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)数据集中的观测数据通常会跨越时间和空间进行关联。正如Beck和Katz(1996)指出的那样，他们的经验分析通常反映了关于这些时间和空间依赖的两种观点之一。一些人认为这种关联令人讨厌。这些分析师关注的是对其他解释变量和因变量之间的关系做出准确的因果推断；只有在这种相关性可能危及这些理论上更核心的推断的情况下，才会对时间和空间相关性产生兴趣。考虑到这些目标，他们并不总是认为有必要直接对空间(或时间)相关性进行建模。他们认为，未能做到这一点的唯一代价是效率降低，因此，对空间(和时间)相关性稳健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)依赖关系更感兴趣，并试图直接对这些关系进行建模。政治学的标准做法现在是直接对动态(即时间相关性)进行建模，通常带有因变量的滞后，并仅通过应用面板校正的(稳健的)标准误差来处理空间相关性。因此，研究人员通常将空间依赖视为一种麻烦。然而，在这个项目中，研究人员认为，直接对空间相关性(可能还有稳健的标准误差)进行建模总是更优越的，无论这些关系是否有实质性的兴趣。直接建模空间相关性提高了效率，在许多情况下，对于获得非空间回归变量的无偏系数估计是必要的。例如，如果因变量和自变量在空间上相关，但统计模型忽略这些相关性或将它们的作用归于调整标准误差估计，则所产生的低效系数估计也将倾向于错误陈述(即偏差)解释变量的直接影响(增加空间扩散的影响或跨空间相关的省略刺激的影响)。这也意味着有偏见的假设检验，零假设被拒绝的频率或多或少超过了真正的保证。可以理解的是，对空间关系本身不感兴趣的分析师会希望对更复杂的扩散过程使用简单的代理，或者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这样简单的指标进行调查。相反，那些对空间相关性更直接感兴趣的人会更喜欢更复杂的建模技术，以估计他们数据中可能复杂的扩散模式。为了达到这些目的，研究人员探索了从计量经济学方法到动态面板模型的估计者的空间相似性(例如，Hsiao 1986；Balagi 1995)。这种复杂的方法论调查既针对对空间关系(空间实体)直接感兴趣的社会科学研究人员，也针对那些主要关注在给定空间依赖数据(空间滋扰)的情况下对其他实质性关系做出最佳推断的人。研究人员从时间依赖中出现的类似的、更好地探索的问题出发，通过解析推导和蒙特卡洛实验，研究了：(1)详细说明了未能直接对空间依赖进行建模(或将其作用归因于标准误差调整)导致其他系数估计有偏差或仅仅是低效的条件，探索在不同的空间依赖条件下的偏差和低效程度；(2)从概念上区分空间扩散与对省略的空间相关因素的相关反应，并探索从经验上进行这种区分的替代方法的性质；(3)开发和评估几种非、半和参数的空间相关性检验和量度，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，空间假人或由其他横截面单位的平均值组成的对称空间滞后。研究人员将创建并免费发布统计软件算法，以实现他们开发和探索的所有技术，并在可能有用的情况下，教授所有技术

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