The Use of Simple Reparameterisations in MCMC Estimation of Multilevel Models with Applications to Discrete-Time Survival Models

Authors
Browne, W.J., Steele, F., Golalizadeh, M. and Green, M.
Year
2009
Journal
Journal of the Royal Statistical Society, Series A, 172(3), 579-598
DOI
10.1111/j.1467-985X.2009.00586.x
Abstract

We consider the application of Markov chain Monte Carlo (MCMC) estimation methods to random-effects models and in particular the family of discrete time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete time survival analysis involves expanding the data set so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However, the data expansion results in very large data sets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterization techniques can be used and assess their performance.

Number of levels
3
Model data structure
Response types
Multivariate response model?
No
Longitudinal data?
Yes
Further model keywords
Substantive discipline
Paper submitted by
Fiona Steele, Graduate School of Education, University of Bristol
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