Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

涉海产业类企业融资效率及影响因素测评研究——基于DEA-Random Effects Models的经验数据

为发展壮大涉海产业类企业并带动海洋产业发展以实现海洋强国战略,有必要对涉海产业类企业融资效率状况进行准确定位并采取相应策略。以企业融资效率理论为基础,运用DEA模型评价涉海产业类企业融资效率及并运用随机效应面板数据模型检验其影响因素。检验结果发现,2008-2013年间涉海产业类企业融资效率整体上处于低效水平,其主要影响因素有宏观经济形势、行业竞争程度、企业规模大小和公司治理机制。企业融资效率与宏观经济形势、行业竞争程度和公司治理机制显著正相关,与企业规模大小显著负相关。这说明涉海产业类企业还有大幅度提高融资效率的空间,政策建议是引导资本市场支持海洋资源开发利用,保持稳定增长的整体经济环境,促进垄断竞争性涉海产业类企业理性投融资,缓解中小型涉海产业类企业融资难困境和深化国有控股涉海产业类企业改革。

EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL

Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.

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.

Bootstrap inference of the skew-normal two-way classification random effects model with interaction

In this paper,we consider the statistical inference problems for the fixed effect and variance component functions in the two-way classification random effects model with skewnormal errors.Firstly,the exact test statistic for the fixed effect is constructed.Secondly,using the Bootstrap approach and generalized approach,the one-sided hypothesis testing and interval estimation problems for the single variance component,the sum and ratio of variance components are discussed respectively.Further,the Monte Carlo simulation results indicate that the exact test statistic performs well in the one-sided hypothesis testing problem for the fixed effect.And the Bootstrap approach is better than the generalized approach in the one-sided hypothesis testing problems for variance component functions in most cases.Finally,the above approaches are applied to the real data examples of the consumer price index and value-added index of three industries to verify their rationality and effectiveness.

Inference Based on Empirical Likelihood for Varying Coefficient Model with Random Effect

In this article, we develop a statistical inference technique for the unknown coefficient functions in the varying coeffi- cient model with random effect. A residual-adjusted block empirical likelihood (RABEL) method is suggested to inves- tigate the model by taking the within-subject correlation into account. Due to the residual adjustment, the proposed RABEL is asymptotically chi-squared distribution. We illustrate the large sample performance of the proposed method via Monte Carlo simulations and a real data application.

Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the Bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.

INFLUENCE ANALYSIS IN NONLINEAR MODELS WITH RANDOM EFFECTS

In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to the mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented. A numerical example illustrates that the method is available.

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).

INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS

This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.

Automatic Variable Selection for Single-Index Random Effects Models with Longitudinal Data

We consider the problem of variable selection for the single-index random effects models with longitudinal data. An automatic variable selection procedure is developed using smooth-threshold. The proposed method shares some of the desired features of existing variable selection methods: the resulting estimator enjoys the oracle property;the proposed procedure avoids the convex optimization problem and is flexible and easy to implement. Moreover, we use the penalized weighted deviance criterion for a data-driven choice of the tuning parameters. Simulation studies are carried out to assess the performance of our method, and a real dataset is analyzed for further illustration.

Generalized Height-Diameter Models for Pinus montezumae Lamb. and Pinus pseudostrobus Lindl. Plantations in Michoacan, Mexico

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.

Mixed-effects modeling for tree height prediction models of Oriental beech in the Hyrcanian forests

Height–diameter relationships are essential elements of forest assessment and modeling efforts.In this work,two linear and eighteen nonlinear height–diameter equations were evaluated to find a local model for Oriental beech（Fagus orientalis Lipsky） in the Hyrcanian Forest in Iran.The predictive performance of these models was first assessed by different evaluation criteria： adjusted R^2（R^2_（adj））,root mean square error（RMSE）,relative RMSE（%RMSE）,bias,and relative bias（%bias） criteria.The best model was selected for use as the base mixed-effects model.Random parameters for test plots were estimated with different tree selection options.Results show that the Chapman–Richards model had better predictive ability in terms of adj R^2（0.81）,RMSE（3.7 m）,%RMSE（12.9）,bias（0.8）,%Bias（2.79） than the other models.Furthermore,the calibration response,based on a selection of four trees from the sample plots,resulted in a reduction percentage for bias and RMSE of about 1.6–2.7%.Our results indicate that the calibrated model produced the most accurate results.

基于指数随机图模型的发明者合作网络形成机制研究

聚焦探讨不同因素是否以及如何影响发明者合作网络形成,基于2004—2021年华为在中国申请的专利数据,构建发明者合作网络,运用指数随机图模型探讨行动者属性和内生结构效应对发明者合作网络形成的影响机理。结果表明:发明者合作网络是稀疏网络,呈现星形结构和闭合三角形结构共存的网络结构模式;发明者协同创新能力抑制新合作关系的形成,但发明者合作伙伴多样性和合作深度均促进新合作关系的形成,且具有相同水平合作伙伴多样性或合作深度的发明者之间更容易建立合作关系;发明者倾向于与处于中心位置的发明者建立合作关系以及与具有共同合作伙伴的直接合作伙伴建立新合作关系。

多变量联合模型在隧道通风系统寿命预测中的应用研究

为了提高隧道通风系统的智能运维水平,将基于数据驱动的联合模型引入隧道通风系统进行剩余使用寿命(Remaining Useful Life,RUL)预测,即综合失效事件和状态监测数据进行RUL动态预测。针对基于失效事件和状态监测数据融合的RUL预测,目前工业领域主要使用两阶段模型法,该方法遵循“先退化建模,后失效建模”的步骤。由于隧道通风系统受到地铁工况环境的影响,退化过程和失效事件存在相互影响,提出了基于多元变量的联合模型,旨在辨识共享随机效应,进而降低退化模型和失效模型估计偏差,提高隧道通风系统RUL动态预测的准确度。基于调研发现,地铁隧道通风系统主要故障模式为风机轴承磨损,研究主要通过风机轴承磨损失效仿真算例,选用平均绝对误差比较所提出的方法与两阶段法、单元联合模型的预测性能。算例研究结果表明,多元联合模型方法能有效辨识出监测状态演变和失效事件的关联关系,降低模型估计的偏差,为地铁隧道安全运行提供决策支持。

考虑空间溢出效应的高速公路交通事故随机参数频次模型

为提高高速公路事故频次模型参数估计的准确性,本文以精细的事故记录、道路属性、交通流状态和天气条件数据为样本,首先,构建传统的事故频次模型并对比拟合效果,选择效果最佳的泊松-对数正态分布模型作为优化的基础模型;之后,为挖掘更多的影响高速公路事故频次的空间效应,在加入条件自回归先验的基础上,本文考虑相邻路段的空间溢出效应,建立一个带有空间溢出协变量的模型分析空间溢出效应对路段事故频次的影响。同时,为描绘数据的异质性对路段事故频次的影响,进一步构建一个随机参数模型。结果表明,空间溢出效应显著有效,考虑空间自相关和空间溢出效应的随机参数模型的拟合优度相较于对照模型明显提升。根据最优模型的参数估计结果进行风险因素甄别,其中,“ln(MADT)”“ln(路段长度)”“1类车”“4类车”“降水”等普通变量以及“1类车S“”圆曲线长S”等空间溢出协变量与事故频次显著相关。

研发投入对黄河流域地区高质量发展效率的影响研究

通过对创新与高质量发展的作用机理研究,基于2011—2020年黄河流域九省(区)面板数据,对研发投入空间差异进行了纵横对比分析。研究借助Malmquist指数,从时间和空间维度测算研发投入对全要素生产率的影响效率,采用熵值法从多维度测评区域高质量发展水平,并建立单位根检验和随机效应模型,探究研发投入对经济高质量发展的影响。结果表明,研究期内黄河流域研发投入绩效整体呈现增长态势,存在研发投入规模和强度非对称现象;经济发展质量呈东强西弱态势,研发投入对经济高质量发展存在显著的正向促进作用,需要整合科技创新链条和资本链条,促进双向融合。

海底长周期地震动预测模型:以日本相模湾海域为例

地震动反应谱预测模型是地震危险性分析的基础,基于日本K-NET台网相模湾地区的892组海域地震动数据和4 033组陆域地震动数据,考虑震级、震源距、震源深度以及震源类型和场地,建立了PGA和0.05~15.0 s的海域地震动加速度反应谱预测模型。通过残差分析以及相关性分析检验了模型的合理性,并分析了震源类型以及震源深度对反应谱的影响,对比了海陆地震动预测模型的差异。结果表明:震源类型以及震源深度对模型预测结果影响显著,水平向海域模型以及长周期(T≥1.0 s)竖向海域模型所预测反应谱大于陆域模型所预测的反应谱值,且水平向和长周期竖向模型的场地放大系数均大于1。该模型可为长周期海域地震动模型的建立和概率地震危险性分析提供参考,为长周期海域工程的抗震设防提供依据。

日本海沟S-net台网水平向海域板缘地震动模型研究

地震动反应谱预测模型是概率地震危险性分析的基础,该文基于日本海沟大型海底台网S-net的海域俯冲带板缘地震动数据库,建立了俯冲带地区的水平向海域板缘地震动预测模型,分析了板缘地震的海陆地震动模型差异。在地震动模型中考虑了与场地信息有关的台站水深和沉积层厚度。由于海底台站的埋设方式不同,在模型中将台站按埋设和未埋设进行区分,通过回归分析和参数平滑建立了考虑震源类型、矩震级、震源深度、断层距、水深、沉积层厚度和埋设方式的水平向海域板缘地震动预测模型。通过对事件内残差进行分离,给出了研究区域的海底板缘模型单台标准差,可用于特定场点的概率地震危险性分析。该文的水平向海域板缘地震动模型可为考虑震源类型的海域区划和海域概率地震危险性分析提供参考。

牧户借贷对收入影响实证分析——基于100个固定调查户面板数据

为明确草原牧户借贷金额对其收入的影响,笔者于2020—2022年对鄂尔多斯市绒山羊核心养殖区牧户进行调研,采用随机效应模型和中介效应检验探索其影响机制。结果表明:鄂尔多斯地区牧户借贷金额不仅可以直接增加其经营性收入,还可以通过增加养殖业的支出间接促进经营性收入增长,牧户养殖业支出在牧户借贷与收入之间具有显著的中介效应,存在“牧户借贷-养殖业支出-收入增加”的作用机制。鉴于此,地方金融机构应大力发展牧户生产性贷款,满足牧户养殖业生产支出;地方政府、社会组织应积极培训牧民合理使用借贷资金,并为牧户的借贷做担保,积极鼓励信贷公司发放涉农涉牧贷款并向牧民养殖业生产提供信贷支持。