Academic journal article Demographic Research

Multistate Event History Analysis with Frailty

Academic journal article Demographic Research

Multistate Event History Analysis with Frailty

Article excerpt

(ProQuest: ... denotes formulae omitted.)

1. Introduction

Demographers are increasingly interested in understanding life histories or the individual life course, with a focus on events, their sequence, ordering and transitions that people make from one state of life to another. A multistate model describes the transitions people experience as life unfolds. When people may change among a set of multiple states and/or may experience repeated changes through time, a multistate event history model, also known as multistate lifetable and increment-decrement life tables, is a proper choice. Typ- ical examples of such processes in demography include migration, (Rogers 1975; 1995), changes in marital status and other life course processes, (Courgeau and Lelièvre 1992 and Willekens 1999). Many other demographic applications of the multistate models exist. Multistate models are also common in medicine and economics. In medicine, the states can designate conditions such as healthy, diseased and death. For an overview of the use of multistate models in biostatistics, see a.o. Commenges (1999), Hougaard (2000), and Putter, Fiocco, and Geskus (2007). In economics the main application of multistate models has been labour force dynamics; see Flinn and Heckman (1983), Van den Berg (2001) and, Fougère and Kamionka (2008). Poverty dynamics and recidivism are other important applications of multistate models. The methodology of multistate models is dis- cussed in several books; the most important are Andersen et al. (1993), Hougaard (2000), and Aalen, Borgan, and Gjessing (2008).

In our empirical application we focus on the return decision of labour migrants and its relation to labour market dynamics. Many migrants only stay temporarily in the host country. On the one hand, return migration is seen as planned and part of optimal decision making to maximize total utility over the whole life cycle, where return migration is mo- tivated by locational preference for the home country. On the other hand, return migration is seen as unplanned and the result of failure either due to imperfect information about the host country in terms of labor market prospects or the cost of living, or the inability to fulfil the migration plans in terms of target savings. In both cases, return behaviour is intrinsically related to the timing of labour market changes of the individual migrant. Migrants who become unemployed are more prone to leave, but when they find a new job again they are more prone to stay, see Bijwaard, Schluter, and Wahba (2014). Migrants who are employed in high paying jobs have a lower probability of becoming unemployed and can accumulate more savings while working. When these migrants have reached tar- get savings they are more prone to leave, see Bijwaard and Wahba (2014). Labour market dynamics may also be affected by the labour market history. These factors suggest that return migration behaviour of labour migrants should be modeled by a multistate model.

The basic parameters of a multistate model are the transition hazard rates or intensi- ties. These intensities may depend on the time spent in a particular state (semi-Markov models) and on observed characteristics. Many multistate models assume that the inten- sities are homogeneous, conditional on these observed factors. Unfortunately, it is hardly ever possible to include all relevant factors, either because the researcher does not know all the relevant factors, or because it is not possible to measure all the relevant factors. Ignoring such unobserved heterogeneity or frailty may have a large impact on inference in multistate models. The duration dependence, the effect of the length of the duration in a particular state on the exit rate out of this state, will be biased towards a more declining ef- fect of the duration when frailty is ignored. The effect of covariates on the transition rates will be biased towards zero when frailty is ignored. For univariate event history data, also called survival data or duration data, a large literature on models with frailty exits, e. …

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