Extending the Discrete-Time Hazard Model
The basic discrete-time hazard model invokes assumptions about the population that may, or may not, hold in practice. This chapter examines its assumptions, demonstrating how to evaluate their tenability and relax their constraints when appropriate. Section 12.1 revisits the original specification for the main effect of TIME in the discrete-time hazard model—which, in the previous chapter, was specified using a system of time indicators—and compares it with other specifications that constrain the shape of the baseline hazard function in different ways. Section 12.2 re-examines the logit link that used to relate hazard to predictors in the previous chapter and compare it to an alternative—the complementary log-log link—which yields an important correspondence with the continuous time hazard models that we will describe subsequently. Section 12.3 deals with time-varying predictors, showing how to include them in the discrete-time model and discussing inferential difficulties that their inclusion raises. Sections 12.4 through 12.6, examines three important assumptions embedded in the discrete-time hazard model—the linear additivity assumption (“all predictors operate only as main effects”); the proportionality assumption (“the effects of each predictor are constant over time”); and the no unobserved heterogeneity assumption (“population hazard depends only on predictor values”). Section 12.7 concludes by describing analytic strategies for “residual” analysis to accompany model fitting.
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