Determinants of Time-to-Under-Five Mortality in Ethiopia: Comparison of Parametric Shared Frailty Models

2. The Problem

Many scholars using logistic regression and semi-parametric proportional hazard models have conducted studies to identify covariates of under-five mortality in Ethiopia. However, logistic regression modelling does not account the censoring observations. That is, logistic regression modelling does not hold for time-to-event data, and in demographic applications, nonparametric and semi-parametric models are often used to model transition data. In such applications, the model assume that all heterogeneity captured by theoretically relevant covariates (Trussell and Richards, 1985; Trussell and Rodriguez, 1990). In many situations, however, there are ample reasons to suspect omitted or unmeasured factors. That is, while some individuals will be more at risk of experiencing the event, it is unlikely the underlying reasons for this variability captured by the observed covariates. If there is unmeasured frailty, the hazard will not only be a function of the covariates but also of the frailty. To assess the true effects of the observed covariates under this circumstance, some have stressed the need to explicitly account for unobserved heterogeneity. Indeed, results from several empirical and simulation studies have shown that accounting for unobserved heterogeneity significantly improves overall model fitness (Aalen 1994; Baker and Melino 2000; Blossfeld and Hamerle 1992; Heckman et al., 1985; Lancaster 1990; Manda and Meyer 2005; Vaupel et al., 1979).