Applications of multilevel modelling: An evaluation of the assumption of no correlation between explanatory variables and random effects

“多层次模型”，这里定义为统计模型，包括随机效应参数，以分析数据结构，在更高层次的单位中，个体案例的聚类特征，是社会科学中流行和广泛使用的分析工具。然而，当在应用研究场景中部署多层模型时，它们经常违反与其统计估计相关的假设，即估计的随机效应与解释变量（以下简称“NCRX”）不相关。如果存在相关性，则已证明参数估计可能存在偏差和/或效率低下。尽管NCRX假设的统计问题已经得到证明，但仍有许多研究应用没有充分探索这一假设，而且在如何认真对待这一假设方面，社会科学学科之间存在显著分歧。该博士项目将回顾社会科学学科中关于NCRX假设的方法论和应用研究文献；分析模拟数据，探讨假设在不同可信情境下的重要性；并对两个案例研究进行二次调查分析（使用“了解社会”，特别许可版本），这些案例研究将说明《残疾人权利法》及其违反行为的不同后果（职业造成的社会经济不平等和地方造成的保健不平等）。博士学位的目的是传达问题及其相关性；比较和对比研究应用中对NCRX假设的反应；并制定和推广适当的理论和操作方法建议。它将通过比较跨学科的应用研究，并通过审查与准备、估计和解释统计模型有关的所有活动，作出原创性贡献。研究结果将对我们如何理解和支持使用复杂统计模型的应用社会研究产生影响。

'Multilevel models', defined here as statistical models that include random effects parameters in order to analyse a data structure that features clustering of individual cases within higher level units, are popular and widely used analytical tools across the social sciences. Nevertheless, when multilevel models are deployed in applied research scenarios, they frequently violate an assumption associated with their statistical estimation, namely that the estimated random effects are uncorrelated with explanatory variables (hereafter 'NCRX'). If there is a correlation, it has been demonstrated that parameter estimates could be biased and/or inefficient. Although the statistical issues of the NCRX assumption have already been demonstrated, there remain many research applications where the assumption is not fully explored, and there are notable divergences between social science disciplines in how seriously the assumption is taken.This PhD project will review methodological and applied research literature on the NCRX assumption across social science disciplines; analyse simulated data to explore the importance of the assumption in different plausible contexts; and pursue secondary survey analyses (using 'Understanding Society', special licence versions) on two case studies that will illustrate varying consequences of NCRX and its violation (on socio-economic inequalities by occupations, and on health inequalities by localities).The aims of the PhD are to communicate the issue and its relevance; to compare and contrast responses to the NCRX assumption in research applications; and to develop and promote appropriate methodological recommendations, both theoretical and operational. It will make an original contribution by comparing applied research across disciplines, and by examining the full spectrum of activities that are associated with preparing, estimating and interpreting statistical models. The outcomes of the research will have an impact on how we understand and support applied social research that uses complex statistical models.