Optimal Credibility Estimation of Random Parameters in Hierarchical Random Effect Linear Model

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.

Analysis of Factors Influencing Second-hand Housing Prices in Beijing based on Hierarchical Linear Model

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.

Neighborhood Effects and Political Trust: A Multi-level Analysis of Chinese Rural-to-Urban Migrants’ Trust in County Government

Massive rural-to-urban migration in China is consequential for political trust: rural-to-urban migrants have been found to hold lower levels of trust in local government than their rural peers who choose to stay in the countryside (mean 4.92 and 6.34 out of 10, respectively, p < 0.001). This article explores why migrants have a certain level of political trust in their county-level government. Using data of rural-to-urban migrants from the China Family Panel Survey, this study performs a hierarchical linear modeling (HLM) to unpack the multi-level explanatory factors of rural-to-urban migrants’ political trust. Findings show that the individual-level socio-economic characteristics and perceptions of government performance (Level-1), the neighborhood-level characteristics-the physical and social status and environment of neighborhoods (Level-2), and the objective macroeconomic performance of county-level government (Level-3), work together to explain migrants’ trust levels. These results suggest that considering the effects of neighborhood-level factors on rural-to-urban migrants’ political trust merits policy and public management attention in rapidly urbanizing countries.

Posterior propriety of an objective prior for generalized hierarchical normal linear models

Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.

Hierarchical Linear Modeling in International Marketing Research： A Review with an Application on Innovation and Export in China

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.

Should phenological information be applied to predict agronomic traits across growth stages of winter wheat?

Most existing agronomic trait models of winter wheat vary across growing seasons, and it is an open question whether a unified statistical model can be developed to predict agronomic traits using a vegetation index(VI) across multiple growing seasons. In this study, we constructed a hierarchical linear model(HLM) to automatically adapt the relationship between VIs and agronomic traits across growing seasons and tested the model’s performance by sensitivity analysis. Results demonstrated that(1) optical VIs give poor performance in predicting AGB and PNC across all growth stages, whereas VIs perform well for LAI, LGB, LNC, and SPAD.(2) The sensitivity indices of the phenological information in the AGB and PNC prediction models were 0.81–0.86 and 0.66–0.73, whereas LAI, LGB, LNC, and SPAD prediction models produced sensitivity indexes of 0.01–0.02, 0.01–0.02, 0.01–0.02, and 0.02–0.08, respectively.(3) The AGB and PNC prediction models considering ZS were more accurate than the prediction models based on VI. Whether or not phenological information is used, there was no difference in model accuracy for LGB,LNC, SPAD, and LAI. This study may provide a guideline for deciding whether phenological correction is required for estimation of agronomic traits across multiple growing seasons.

The Impacts of Income from Non-agricultural Industries Operated by Rural households on Farmers' Income

Income from non-agricultural industries operated by rural households is an important income source of farmers' income. According to the Regional Rural Residents' Net Income Per Capita in 2004 issued by the State Statistics Bureau and the relevant statistics of national comprehensive investigation(CGSS2005) in 2005, the impacts of farmers' income gap and farmers' individual features on their income and the impacts of income from non-agricultural industries operated by rural households on farmers' individual income differences are analyzed by applying Hierarchical Linear Models (HLM) as an analysis tool to establish the null model of HLM, excluding the second level model of the second level prediction variables and including the second level model of the second layer prediction variables. The analysis assumes that farmers' individual income varies hugely in different provinces; farmers' individual income has close relation with farmers' individual features; the improvement of income from non-agricultural industries operated by rural households has different impacts on farmers' income.

多维蓝绿空间特征与老年心理健康的关系探究

According to the Theory of Justice,the characteristics of vulnerable groups should be considered in realizing the mental health benefits of blue-green spaces,so as to promote substantive equity and welfare in cities.The unclear relationship between the blue-green space indicator system and the mental health of older adults at both the quantitative and qualitative levels has hindered the development of spatial justice and health equity in cities.Based on the theories of stress reduction and attention restoration,this paper uses the Hierarchical Linear Model to systematically explore the relationship between the qualitative(environmental characteristics and landscape patterns of parks and water bodies)and quantitative(visibility and accessibility)characteristics of blue-green spaces and the mental health of older adults.The research finds that in the spatial dimension,there is a significant difference in the relationship between the qualitative and quantitative indicators of blue-green space and the mental health of older adults,and the relationship between the availability,visibility,and accessibility of blue-green space and the mental health of older adults is weakened in turn.In the social dimension,resilient ecological spaces can regulate and buffer the negative impacts on the mental health of older adults that are brought about by unfavorable socio-economic factors like having no homeownership.The research can provide guidance for environmental design and the selection of planning indicators to improve the mental health of older adults,and give empirical evidence for reaching a more“equitable”layout of urban blue-green spaces,so as to promote the development of age friendly cities and green and healthy cities.