Characterizing the correspondence between an ordinal measurement and a continuous measurement is often of interest in mental health studies. To this end, Peng, Li, Guo, and Manatunga (2011) introduced the concept of broad sense agreement (BSA) and developed nonparametric estimation and inference for a BSA measure. In this work, we propose a non-parametric regression framework for BSA, which provides a robust tool to further investigate population heterogeneity in BSA. We develop inferential procedures including regression function estimation and hypothesis testing. Extensive simulation studies demonstrate satisfactory performance of the proposed method. We also apply the new method to a recent Grady Trauma Study and reveal an interesting impact of depression severity on the alignment between a self-reported symptom instrument and clinician diagnosis in posttraumatic stress disorder (PSTD) patients.
Keywords: Broad sense agreement; Jackknife; Nonparametric regression; Primary: 62G08; Secondary: 62G20; U-statistic.