Statistics and Computing

, Volume 24, Issue 2, pp 155–164

Estimating parametric semi-Markov models from panel data using phase-type approximations



Inference for semi-Markov models under panel data presents considerable computational difficulties. In general the likelihood is intractable, but a tractable likelihood with the form of a hidden Markov model can be obtained if the sojourn times in each of the states are assumed to have phase-type distributions. However, using phase-type distributions directly may be undesirable as they require estimation of parameters which may be poorly identified. In this article, an approach to fitting semi-Markov models with standard parametric sojourn distributions is developed. The method involves establishing a family of Coxian phase-type distribution approximations to the parametric distribution and merging approximations for different states to obtain an approximate semi-Markov process with a tractable likelihood. Approximations are developed for Weibull and Gamma distributions and demonstrated on data relating to post-lung-transplantation patients.


B-splines Gamma distribution Hidden Markov model Misclassification Panel data Phase-type distribution Semi-Markov Weibull 

Supplementary material

11222_2012_9360_MOESM1_ESM.pdf (297 kb)
(PDF 297 kB)

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterUK

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