Title: Partial association between ordinal variables: Quantification, visualization and estimation
Authors: Shaobo Li - University of Cincinnati (United States) [presenting]
Dungang Liu - University of Cincinnati (United States)
Yan Yu - University of Cincinnati (United States)
Abstract: Partial association measures the relationship between two variables $Y_1$ and $Y_2$ after adjusting a set of covariates $X$. It remains unknown how to fully characterize such an association if both $Y_1$ and $Y_2$ are recorded on ordinal scales. We propose a general measure, labeled as $\phi$, to characterize ordinal-ordinal partial association. It is based on surrogate residuals derived from fitting cumulative link regression models for each $Y_1$ and $Y_2$. We show the measure has the following properties: (1) its size reflects the strength of association for ordinal data, rather than the hypothetical latent variables; (2) it does not rely on the normality assumption or models with the probit link, but instead it broadly applies to models with any link functions; and (3) it can capture non-linear association and has a potential to detect dependence of any complex structures. We stress that the focus is not on hypothesis testing, but quantification and visualization. We demonstrate that our numerical and graphic assessment can reveal microstructure of partial association, which can inform statistical modeling of multivariate ordinal data.