Linear regression remains an important framework in the era of big and complex data. In this talk I present some recent examples where we resort to the classical simple linear regression model and its celebrated extensions in novel settings. The Eureka moment came while reading Wu and Guan's (2015) comments on our generalized Kruskal-Wallis (GKW) test (Elif Acar and Sun 2013, Biometrics). Wu and Guan presented an alternative “rank linear regression model and derived the proposed GKW statistic as a score test statistic', and astutely pointed out that “the linear model approach makes the derivation more straightforward and transparent, and leads to a simplified and unified approach to the general rank based multi-group comparison problem.' More recently, we turned our attention to extending Levene's variance test for data with group uncertainty and sample correlation. While a direct modification of the original statistic is indeed challenging, I will demonstrate that a two-stage regression framework makes the ensuing development quite straightforward, eventually leading to a generalized joint location-scale test (David Soave and Sun 2017, Biometrics). Finally, I will discuss on-going work, with graduate student Lin Zhang, on developing an allele-based association test that is robust to the assumption of Hardy-Weinberg equilibrium and is generalizable to complex data structure. The crux of this work is, again, reformulating the problem as a regression!
