In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic ...In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.展开更多
Several computer packages have been developed to accomplish improved programs for animal breeding and genetic selection. This paper described most of the currant software and provided suggestions for improved software...Several computer packages have been developed to accomplish improved programs for animal breeding and genetic selection. This paper described most of the currant software and provided suggestions for improved software. Khon Kaen University, Thailand, will provide free of charge the new software developed at Khon Kaen University by the author of this paper. The contact for requesting the software is listed: monchai@kku.ac.th.展开更多
Today, Linear Mixed Models (LMMs) are fitted, mostly, by assuming that random effects and errors have Gaussian distributions, therefore using Maximum Likelihood (ML) or REML estimation. However, for many data sets, th...Today, Linear Mixed Models (LMMs) are fitted, mostly, by assuming that random effects and errors have Gaussian distributions, therefore using Maximum Likelihood (ML) or REML estimation. However, for many data sets, that double assumption is unlikely to hold, particularly for the random effects, a crucial component </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">in </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">which assessment of magnitude is key in such modeling. Alternative fitting methods not relying on that assumption (as ANOVA ones and Rao</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">’</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s MINQUE) apply, quite often, only to the very constrained class of variance components models. In this paper, a new computationally feasible estimation methodology is designed, first for the widely used class of 2-level (or longitudinal) LMMs with only assumption (beyond the usual basic ones) that residual errors are uncorrelated and homoscedastic, with no distributional assumption imposed on the random effects. A major asset of this new approach is that it yields nonnegative variance estimates and covariance matrices estimates which are symmetric and, at least, positive semi-definite. Furthermore, it is shown that when the LMM is, indeed, Gaussian, this new methodology differs from ML just through a slight variation in the denominator of the residual variance estimate. The new methodology actually generalizes to LMMs a well known nonparametric fitting procedure for standard Linear Models. Finally, the methodology is also extended to ANOVA LMMs, generalizing an old method by Henderson for ML estimation in such models under normality.展开更多
Background:We used mixed models with random components to develop height-diameter(h-d) functions for mixed,uneven-aged stands in northwestern Durango(Mexico),considering the breast height diameter(d) and stand variabl...Background:We used mixed models with random components to develop height-diameter(h-d) functions for mixed,uneven-aged stands in northwestern Durango(Mexico),considering the breast height diameter(d) and stand variables as predictors.Methods:The data were obtained from 44 permanent plots used to monitor stand growth under forest management in the study area.Results:The generalized Bertalanffy-Richards model performed better than the other generalized models in predicting the total height of the species under study.For the genera Pinus and Quercus,the models were successfully calibrated by measuring the height of a subsample of three randomly selected trees close to the mean d,whereas for species of the genera Cupressus,Arbutus and Alnus,three trees were also selected,but they are specifically the maximum,minimum and mean d trees.Conclusions:The presented equations represent a new tool for the evaluation and management of natural forest in the region.展开更多
Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis...Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.展开更多
The transient behaviors of traditional adaptive control may be very poor in general. A practically feasible approach to improve the transient performances is the adoption of adaptive switc- hing control. For a typical...The transient behaviors of traditional adaptive control may be very poor in general. A practically feasible approach to improve the transient performances is the adoption of adaptive switc- hing control. For a typical class of nonlinear systems disturbed by random noises, mixed multiple models consisting of adaptive model and fixed models were considered to design the switching con- trol law. Under certain assumptions, the nonlinear system with the switching control law was proved rigorously to be stable and optimal A simulation example was provided to compare the performance of the switching control and the traditional adaptive control.展开更多
Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation.Due to the optimality of insurance loss data groupings,clustering methods become the natural choice for suc...Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation.Due to the optimality of insurance loss data groupings,clustering methods become the natural choice for such territory risk classification.In this work,spatially constrained clustering is first applied to insurance loss data to form rating territories.The generalized linear model(GLM)and generalized linear mixed model(GLMM)are then proposed to derive the risk relativities of obtained clusters.Each basic rating unit within the same cluster,namely Forward Sortation Area(FSA),takes the same risk relativity value as its cluster.The obtained risk relativities from GLM or GLMM are used to calculate the performance metrics,including RMSE,MAD,and Gini coefficients.The spatially constrained clustering and the risk relativity estimate help obtain a set of territory risk benchmarks used in rate filings to guide the rate regulation process.展开更多
For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its...For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.展开更多
In this paper, the problem of estimating the covariance matrix in general linear mixed models is considered. A new class of estimators is proposed. It is shown that this new estimator dominates the analysis of varianc...In this paper, the problem of estimating the covariance matrix in general linear mixed models is considered. A new class of estimators is proposed. It is shown that this new estimator dominates the analysis of variance estimate under two squared loss functions. Finally, some simulation results to compare the performance of the proposed estimator with that of the analysis of variance estimate are reported. The simulation results indicate that this new estimator provides a substantial improvement in risk under most situations.展开更多
Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered. A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and th...Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered. A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance （Hendreson III＇s） estimate of variance components being uniformly minimum variance unbiased estimates simultaneously. This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest, and for finding equivalences of several common estimates of variance components.展开更多
In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that i...In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that is self scale invariant and then does not involve estimating limiting variance of the test statistic to avoid deteri- orating power of test. Furthermore, the bias correction makes the limit to be a process in which every variable is standard chi-squared. This simple structure of the process enables us to construct a Monte Carlo test proce- dure to approximate the null distribution. Thus, it overcomes a problem we encounter when classical empirical likelihood test is used, as it is asymptotically a functional of Gaussian process plus a normal shift function. The complicated covariance function makes it difficult to employ any approximation for the null distribution. The test is omnibus and power study shows that the test can detect local alternatives approaching the null at parametric rate. Simulations are carried out for illustration and for a comparison with existing method.展开更多
This paper discusses the estimation of fixed polynomial effects of mixed models based on PBIB, gives three concrete estimation, and analyses the condition of the design block while is orthogonal in these models. It al...This paper discusses the estimation of fixed polynomial effects of mixed models based on PBIB, gives three concrete estimation, and analyses the condition of the design block while is orthogonal in these models. It also shows in mixed models that the three estimations of fixed polynomial effects T are identical under tile fact that the design block is orthogonal.展开更多
DNA microarray technology is an extremely effective technique for studying gene expression patterns in cells, and the main challenge currently faced by this technology is how to analyze the large amount of gene expres...DNA microarray technology is an extremely effective technique for studying gene expression patterns in cells, and the main challenge currently faced by this technology is how to analyze the large amount of gene expression data generated. To address this, this paper employs a mixed-effects model to analyze gene expression data. In terms of data selection, 1176 genes from the white mouse gene expression dataset under two experimental conditions were chosen, setting up two conditions: pneumococcal infection and no infection, and constructing a mixed-effects model. After preprocessing the gene chip information, the data were imported into the model, preliminary results were calculated, and permutation tests were performed to biologically validate the preliminary results using GSEA. The final dataset consists of 20 groups of gene expression data from pneumococcal infection, which categorizes functionally related genes based on the similarity of their expression profiles, facilitating the study of genes with unknown functions.展开更多
Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to en...Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to engineering requirements, aiming to optimize satellite heat dissipation while considering constraints on static stability, 3D geometric relationships between components, and special component positions. The 3D-SCALO problem is a challenging bilevel combinatorial optimization task, involving the optimization of discrete component assignment variables in the outer layer and continuous component position variables in the inner layer,with both influencing each other. To address this issue, first, a Mixed Integer Programming(MIP) model is proposed, which reformulates the original bilevel problem into a single-level optimization problem, enabling the exploration of a more comprehensive optimization space while avoiding iterative nested optimization. Then, to model the 3D geometric relationships between components within the MIP framework, a linearized 3D Phi-function method is proposed, which handles non-overlapping and safety distance constraints between cuboid components in an explicit and effective way. Subsequently, the Finite-Rectangle Method(FRM) is proposed to manage 3D geometric constraints for complex-shaped components by approximating them with a finite set of cuboids, extending the applicability of the geometric modeling approach. Finally, the feasibility and effectiveness of the proposed MIP model are demonstrated through two numerical examples"and a real-world engineering case, which confirms its suitability for complex-shaped components and real engineering applications.展开更多
Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute s...Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute system. The reliability and availability equations of MRM were deduced. Results and Conclusion Compared with several other reliability models, it has obvious effect upon improving the system reliability. The effect? cost rate is very high among these models. The model can be used in reliability design, evaluation and check of C 3I system. Only a little attached cost is needed to improve C 3I system reliability effectively.展开更多
Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochast...Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.展开更多
Background: Predictive models shed light on aboveground fungal yield dynamics and can assist decision-making in forestry by integrating this valuable non-wood forest product into forest management planning. However, t...Background: Predictive models shed light on aboveground fungal yield dynamics and can assist decision-making in forestry by integrating this valuable non-wood forest product into forest management planning. However, the currently existing models are based on rather local data and, thus, there is a lack of predictive tools to monitor mushroom yields on larger scales.Results: This work presents the first empirical models for predicting the annual yields of ectomycorrhizal mushrooms and related ecosystem services in Pinus sylvestris and Pinus pinaster stands in northern Spain, using a long-term dataset suitable to account for the combined effect of meteorological conditions and stand structure.Models were fitted for the following groups of fungi separately: all ectomycorrhizal mushrooms, edible mushrooms and marketed mushrooms. Our results show the influence of the weather variables(mainly precipitation) on mushroom yields as well as the relevance of the basal area of the forest stand that follows a right-skewed unimodal curve with maximum predicted yields at stand basal areas of 30–40 m2·ha-1.Conclusion: These models are the first empirical models for predicting the annual yields of ectomycorrhizal mushrooms in Pinus sylvestris and Pinus pinaster stands in northern Spain, being of the highest resolution developed to date and enable predictions of mushrooms productivity by taking into account weather conditions and forests’ location, composition and structure.展开更多
A linear mixed model is used to determine the explaining infant mortality rate data of United Nations countries. The HDI （human development index） has a significant negative linear relationship with infant mortality...A linear mixed model is used to determine the explaining infant mortality rate data of United Nations countries. The HDI （human development index） has a significant negative linear relationship with infant mortality rate. United Nations data shows that the infant mortality rate has a descending trend over the period 1990-2010. This study aims to assess the value of the HDI as a predictor of infant mortality rate. Findings in the paper suggest that significant percentage reductions in infant mortality might be possible for countries for controlling the HDI.展开更多
Tree height (H) in a natural stand or forest plantation is a fundamental variable in management, and the use of mathematical expressions that estimate H as a function of diameter at breast height (d) or variables at t...Tree height (H) in a natural stand or forest plantation is a fundamental variable in management, and the use of mathematical expressions that estimate H as a function of diameter at breast height (d) or variables at the stand level is a valuable support tool in forest inventories. The objective was to fit and propose a generalized H-d model for Pinus montezumae and Pinus pseudostrobus established in forest plantations of Nuevo San Juan Parangaricutiro, Michoacan, Mexico. Using nonlinear least squares (NLS), 10 generalized H-d models were fitted to 883 and 1226 pairs of H-d data from Pinus montezumae and Pinus pseudostrobus, respectively. The best model was refitted with the maximum likelihood mixed effects model (MEM) approach by including the site as a classification variable and a known variance structure. The Wang and Tang equation was selected as the best model with NLS;the MEM with an additive effect on two of its parameters and an exponential variance function improved the fit statistics for Pinus montezumae and Pinus pseudostrobus, respectively. The model validation showed equality of means among the estimates for both species and an independent subsample. The calibration of the MEM at the plot level was efficient and might increase the applicability of these results. The inclusion of dominant height in the MEM approach helped to reduce bias in the estimates and also to better explain the variability among plots.展开更多
WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted ma...WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http：//agbu. une.edu.au/-kmeyer/wombat.html展开更多
基金supported by the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (0506011200702)National Natural Science Foundation of China+2 种基金Tian Yuan Special Foundation (10926059)Foundation of Zhejiang Educational Committee (Y200803920)Scientific Research Foundation of Hangzhou Dianzi University(KYS025608094)
文摘In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.
文摘Several computer packages have been developed to accomplish improved programs for animal breeding and genetic selection. This paper described most of the currant software and provided suggestions for improved software. Khon Kaen University, Thailand, will provide free of charge the new software developed at Khon Kaen University by the author of this paper. The contact for requesting the software is listed: monchai@kku.ac.th.
文摘Today, Linear Mixed Models (LMMs) are fitted, mostly, by assuming that random effects and errors have Gaussian distributions, therefore using Maximum Likelihood (ML) or REML estimation. However, for many data sets, that double assumption is unlikely to hold, particularly for the random effects, a crucial component </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">in </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">which assessment of magnitude is key in such modeling. Alternative fitting methods not relying on that assumption (as ANOVA ones and Rao</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">’</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s MINQUE) apply, quite often, only to the very constrained class of variance components models. In this paper, a new computationally feasible estimation methodology is designed, first for the widely used class of 2-level (or longitudinal) LMMs with only assumption (beyond the usual basic ones) that residual errors are uncorrelated and homoscedastic, with no distributional assumption imposed on the random effects. A major asset of this new approach is that it yields nonnegative variance estimates and covariance matrices estimates which are symmetric and, at least, positive semi-definite. Furthermore, it is shown that when the LMM is, indeed, Gaussian, this new methodology differs from ML just through a slight variation in the denominator of the residual variance estimate. The new methodology actually generalizes to LMMs a well known nonparametric fitting procedure for standard Linear Models. Finally, the methodology is also extended to ANOVA LMMs, generalizing an old method by Henderson for ML estimation in such models under normality.
基金financially supported by the"Programa de Mejoramiento del Profesorado"(project:Seguimiento y Evaluacion de Sitios Permanentes de Investigación Forestal y el Impacto Socioeconómico delManejo Forestal en Norte de México)supported by"Programa Banco Santander-USC"(becas para estancias predoctorales destinadas a docentes e investigadores de America Latina)
文摘Background:We used mixed models with random components to develop height-diameter(h-d) functions for mixed,uneven-aged stands in northwestern Durango(Mexico),considering the breast height diameter(d) and stand variables as predictors.Methods:The data were obtained from 44 permanent plots used to monitor stand growth under forest management in the study area.Results:The generalized Bertalanffy-Richards model performed better than the other generalized models in predicting the total height of the species under study.For the genera Pinus and Quercus,the models were successfully calibrated by measuring the height of a subsample of three randomly selected trees close to the mean d,whereas for species of the genera Cupressus,Arbutus and Alnus,three trees were also selected,but they are specifically the maximum,minimum and mean d trees.Conclusions:The presented equations represent a new tool for the evaluation and management of natural forest in the region.
基金supported in part by a grant of Research Grants Council of Hong Kong,and National Natural Science Foundation of China (Grant No. 11101157)
文摘Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.
基金Supported by the National Natural Science Foundation of China (60704002)
文摘The transient behaviors of traditional adaptive control may be very poor in general. A practically feasible approach to improve the transient performances is the adoption of adaptive switc- hing control. For a typical class of nonlinear systems disturbed by random noises, mixed multiple models consisting of adaptive model and fixed models were considered to design the switching con- trol law. Under certain assumptions, the nonlinear system with the switching control law was proved rigorously to be stable and optimal A simulation example was provided to compare the performance of the switching control and the traditional adaptive control.
文摘Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation.Due to the optimality of insurance loss data groupings,clustering methods become the natural choice for such territory risk classification.In this work,spatially constrained clustering is first applied to insurance loss data to form rating territories.The generalized linear model(GLM)and generalized linear mixed model(GLMM)are then proposed to derive the risk relativities of obtained clusters.Each basic rating unit within the same cluster,namely Forward Sortation Area(FSA),takes the same risk relativity value as its cluster.The obtained risk relativities from GLM or GLMM are used to calculate the performance metrics,including RMSE,MAD,and Gini coefficients.The spatially constrained clustering and the risk relativity estimate help obtain a set of territory risk benchmarks used in rate filings to guide the rate regulation process.
基金supported by National Natural Science Foundation of China(Grant No.11401148)Ministry of Education of China,Humanities and Social Science Projects(Grant Nos.14YJC910005,10YJC790184)+2 种基金Zhejiang Provincial Natural Science Foundation of China(Grant No.LY14A010030)Zhejiang Provincial Philosophy and Social Science Planning Project of China(Grant No.13NDJC089YB)Houji Scholar Fund of Northwest A and F University,China
文摘For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.
基金This research is supported by National Natural Science Foundation of China, Tian Yuan Special Foundation under Grant No. 10926059 and Zhejiang Provincial Natural Science Foundation of China under Grant No. Y6100053.
文摘In this paper, the problem of estimating the covariance matrix in general linear mixed models is considered. A new class of estimators is proposed. It is shown that this new estimator dominates the analysis of variance estimate under two squared loss functions. Finally, some simulation results to compare the performance of the proposed estimator with that of the analysis of variance estimate are reported. The simulation results indicate that this new estimator provides a substantial improvement in risk under most situations.
基金Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality PHR (IHLB)National Natural Science Foundation of China (NSFC) (10801005) and (NSFC) (10771010)the Intramural Research Program of the National Institute of Child Health and Human Development,National Institute of Health
文摘Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered. A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance （Hendreson III＇s） estimate of variance components being uniformly minimum variance unbiased estimates simultaneously. This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest, and for finding equivalences of several common estimates of variance components.
基金Supported by the National Natural Science Foundation of China(No.10901109)a grant(HKBU2030/07P)from the Research Grants Council of Hong Kong,Hong Kong,China
文摘In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that is self scale invariant and then does not involve estimating limiting variance of the test statistic to avoid deteri- orating power of test. Furthermore, the bias correction makes the limit to be a process in which every variable is standard chi-squared. This simple structure of the process enables us to construct a Monte Carlo test proce- dure to approximate the null distribution. Thus, it overcomes a problem we encounter when classical empirical likelihood test is used, as it is asymptotically a functional of Gaussian process plus a normal shift function. The complicated covariance function makes it difficult to employ any approximation for the null distribution. The test is omnibus and power study shows that the test can detect local alternatives approaching the null at parametric rate. Simulations are carried out for illustration and for a comparison with existing method.
文摘This paper discusses the estimation of fixed polynomial effects of mixed models based on PBIB, gives three concrete estimation, and analyses the condition of the design block while is orthogonal in these models. It also shows in mixed models that the three estimations of fixed polynomial effects T are identical under tile fact that the design block is orthogonal.
文摘DNA microarray technology is an extremely effective technique for studying gene expression patterns in cells, and the main challenge currently faced by this technology is how to analyze the large amount of gene expression data generated. To address this, this paper employs a mixed-effects model to analyze gene expression data. In terms of data selection, 1176 genes from the white mouse gene expression dataset under two experimental conditions were chosen, setting up two conditions: pneumococcal infection and no infection, and constructing a mixed-effects model. After preprocessing the gene chip information, the data were imported into the model, preliminary results were calculated, and permutation tests were performed to biologically validate the preliminary results using GSEA. The final dataset consists of 20 groups of gene expression data from pneumococcal infection, which categorizes functionally related genes based on the similarity of their expression profiles, facilitating the study of genes with unknown functions.
基金supported by the National Natural Science Foundation of China(No.92371206)the Postgraduate Scientific Research Innovation Project of Hunan Province,China(No.CX2023063).
文摘Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to engineering requirements, aiming to optimize satellite heat dissipation while considering constraints on static stability, 3D geometric relationships between components, and special component positions. The 3D-SCALO problem is a challenging bilevel combinatorial optimization task, involving the optimization of discrete component assignment variables in the outer layer and continuous component position variables in the inner layer,with both influencing each other. To address this issue, first, a Mixed Integer Programming(MIP) model is proposed, which reformulates the original bilevel problem into a single-level optimization problem, enabling the exploration of a more comprehensive optimization space while avoiding iterative nested optimization. Then, to model the 3D geometric relationships between components within the MIP framework, a linearized 3D Phi-function method is proposed, which handles non-overlapping and safety distance constraints between cuboid components in an explicit and effective way. Subsequently, the Finite-Rectangle Method(FRM) is proposed to manage 3D geometric constraints for complex-shaped components by approximating them with a finite set of cuboids, extending the applicability of the geometric modeling approach. Finally, the feasibility and effectiveness of the proposed MIP model are demonstrated through two numerical examples"and a real-world engineering case, which confirms its suitability for complex-shaped components and real engineering applications.
文摘Aim To define a mixed redundant model(MRM), improving the reliability of C 3I system. Methods The model combined the technology characters of two? unit system with one warm stand by unit and function substitute system. The reliability and availability equations of MRM were deduced. Results and Conclusion Compared with several other reliability models, it has obvious effect upon improving the system reliability. The effect? cost rate is very high among these models. The model can be used in reliability design, evaluation and check of C 3I system. Only a little attached cost is needed to improve C 3I system reliability effectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.82173620 to Yang Zhao and 82041024 to Feng Chen)partially supported by the Bill&Melinda Gates Foundation(Grant No.INV-006371 to Feng Chen)Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.
基金partially supported by the Spanish Ministry of Science,Innovation and Universities(grant number RTI2018-099315-A-I00)by the Spanish Ministry of Economy and Competitivity(MINECO)(Grant number AGL2015–66001-C3)+1 种基金by the Cost action FP1203:European Non-Wood Forest Products Networkby the European project Star Tree–Multipurpose trees and non-wood forest products(Grant number 311919)a Serra-Húnter Fellowship provided by the Generalitat of Catalunya
文摘Background: Predictive models shed light on aboveground fungal yield dynamics and can assist decision-making in forestry by integrating this valuable non-wood forest product into forest management planning. However, the currently existing models are based on rather local data and, thus, there is a lack of predictive tools to monitor mushroom yields on larger scales.Results: This work presents the first empirical models for predicting the annual yields of ectomycorrhizal mushrooms and related ecosystem services in Pinus sylvestris and Pinus pinaster stands in northern Spain, using a long-term dataset suitable to account for the combined effect of meteorological conditions and stand structure.Models were fitted for the following groups of fungi separately: all ectomycorrhizal mushrooms, edible mushrooms and marketed mushrooms. Our results show the influence of the weather variables(mainly precipitation) on mushroom yields as well as the relevance of the basal area of the forest stand that follows a right-skewed unimodal curve with maximum predicted yields at stand basal areas of 30–40 m2·ha-1.Conclusion: These models are the first empirical models for predicting the annual yields of ectomycorrhizal mushrooms in Pinus sylvestris and Pinus pinaster stands in northern Spain, being of the highest resolution developed to date and enable predictions of mushrooms productivity by taking into account weather conditions and forests’ location, composition and structure.
文摘A linear mixed model is used to determine the explaining infant mortality rate data of United Nations countries. The HDI （human development index） has a significant negative linear relationship with infant mortality rate. United Nations data shows that the infant mortality rate has a descending trend over the period 1990-2010. This study aims to assess the value of the HDI as a predictor of infant mortality rate. Findings in the paper suggest that significant percentage reductions in infant mortality might be possible for countries for controlling the HDI.
文摘Tree height (H) in a natural stand or forest plantation is a fundamental variable in management, and the use of mathematical expressions that estimate H as a function of diameter at breast height (d) or variables at the stand level is a valuable support tool in forest inventories. The objective was to fit and propose a generalized H-d model for Pinus montezumae and Pinus pseudostrobus established in forest plantations of Nuevo San Juan Parangaricutiro, Michoacan, Mexico. Using nonlinear least squares (NLS), 10 generalized H-d models were fitted to 883 and 1226 pairs of H-d data from Pinus montezumae and Pinus pseudostrobus, respectively. The best model was refitted with the maximum likelihood mixed effects model (MEM) approach by including the site as a classification variable and a known variance structure. The Wang and Tang equation was selected as the best model with NLS;the MEM with an additive effect on two of its parameters and an exponential variance function improved the fit statistics for Pinus montezumae and Pinus pseudostrobus, respectively. The model validation showed equality of means among the estimates for both species and an independent subsample. The calibration of the MEM at the plot level was efficient and might increase the applicability of these results. The inclusion of dominant height in the MEM approach helped to reduce bias in the estimates and also to better explain the variability among plots.
基金Project (No. BFGEN.100B) supported by the Meat and LivestockLtd., Australia (MLA)
文摘WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http：//agbu. une.edu.au/-kmeyer/wombat.html
