The Annals of Statistics

Missing at random, likelihood ignorability and model completeness

Guobing Lu and John B. Copas

Full-text: Open access

Abstract

This paper provides further insight into the key concept of missing at random (MAR) in incomplete data analysis. Following the usual selection modelling approach we envisage two models with separable parameters: a model for the response of interest and a model for the missing data mechanism (MDM). If the response model is given by a complete density family, then frequentist inference from the likelihood function ignoring the MDM is valid if and only if the MDM is MAR. This necessary and sufficient condition also holds more generally for models for coarse data, such as censoring. Examples are given to show the necessity of the completeness of the underlying model for this equivalence to hold.

Article information

Source
Ann. Statist. Volume 32, Number 2 (2004), 754-765.

Dates
First available in Project Euclid: 28 April 2004

Permanent link to this document
http://projecteuclid.org/euclid.aos/1083178945

Digital Object Identifier
doi:10.1214/009053604000000166

Mathematical Reviews number (MathSciNet)
MR2060176

Zentralblatt MATH identifier
1048.62007

Subjects
Primary: 62B99: None of the above, but in this section 62F10: Point estimation 62N01: Censored data models

Keywords
Incomplete data missing at random coarsening at random ignorability complete distribution family

Citation

Lu, Guobing; Copas, John B. Missing at random, likelihood ignorability and model completeness. Ann. Statist. 32 (2004), no. 2, 754--765. doi:10.1214/009053604000000166. http://projecteuclid.org/euclid.aos/1083178945.


Export citation

References

  • Arnold, B. C., Castillo, E. and Sarabia, J. M. (1999). Conditional Specification of Statistical Models. Springer, New York.
  • Heitjan, D. F. (1993). Ignorability and coarse data: Some biomedical examples. Biometrics 49 1099--1109.
  • Heitjan, D. F. (1994). Ignorability in general incomplete-data models. Biometrika 81 701--708.
  • Heitjan, D. F. (1997). Ignorability, sufficiency and ancillarity. J. Roy. Statist. Soc. Ser. B 59 375--381.
  • Heitjan, D. F. and Rubin, D. B. (1991). Ignorability and coarse data. Ann. Statist. 19 2244--2253.
  • Jacobsen, M. and Keiding, N. (1995). Coarsening at random in general sample spaces and random censoring in continuous time. Ann. Statist. 23 774--786.
  • Kenward, M. G. and Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statist. Sci. 13 236--247.
  • Little, R. J. A. (1994). A class of pattern-mixture models for normal incomplete data. Biometrika 81 471--483.
  • Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data, 2nd ed. Wiley, New York.
  • Rubin, D. B. (1976). Inference and missing data (with discussion). Biometrika 63 581--592.
  • Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data. Chapman and Hall, London.
  • Tanner, M. A. (1993). Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 2nd ed. Springer, New York.
  • Zacks, S. (1971). The Theory of Statistical Inference. Wiley, New York.