Diagnosing, Modeling, Interpreting, and Leveraging Spatial Relationships in Time-Series-Cross-Section Data

社会科学家认识到，时间序列横截面（TSCS）数据集中的观测通常会在时间和空间上相互关联。正如Beck和Katz（1996）所指出的，他们的经验分析通常反映了对这些时间和空间依赖性的两种观点之一。有些人认为这种相关性是一种麻烦。这些分析师的关注点围绕着对其他解释变量和因变量之间的关系进行准确的因果推断;只有在这种依赖可能危及这些理论上更重要的推断的情况下，才对时间和空间依赖感兴趣。考虑到这些目标，他们并不总是认为有必要直接建模空间（或时间）依赖性。他们认为，不这样做的唯一代价是效率降低，因此，对空间（和时间）相关性鲁棒的标准误差估计可能足以确保合理的推断，这一点有时是错误的。其他人对空间（和时间）依赖性有更实质性的兴趣，并试图直接建模这些关系。政治学的标准做法现在是对动态进行建模（即，时间依赖性），通常具有因变量的滞后，并且仅通过应用面板校正（鲁棒）标准误差来解决空间依赖性。因此，研究人员通常将空间依赖视为一种讨厌的东西。 然而，在这个项目中，研究人员认为，直接建立空间依赖模型（也许加上稳健的标准误差）总是上级的，不管对这些关系的实质性兴趣如何。直接建模的空间依赖性提高了效率，在许多情况下，是必要的，以获得非空间回归的无偏系数估计。如果，例如，因变量和自变量都在空间上相关，但是统计模型忽略了这些相关性或者将它们的作用降级为调整标准误差估计，所得到的无效系数估计也将倾向于误报（即，偏差）解释变量的直接影响（加上空间扩散或忽略的刺激的影响，这些刺激在空间上相互关联）。这也意味着有偏见的假设检验，与零假设拒绝或多或少经常比真正的保证。可以理解的是，对空间关系本身不感兴趣的分析师将希望使用简单的代理来处理更复杂的扩散过程或省略空间相关的刺激。 研究人员将空间滞后和指标作为两个简单的替代指标进行了研究。相反，那些对空间依赖性更直接感兴趣的人将更喜欢更复杂的建模技术来估计其数据中可能复杂的扩散模式。 为了这些目的，研究人员探索从计量经济学方法到动态面板模型（例如，Hsiao 1986;这个复杂的方法论研究既针对对空间关系（空间实质）直接感兴趣的社会科学研究人员，也针对那些主要关心在给定空间依赖数据（空间干扰）的情况下对其他实质关系做出最佳推断的人。从类比的角度出发，通过分析推导和蒙特卡罗实验，研究人员：（1）详细说明了无法直接建模空间依赖性的条件（或将其作用归于标准误差调整）使其他系数估计值有偏差或仅仅是无效的，在不同的空间依赖条件下探索偏差和无效的程度;（2）从概念上区分空间扩散和对省略的空间相关因素的相关反应，并探索经验上进行这种区分的替代方法的性质;（3）开发和评估几种空间相关性的非、半和参数检验和测量，在模型中有和没有空间滞后;（4）比较真实空间扩散或共同遗漏因素的完整模型的简单代理的性质--例如，由其他横截面单元的平均值组成的空间虚拟或对称空间滞后。每个时间段的因变量--相互之间，单独的PCSE，以及估计更完整模型的不同方法。研究人员将创建并免费发布教学软件算法，并在可能有用的地方，教学模块，教授他们开发和探索的所有技术

Social scientists recognize that observations in time-series-cross-section (TSCS) datasets will usually correlate across time and space. As Beck and Katz (1996) noted, their empirical analyses typically reflect one of two perspectives on these temporal and spatial dependencies. Some see such correlations as a nuisance. These analysts' concerns surround the drawing of accurate causal inferences about relations between other explanatory variables and the dependent variables; interest in temporal and spatial dependence arises only insofar as such dependence might jeopardize these theoretically more-central inferences. Given these goals, they do not always see a need to model spatial (or temporal) dependence directly. They argue, sometimes incorrectly, that the only cost of failing to do so lies in reduced efficiency, and that, therefore, estimation of standard errors robust to spatial (and temporal) correlation may suffice to ensure sound inferences. Others have more-substantive interest in spatial (and temporal) dependence and attempt to model these relationships directly. Standard practice in political science is now to model dynamics (i.e., temporal dependence) directly, typically with lags of the dependent variable, and to address spatial dependence solely by applying panel-corrected (robust) standard-errors. Thus, researchers commonly treat spatial dependence as a nuisance. In this project, the researchersargue, however, that direct modeling of spatial dependence (plus robust standard-errors perhaps) is always superior, regardless of the substantive interest in these relationships. Directly modeling spatial dependence enhances efficiency and, under many circumstances, is necessary to obtain unbiased coefficient estimates for non-spatial regressors. If, e.g., both dependent and independent variables correlate spatially, yet the statistical model ignores these correlations or relegates their role to adjusting standard-error estimates, the resulting inefficient coefficient estimates will also tend to misstate (i.e., bias) the direct effects of explanatory variables (adding to them the effects of spatial diffusion or of omitted stimuli that correlate across space). This also implies biased hypothesis tests, with null hypotheses rejected more or less often than truly warranted. Understandably, analysts uninterested in spatial relationships per se will want to employ simple proxies for more-complicated diffusion processes or omitted spatially correlated stimuli. The researchers investigate spatial lags and indicators as two such simple proxies. Those more directly interested in spatial dependence, contrarily, will prefer more sophisticated modeling techniques to estimate the possibly complex diffusion patterns in their data. For these purposes, the investigators explore spatial analogues to estimators from econometric approaches to dynamic-panel models (e.g., Hsiao 1986; Baltagi 1995).This sophisticated methodological investigation is addressed both to social-science researchers directly interested in spatial relationships (spatial substance) and to those primarily concerned to make optimal inferences regarding other substantive relationships given spatially dependent data (spatial nuisance). Building from analogies to similar, better-explored issues arising in temporal dependence and through analytic derivation and Monte Carlo experimentation, the investigators: (1) detail the conditions under which failing to model spatial dependence directly (or relegating its role to standard-error adjustment) renders other coefficient estimates biased or merely inefficient, exploring bias and inefficiency magnitudes under varying spatial-dependence conditions; (2) distinguish spatial diffusion from correlated responses to omitted spatially correlated factors conceptually and explore the properties of alternative approaches to making this distinction empirically; (3) develop and evaluate several non-, semi-, and parametric tests for and gauges of spatial correlation, with and without spatial lags in the model; (4) compare the properties of simple proxies for full models of the true spatial-diffusion or common omitted-factors--e.g., spatial dummies or symmetric spatial-lags comprised of averages of other cross-section units. dependent variables each time-period--to each other, to PCSE's alone, and to differing methods of estimating fuller models.The researchers will create and publish freely statistical-software algorithms to implement, and, where potentially useful, pedagogical modules, to teach, all of the techniques that they develop and explore