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

“多层次模型”，在这里定义为统计模型，包括随机效应参数，以分析数据结构，其特征是在更高级别的单位内的个别情况的聚类，是流行的，广泛使用的分析工具，在社会科学。然而，当多层次模型部署在应用研究的情况下，他们经常违反与他们的统计估计，即估计的随机效应是不相关的解释变量（以下简称“NCRX”）的假设。如果存在相关性，则已证明参数估计值可能存在偏倚和/或效率低下。虽然NCRX假设的统计问题已经得到证明，但仍然有许多研究应用中的假设没有得到充分的探讨，社会科学学科之间在如何认真对待假设方面存在显着的分歧。分析模拟数据，以探索假设在不同合理背景下的重要性;并进行二次调查分析（使用“理解社会”，特别许可证版本）关于两个案例研究，将说明NCRX及其违反的不同后果博士学位的目的是沟通的问题及其相关性;比较和对比响应NCRX假设在研究应用;并制定和促进适当的方法建议，理论和操作。它将通过比较跨学科的应用研究，并通过审查与编制，估计和解释统计模型相关的全部活动，作出原创性贡献。研究的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.