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

'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.