QUANTILE REGRESSION AS A METHODOLOGY FOR UNDERPINNING PROPORTIONATE UNIVERSALISM
In the social sciences, and beyond, we are often interested in the impact of factors on some outcome. These research questions of interest are traditionally addressed with linear regression, which informs on those factors impacting on the average. Frequently though the interest is not in the ‘average’ but with those in the tails of the outcome distribution, where for example the low performing or high scoring are contained. This is particularly the case when these analyses are to inform policies to improve on those low performing and the identification and targeting of possible interventions for this. Focusing solely on the average and applying interventions across the board can only widen the gap between those low scoring and better performing. These traditional modelling methods will not provide information on differential impact of a factor across the distribution and indeed can fail to identify important factors. In addition to the analysis suitable to the research question there are inherent linear regression model assumptions which must be met. To try and address this using traditional techniques by segmenting the data to assess factor impact is inefficient and can have power implications. Also a logistic regression approach provides a cut-point with those on either side, regardless of their proximity to that cut-point being in one group or the other. Therefore to understand the effect of factors across the outcome distribution we must use different techniques and a quantile regression approach offers an assessment across the outcome distribution and can identify those factors which are influential at different locations on that distribution and is also robust to the assumptions which dog those other traditional methods. Thus with a principled method such as quantile regression analysis, there exists an enormous potential to inform not just basic policy questions, as to relationships amongst factors and outcome, but with the resulting more nuanced answers provide those key policymakers with a more complete evidence base with robust informative estimates on those mediating factors and on who to target.