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Biometrika 2002 89(1):95-110; doi:10.1093/biomet/89.1.95
© 2002 by Biometrika Trust
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Estimating and interpolating a Markov chain from aggregate data

B.A. Davis1, C.R. Heathcote2 and T.J. O'neill3

1 School of Finance and Applied Statistics, Australian National University, Canberra ACT 0200, Australia brett.davis{at}anu.edu.au 2 Centre for Mathematics and its Applications, Australian National University, Canberra ACT 0200, Australia heacstat{at}maths.anu.edu.au 3 School of Finance and Applied Statistics, Australian National University, Canberra ACT 0200, Australia terry.oneill{at}anu.edu.au

Given aggregated longitudinal data generated by a Markov chain, which may be nonhomogeneous, the problem considered is that of modelling, estimating and interpolating the logarithms of partial odds and hence the transition probabilities.By partial odds is meant the probability of a transition to another state divided by the probability of no transition. A result establishing asymptotic normality leads to vector weighted least squares estimation of parameterised partial odds using standard regression methods. It is shown how to obtain estimates of one-step transition probabilities from widely or irregularly spaced data. The methods are illustrated on an example concerning competing causes of death.

Key Words: Interpolation; Longitudinal data; Markov chain; Odds; Vector regression; Weighted least squares

Received June 2000. Revised July 2001


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