Turning Hazard Models Inside Out

Abstract Regression Inside Out (RIO) describes a set of related methods based on a decomposition of regression coefficients by individual cases. In this article, we offer three important extensions of RIO: 1) we generalize RIO to any model for which linear predictors are estimated; 2) we introduce an adapted bootstrap approach for determining whether case-level contributions differ from the baseline average contribution for cases; and 3) we describe how RIO is related to model diagnostics, particularly DFBETA. To illustrate the value added of these extensions, we apply RIO to a published example of the Cox proportional hazard model exploring factors associated with democratic durability.