空间随机截距模型及其参数估计

空间分层数据因为地理位置的原因，层与层之间会具有空间依赖性，区别于传统的分层数据。首先，文章将空间自相关的思想引入到随机截距模型中，在层-2模型中加入空间参数来反映空间自相关性，构建了空间随机截距模型；然后，针对空间随机截距模型，给出了基于EM算法和Fisher得分的最大似然估计。     

空间分层数据无条件模型的改进及其估计

抽样调查中得到的数据经常既包含个体信息又包含地理单元信息,形成以地区集聚的分层数据.空间分层数据中地理单元间往往具有空间依赖性,区别于传统的分层数据.分析空间分层数据时需要首先建立无条件模型用作初步分析.因此,在传统分层无条件模型中引入完全空间自回归模型来表达空间相关性,建立空间分层数据的无条件模型,并研究其估计方法,借助参数估计值可做模型选择.     

两个潜变量的PLS算法模拟数据分析

文章根据结构方程模型(SEM)数学定义和偏最小二乘法(PLS)形式规范,构建具有两个潜变量的路径模型。在潜变量因子值和模型系数假设已知情况下,生成仿真观测数据。通过对PLS算法处理结果与假设数据之间偏差比较,分析PLS算法特性,结果发现:潜变量模式选择影响测量模型系数;结构模型系数比假设值偏小而测量模型系数比假设值偏大。根据该算法特性可以优化模型,以获得更好的模型解释与预测能力。     

空气质量对生活满意度的效应研究——基于序数分层空间自回归Probit模型

在居民生活满意度的相关研究中,除考虑人口学特征外,越来越多的实证同时考虑了微观个体所处的宏观环境,对这类呈嵌套结构的分层数据需构建分层统计模型,但传统的分层统计模型未考虑真实的空间依赖。本文将分层统计模型和空间自回归模型相结合,创新性地构建了四种序数分层空间自回归Probit模型,该类模型能够合理地对因变量为序数且存在空间依赖情况并呈分层结构的数据进行建模,模型可避免忽略真实的空间依赖对模型估计的不利影响,且能够对高层组间的空间效应和低层个体间的空间效应区别对待,更有利于模型的解释。最后,空气质量对居民生活满意度的效应实证研究表明:空气质量确实能够对生活满意度产生影响,居民对空气质量的认识和要求并非孤立地局限于本地,而是对一个区域空气质量的空间综合结果。对比2018年和2016年模型结果可知:空气质量的福利效应无法被其他民生福祉因素所取代,并且随着空气质量相关统计信息的高度开放和广泛传播,居民更加重视空气质量,也形成了更加全局的了解。     

人口空间分布及迁移影响的实证分析——基于空间计量方法与河南省数据

在传统研究方法的基础上考虑空间相关性,运用空间计量经济学的理论与方法,并以河南省人口数据为例进行人口空间分布及迁移的实证研究。一方面,研究中运用全域空间性和局域空间性的相关知识分析河南省人口空间分布,通过定量性指标的运用得出河南省人口空间分布存在相关性,且是高值集聚,即人口密度较高的地区集中在一起;另一方面,在考虑空间相关性的基础上建立空间计量模型,主要研究各个政府支出对河南省人口迁移和分布的影响,结果发现各支出的影响显著。     

基于高维波动率网络模型的股票市场风险特征研究

波动率是金融风险管理研究的重要内容之一。本文基于复杂网络理论和数据挖掘技术提出股票市场的高维波动率网络模型。首先运用互信息度量不同股票价格波动之间的相关关系,其次对股票市场不同周期下的波动情况建立度的中心势、平均距离、幂律分布等网络拓扑指标,再次根据这些指标利用Prim算法构建出高维波动率网络模型,最后运用Newman-Girvan算法对股票价格波动率的相关性进行分层研究。高维波动率网络模型突破了传统波动率模型关于变量维数的限制,能够在依赖少量假设的基础上,挖掘出多个金融市场主体间的相互关系,反映金融市场的风险特征及网络拓扑性质。实证结果发现：与常用的Pearson相关系数法相比,在互信息框架下,股价波动的非线性相关关系得到了更好的度量;股票市场的整体波动性与个股波动率相关性变化趋势相反,市场处在高波动时期资产组合分散化效果较好;网络中存在少量度数大的关键节点和中心节点,风险通过这些节点可以迅速传递到整个市场;股票市场的运行具有明显的行业聚集现象;网络分层研究进一步直观的展现了风险在层与层之间的传递规律和与之对应的行业特征。高维波动率网络模型为挖掘股票市场的风险特征与管理金融风险提供了一个新的工具。     

索赔频率与索赔强度的相依性模型

为了解决索赔频率与索赔强度之间的相依性问题,本文提出了一种相依性调整模型,即首先在索赔频率和索赔强度相互独立的假设下预测纯保费,然后通过索赔频率与索赔强度之间的相关关系对独立性假设下的纯保费预测值进行调整.与现有模型相比,该模型的优点是可以将纯保费的预测值分解为两部分,即独立性假设下的纯保费和相依性对纯保费的影响,便于模型的解释和应用.本文将该方法应用于一组实际数据,并与其他方法进行了比较.实证研究结果表明,本文对纯保费的预测结果在一定程度上优于现有模型,而且更加清晰地揭示了索赔频率与索赔强度之间的相依性对纯保费预测值的影响,即纯保费较低的保单受相依性的影响较大,而纯保费较高的保单受相依性的影响较小.     

VIX指数对股票市场间联动性影响的实证研究

近期金融危机频繁发生,国际金融市场之间的动态联动性成为一个重要的研究课题。以往学者大都直接研究金融市场间的相关性,而忽略了外生金融变量对金融市场间相关性的影响。本文将对上述问题进行研究,借鉴Silvennoinen和Terasvirta(2015) STCC模型的思想,假定Copula参数受外生变量的影响,建立时变动态Copula模型——ST-VCopula模型,并基于该模型探究市场波动率（VIX指数）对股票市场之间相关性的影响,进而对几个国家的股票指数数据进行了实证分析。实证结果表明VIX指数对股票市场间联动性产生了显著的影响。VIX指数的获取简单便捷且更为直观,为市场间动态联动性的研究提供了另一种途径,可以为投资者在进行分散投资等金融活动时提供一定的指导和建议。     

中国城市住房价格的空间效应与滞后效应研究

本文首先借鉴适应性预期和理性预期的相关思想,构建新的住房价格预期形式,并将其引入住房存量调整模型,从预期的角度分析不同城市住房价格之间相互影响的机制.其次运用探索性空间数据分析工具研究了2002-2013年我国35个城市房价空间分布特征,结果显示,城市住房价格之间存在显著的正空间自相关性;城市房价的空间相关性随城市空间距离的增加而趋于减弱;城市房价的空间相关性随时间的推移逐步增强.最后通过构建空间动态面板模型实证研究城市房价在时间和空间上的特征,分析发现我国城市住房价格互动存在显著的时间滞后效应、空间溢出效应和空间滞后效应.     

带有覆盖半径的平面选址研究

选址结果受覆盖半径影响很大。传统的覆盖选址问题假设覆盖半径已知,基于集覆盖问题,首次提出考虑半径选择的覆盖选平面址模型,目标函数是使固定选址费用和覆盖费用之和最小。提出了一种新的混合遗传算法。最后通过大量随机算例仿真表明该算法计算结果较好。     

An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach – the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the statistical local area-based and grid-based approaches perform equally well for spatially dense data.     

基于分层模型的缺失数据插补方法研究

大规模抽样调查多采用复杂抽样设计,得到具有分层嵌套结构的调查数据集,其中不可避免会遇到数据缺失问题,针对分层结构含缺失数据集的插补策略目前鲜有研究。本文将Gibbs算法应用到分层含缺失数据集的多重插补过程中,分别研究了固定效应模型插补法和随机效应模型插补法,进而通过理论推导和数值模拟,在不同组内相关系数、群组规模、数据缺失比例等情形下,从参数估计结果的无偏性和有效性两方面,比较不同方法的插补效果,给出插补模型的选择建议。研究结果表明,采用随机效应模型作为插补模型时,得到的参数估计结果更准确,而固定效应模型作为插补模型操作相对简便,在数据缺失比例较小、组内相关系数较大、群组规模较大等情形下,可以采用固定效应插补模型,否则建议采用随机效应插补模型。     

A comparison of univariate and multivariate multilevel models for repeated measures of use of antenatal care in Uttar Pradesh

Summary.  We compare two different multilevel modelling approaches to the analysis of repeated measures data to assess the effect of mother level characteristics on women's use of prenatal care services in Uttar Pradesh, India. We apply univariate multilevel models to our data and find that the model assumptions are severely violated and the parameter estimates are not stable, particularly for the mother level random effect. To overcome this we apply a multivariate multilevel model. The correlation structure shows that, once the decision has been made regarding use of antenatal care by the mother for her first observed birth in the data, she does not tend to change this decision for higher order births.     

Assessing inter- and intra-agreement for dependent binary data: a Bayesian hierarchical correlation approach

Agreement measures are designed to assess consistency between different instruments rating measurements of interest. When the individual responses are correlated with multilevel structure of nestings and clusters, traditional approaches are not readily available to estimate the inter- and intra-agreement for such complex multilevel settings. Our research stems from conformity evaluation between optometric devices with measurements on both eyes, equality tests of agreement in high myopic status between monozygous twins and dizygous twins, and assessment of reliability for different pathologists in dysplasia. In this paper, we focus on applying a Bayesian hierarchical correlation model incorporating adjustment for explanatory variables and nesting correlation structures to assess the inter- and intra-agreement through correlations of random effects for various sources. This Bayesian generalized linear mixed-effects model (GLMM) is further compared with the approximate intra-class correlation coefficients and kappa measures by the traditional Cohen’s kappa statistic and the generalized estimating equations (GEE) approach. The results of comparison studies reveal that the Bayesian GLMM provides a reliable and stable procedure in estimating inter- and intra-agreement simultaneously after adjusting for covariates and correlation structures, in marked contrast to Cohen’s kappa and the GEE approach.     

Robust estimation of a multilevel model with structural change

We postulate a spatiotemporal multilevel model and estimate using forward search algorithm and MLE imbedded into the backfitting algorithm. Forward search algorithm ensures robustness of the estimates by filtering the effect of temporary structural changes in the estimation of the group-level covariates, the individual-level covariates and spatial parameters. Backfitting algorithm provides computational efficiency of estimation procedure assuming an additive model. Simulation studies show that estimates are robust even in the presence of structural changes induced for example by epidemic outbreak. The model also produced robust estimates even for small sample and short time series common in epidemiological settings.     

空间动态面板模型的时间滞后效应检验

空间面板数据模型由于考虑了经济变量间的空间相关性,其优势日益凸显,已成为计量经济学的热点研究领域。将空间相关性与动态模式同时扩展到面板模型中的空间动态面板模型,不仅考虑了经济变量之间的空间相关性,还考虑了时间上的滞后性,是空间面板模型的发展,增强了模型的解释力。考虑一种带固定个体效应、因变量的时间滞后项、因变量与随机误差项均存在空间自相关性的空间动态面板回归模型,提出了在个体数n和时间数T都很大,且T相对地大于n的条件下空间动态面板模型中时间滞后效应存在性的LM和LR检验方法,其检验方法包括联合检验、一维及二维的边际和条件检验;推导出这些检验在零假设下的极限分布;其极限分布均服从卡方分布。通过模拟试验研究检验统计量的小样本性质,结果显示其具有优良的统计性质。     

A practical approach for assessing the effect of grouping in hierarchical spatio-temporal models

Hierarchical spatio-temporal models allow for the consideration and estimation of many sources of variability. A general spatio-temporal model can be written as the sum of a spatio-temporal trend and a spatio-temporal random effect. When spatial locations are considered to be homogeneous with respect to some exogenous features, the groups of locations may share a common spatial domain. Differences between groups can be highlighted both in the large-scale, spatio-temporal component and in the spatio-temporal dependence structure. When these differences are not included in the model specification, model performance and spatio-temporal predictions may be weak. This paper proposes a method for evaluating and comparing models that progressively include group differences. Hierarchical modeling under a Bayesian perspective is followed, allowing flexible models and the statistical assessment of results based on posterior predictive distributions. This procedure is applied to tropospheric ozone data in the Italian Emilia–Romagna region for 2001, where 30 monitoring sites are classified according to environmental laws into two groups by their relative position with respect to traffic emissions.     

Multilevel dimensionality-reduction methods

When data sets are multilevel (group nesting or repeated measures), different sources of variations must be identified. In the framework of unsupervised analyses, multilevel simultaneous component analysis (MSCA) has recently been proposed as the most satisfactory option for analyzing multilevel data. MSCA estimates submodels for the different levels in data and thereby separates the “within”-subject and “between”-subject variations in the variables. Following the principles of MSCA and the strategy of decomposing the available data matrix into orthogonal blocks, and taking into account the between- and the within data structures, we generalize, in a multilevel perspective, multivariate models in which a matrix of response variables can be used to guide the projections (formed by responses predicted by explanatory variables or by a limited number of their combinations/composites) into choices of meaningful directions. To this end, the current paper proposes the multilevel version of the multivariate regression model and dimensionality-reduction methods (used to predict responses with fewer linear composites of explanatory variables). The principle findings of the study are that the minimization of the loss functions related to multivariate regression, principal-component regression, reduced-rank regression, and canonical-correlation regression are equivalent to the separate minimization of the sum of two separate loss functions corresponding to the between and within structures, under some constraints. The paper closes with a case study of an application focusing on the relationships between mental health severity and the intensity of care in the Lombardy region mental health system.     

Imputation of Household Survey Data Using Linear Mixed Models

Mixed models are regularly used in the analysis of clustered data, but are only recently being used for imputation of missing data. In household surveys where multiple people are selected from each household, imputation of missing values should preserve the structure pertaining to people within households and should not artificially change the apparent intracluster correlation (ICC). This paper focuses on the use of multilevel models for imputation of missing data in household surveys. In particular, the performance of a best linear unbiased predictor for both stochastic and deterministic imputation using a linear mixed model is compared to imputation based on a single level linear model, both with and without information about household respondents. In this paper an evaluation is carried out in the context of imputing hourly wage rate in the Household, Income and Labour Dynamics of Australia Survey. Nonresponse is generated under various assumptions about the missingness mechanism for persons and households, and with low, moderate and high intra‐household correlation to assess the benefits of the multilevel imputation model under different conditions. The mixed model and single level model with information about the household respondent lead to clear improvements when the ICC is moderate or high, and when there is informative missingness.