A nonparametric random coefficient approach for life expectancy growth using a hierarchical mixture likelihood model with application to regional data from North Rhine-Westphalia (Germany)

Dankmar Böhning,Rolf Annuß,Rainer Fehr,Claudia Terschüren,Sarah Karasek

doi:10.1186/1471-2288-13-36

Abstract

BackgroundLife expectancy is of increasing prime interest for a variety of reasons. In many countries, life expectancy is growing linearly, without any indication of reaching a limit. The state of North Rhine–Westphalia (NRW) in Germany with its 54 districts is considered here where the above mentioned growth in life expectancy is occurring as well. However, there is also empirical evidence that life expectancy is not growing linearly at the same level for different regions.MethodsTo explore this situation further a likelihood-based cluster analysis is suggested and performed. The modelling uses a nonparametric mixture approach for the latent random effect. Maximum likelihood estimates are determined by means of the EM algorithm and the number of components in the mixture model are found on the basis of the Bayesian Information Criterion. Regions are classified into the mixture components (clusters) using the maximum posterior allocation rule.ResultsFor the data analyzed here, 7 components are found with a spatial concentration of lower life expectancy levels in a centre of NRW, formerly an enormous conglomerate of heavy industry, still the most densely populated area with Gelsenkirchen having the lowest level of life expectancy growth for both genders. The paper offers some explanations for this fact including demographic and socio-economic sources.ConclusionsThis case study shows that life expectancy growth is widely linear, but it might occur on different levels.

Highlights

Life expectancy is of increasing prime interest for a variety of reasons
The approach is less focussed on explaining differentials in life expectancy by other factors, say socio–economic factors (Gallo et al [3]), in the sense of an ecological study analysis, we will take up this string in the discussion
Model and associated likelihoods We assume that the life expectancy Yit in region i and year t is available for i = 1, · · ·, n and t = 1, · · ·, T

Summary

Introduction

Life expectancy is of increasing prime interest for a variety of reasons. In many countries, life expectancy is growing linearly, without any indication of reaching a limit. There is empirical evidence that life expectancy is not growing linearly at the same level for different regions. Life expectancy in Germany is increasing unbrokenly at linear rate. This corresponds to a world–wide trend – despite controversial statements (see Oeppen and Vaupel [1] for this point). For each of the 54 regions a straight line model Yt = α + βt + is assumed for the life expectancy Yt at year t. In Section ‘Methods’, the nonparametric mixture model used for the cluster analysis is presented in parallel with life expectancy males

Methods

Results

Conclusion