In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases. This paper derives the...In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases. This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.展开更多
According to the hierarchical characteristics of monthly rainfall in different regions, the paper takes the geographical factors and seasonal factors into the hierarchical linear model as the level effect. Through clu...According to the hierarchical characteristics of monthly rainfall in different regions, the paper takes the geographical factors and seasonal factors into the hierarchical linear model as the level effect. Through clustering methods we select two more representative regional meteorological data. We establish three-layer model by transforming the interactive structure date into nested structure data. According the model theory we perform the corresponding model calculations, optimization and analysis, accordingly to interpret the level effects, and residual test. The results show that most of the difference in Monthly Rainfall was respectively explained by Variables (Meteorological factors, seasonal effects, geographic effects) in different levels.展开更多
In recent years,housing prices have attracted widespread attention,and the fluctuation of housing prices is due to a combination of many factors.In addition to the characteristics of the house itself,the price of a ho...In recent years,housing prices have attracted widespread attention,and the fluctuation of housing prices is due to a combination of many factors.In addition to the characteristics of the house itself,the price of a house is also affected by other factors,such as the community in which the house is located.This article used Beijing’s 2017 second-hand housing transaction data (based on second-hand housing transaction records on Lianjia.com),introduced a hierarchical linear model,and employed Stata software to analyze from different levels.It is intended to find the correlation between housing prices and different levels of characteristics,so to pin down the factors that affect prices of the second-hand housing.展开更多
Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studie...Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.展开更多
Ore sorting is a preconcentration technology and can dramatically reduce energy and water usage to improve the sustainability and profitability of a mining operation.In porphyry Cu deposits,Cu is the primary target,wi...Ore sorting is a preconcentration technology and can dramatically reduce energy and water usage to improve the sustainability and profitability of a mining operation.In porphyry Cu deposits,Cu is the primary target,with ores usually containing secondary‘pay’metals such as Au,Mo and gangue elements such as Fe and As.Due to sensing technology limitations,secondary and deleterious materials vary in correlation type and strength with Cu but cannot be detected simultaneously via magnetic resonance(MR)ore sorting.Inferring the relationships between Cu and other elemental abundances is particularly critical for mineral processing.The variations in metal grade relationships occur due to the transition into different geological domains.This raises two questions-how to define these geological domains and how the metal grade relationship is influenced by these geological domains.In this paper,linear relationship is assumed between Cu grade and other metal grades.We applies a Bayesian hierarchical(partial-pooling)model to quantify the linear relationships between Cu,Au,and Fe grades from geochemical bore core data.The hierarchical model was compared with two other models-‘complete-pooling’model and‘nopooling’model.Mining blocks were split based on spatial domain to construct hierarchical model.Geochemical bore core data records metal grades measured from laboratory assay with spatial coordinates of sample location.Two case studies from different porphyry Cu deposits were used to evaluate the performance of the hierarchical model.Markov chain Monte Carlo(MCMC)was used to sample the posterior parameters.Our results show that the Bayesian hierarchical model dramatically reduced the posterior predictive variance for metal grades regression compared to the no-pooling model.In addition,the posterior inference in the hierarchical model is insensitive to the choice of prior.The data is wellrepresented in the posterior which indicates a robust model.The results show that the spatial domain can be successfully utilised for metal grade regression.Uncertainty in estimating the relationship between pay metals and both secondary and gangue elements is quantified and shown to be reduced with partial-pooling.Thus,the proposed Bayesian hierarchical model can offer a reliable and stable way to monitor the relationship between metal grades for ore sorting and other mineral processing options.展开更多
While much of international marketing research involves two or more levels, limited work in the international marketing literature uses hierarchical linear modeling to examine different level effects. This study condu...While much of international marketing research involves two or more levels, limited work in the international marketing literature uses hierarchical linear modeling to examine different level effects. This study conducts a thorough literature review on hierarchical linear modeling （HLM） in 28 international marketing papers that employed HLM from 2005-2014 and evaluates the use of HLM in these papers on the objects, operating levels, and other issues. We call for more applications of HLM in international marketing research, particularly for research on emerging markets with significant sub-national and institutional variations. The paper provides an illustrative empirical study that employs HLM to test the moderating role of industry-level government subsidies in the relationship between firm innovation and exporter performance in China.展开更多
基金supported by the National Science Foundation of China under Grant Nos.71361015,71340010,71371074the Jiangxi Provincial Natural Science Foundation under Grant No.20142BAB201013+2 种基金China Postdoctoral Science Foundation under Grant No.2013M540534China Postdoctoral Fund special Project under Grant No.2014T70615Jiangxi Postdoctoral Science Foundation under Grant No.2013KY53
文摘In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases. This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.
文摘According to the hierarchical characteristics of monthly rainfall in different regions, the paper takes the geographical factors and seasonal factors into the hierarchical linear model as the level effect. Through clustering methods we select two more representative regional meteorological data. We establish three-layer model by transforming the interactive structure date into nested structure data. According the model theory we perform the corresponding model calculations, optimization and analysis, accordingly to interpret the level effects, and residual test. The results show that most of the difference in Monthly Rainfall was respectively explained by Variables (Meteorological factors, seasonal effects, geographic effects) in different levels.
文摘In recent years,housing prices have attracted widespread attention,and the fluctuation of housing prices is due to a combination of many factors.In addition to the characteristics of the house itself,the price of a house is also affected by other factors,such as the community in which the house is located.This article used Beijing’s 2017 second-hand housing transaction data (based on second-hand housing transaction records on Lianjia.com),introduced a hierarchical linear model,and employed Stata software to analyze from different levels.It is intended to find the correlation between housing prices and different levels of characteristics,so to pin down the factors that affect prices of the second-hand housing.
文摘Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.
基金This research was funded by the CSIRO ResearchPlus Science Leader Grant Program.
文摘Ore sorting is a preconcentration technology and can dramatically reduce energy and water usage to improve the sustainability and profitability of a mining operation.In porphyry Cu deposits,Cu is the primary target,with ores usually containing secondary‘pay’metals such as Au,Mo and gangue elements such as Fe and As.Due to sensing technology limitations,secondary and deleterious materials vary in correlation type and strength with Cu but cannot be detected simultaneously via magnetic resonance(MR)ore sorting.Inferring the relationships between Cu and other elemental abundances is particularly critical for mineral processing.The variations in metal grade relationships occur due to the transition into different geological domains.This raises two questions-how to define these geological domains and how the metal grade relationship is influenced by these geological domains.In this paper,linear relationship is assumed between Cu grade and other metal grades.We applies a Bayesian hierarchical(partial-pooling)model to quantify the linear relationships between Cu,Au,and Fe grades from geochemical bore core data.The hierarchical model was compared with two other models-‘complete-pooling’model and‘nopooling’model.Mining blocks were split based on spatial domain to construct hierarchical model.Geochemical bore core data records metal grades measured from laboratory assay with spatial coordinates of sample location.Two case studies from different porphyry Cu deposits were used to evaluate the performance of the hierarchical model.Markov chain Monte Carlo(MCMC)was used to sample the posterior parameters.Our results show that the Bayesian hierarchical model dramatically reduced the posterior predictive variance for metal grades regression compared to the no-pooling model.In addition,the posterior inference in the hierarchical model is insensitive to the choice of prior.The data is wellrepresented in the posterior which indicates a robust model.The results show that the spatial domain can be successfully utilised for metal grade regression.Uncertainty in estimating the relationship between pay metals and both secondary and gangue elements is quantified and shown to be reduced with partial-pooling.Thus,the proposed Bayesian hierarchical model can offer a reliable and stable way to monitor the relationship between metal grades for ore sorting and other mineral processing options.
基金The anthors are grateful for the financial support of the Research Funding for the Doctoral Programs of Higher Education, Ministry of Education, China （20120004120005）, the Beijing Youth Talent Project, and National Natural Science Foundation of China （71202149）.
文摘While much of international marketing research involves two or more levels, limited work in the international marketing literature uses hierarchical linear modeling to examine different level effects. This study conducts a thorough literature review on hierarchical linear modeling （HLM） in 28 international marketing papers that employed HLM from 2005-2014 and evaluates the use of HLM in these papers on the objects, operating levels, and other issues. We call for more applications of HLM in international marketing research, particularly for research on emerging markets with significant sub-national and institutional variations. The paper provides an illustrative empirical study that employs HLM to test the moderating role of industry-level government subsidies in the relationship between firm innovation and exporter performance in China.
