spinels, the slag corrosion resistance of the magnesiacarbon refractory is promoted.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models

Background: Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike’s information criterion using h-likelihood to select the best fitting model. Methods: We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike’s information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters. Results: Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike’s information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed. Conclusion: The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.

Hglm: A package for fitting hierarchical generalized linear models

We present the hglm package for fitting hierarchical generalized linear models. It can be used for linear mixed models and generalized linear mixed models with random effects for a variety of links and a variety of distributions for both the outcomes and the random effects. Fixed effects can also be fitted in the dispersion part of the model.

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.

Likelihood prediction for generalized linear mixed models under covariate uncertainty

This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable generalized linear model, it has been shown that in complicated cases LP produces better results than already know methods.

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.