Identifiability of the misspecified split hazard models

Abstract

Unlike standard models, a split population hazard model allows the exit probability to be less than one. Although conceptually attractive, split models are prone to identification problems. In the reduced form estimation of the hazard function, the influence of split may not be distinguishable from that of neglected heterogeneity. For illustration, I use Monte Carlo simulations to highlight the problem of interpreting the structural parameters of the split Weibull and the Weibull-gamma models.

Notes

¹ In biostatistics, these models, referred to as cure models, allow for a cured fraction of individuals who will never experience a reoccurrence of disease. For applications in economics and finance, see Bandopadhyaya and Jaggia (2001), DeYoung (2003), Mavromaras and Orme (2004), Chang and Yeh (2007), Madden (2007) etc.

² See Kiefer (1988) and Lancaster (1990).

³ See Schmidt and Witte (1989) and Bandopadhyaya and Jaggia (2001) for details.

⁴ Jaggia and Thosar (1995) suggest that the mixing distribution is used not only to compensate for omitted factors, but also to correct for an overly restrictive Weibull hazard function.

⁵ Note that for , the Weibull-gamma model specializes to a log-logistic model. Further, for , the model reduces to a basic Weibull with no heterogeneity.