Abstract
In a companion paper we described what intuitively would seem to be the most general possible way to generate Coarsening at Random mechanisms, a sequential procedure called randomized monotone coarsening. Counter-examples showed that CAR mechanisms exist which cannot be represented in this way. Here, we further develop these results in two directions. Firstly, we consider what happens when data is coarsened at random in two or more phases. We show that the resulting coarsening mechanism is not CAR anymore, but under suitable assumptions is identified and can provide interesting alternative analysis of data under a non-CAR model. Secondly, we look at sequential mechanisms for generating MAR data, missing components of a multivariate random vector. Randomised monotone missingness schemes, in which one variable at a time is observed and depending on its value, another variable is chosen or the procedure is terminated, supply in our opinion the broadest class of physically interpretable MAR mechanisms. We show that every randomised monotone missingness scheme can be represented by a Markov monotone missingness scheme, in which the choice of which variable to observe next only depends on the set of previously observed variables and their values, not on the sequence in which they were measured. We also show that MAR mechanisms exist which cannot be represented sequentially.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Bibliography
R.D. Gill, M.J. van der Laan and J.M. Robins (1997), Coarsening at random: characterizations, conjectures, counter-examples, Proc. First Seattle Symposium on Bio statistics: Survival Analysis, ed. D.Y. Lin, Springer-Verlag.
R.J.A. Little and D.B. Rubin (1987), Statistical Analysis with Missing Data, Wiley, New York.
J.M. Robins (1996), Non-response models for the analysis of non-monotone non-ignorable missing data. Statististics in Medicine, Special Issue, to appear.
J.M. Robins and R.D. Gill (1996), Non-response models for the analysis of non-monotone ignorable missing data, Statistics in Medicine.
D.B. Rubin (1976), Inference and missing data, Biometrika 63, 581–592.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Gill, R.D., Robins, J.M. (1997). Sequential Models for Coarsening and Missingness. In: Lin, D.Y., Fleming, T.R. (eds) Proceedings of the First Seattle Symposium in Biostatistics. Lecture Notes in Statistics, vol 123. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6316-3_15
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6316-3_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94992-5
Online ISBN: 978-1-4684-6316-3
eBook Packages: Springer Book Archive