Missing at random, likelihood ignorability and model completeness. (English) Zbl 1048.62007

Lu, Guobing; Copas, John B.

Ann. Stat. 32, No. 2, 754-765 (2004).

Summary: 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.

MSC:

62A01	Foundations and philosophical topics in statistics
62B99	Sufficiency and information
62F10	Point estimation
62N01	Censored data models

Keywords:

incomplete data; missing at random; coarsening at random; ignorability; complete distribution family

References:

[1]	Arnold, B. C., Castillo, E. and Sarabia, J. M. (1999). Conditional Specification of Statistical Models . Springer, New York. · Zbl 0932.62001 · doi:10.1007/b97592
[2]	Heitjan, D. F. (1993). Ignorability and coarse data: Some biomedical examples. Biometrics 49 1099–1109. · Zbl 0825.62755 · doi:10.2307/2532251
[3]	Heitjan, D. F. (1994). Ignorability in general incomplete-data models. Biometrika 81 701–708. · Zbl 0810.62008 · doi:10.1093/biomet/81.4.701
[4]	Heitjan, D. F. (1997). Ignorability, sufficiency and ancillarity. J. Roy. Statist. Soc. Ser. B 59 375–381. · Zbl 0886.62006 · doi:10.1111/1467-9868.00073
[5]	Heitjan, D. F. and Rubin, D. B. (1991). Ignorability and coarse data. Ann. Statist. 19 2244–2253. JSTOR: · Zbl 0745.62004 · doi:10.1214/aos/1176348396
[6]	Jacobsen, M. and Keiding, N. (1995). Coarsening at random in general sample spaces and random censoring in continuous time. Ann. Statist. 23 774–786. JSTOR: · Zbl 0839.62001 · doi:10.1214/aos/1176324622
[7]	Kenward, M. G. and Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statist. Sci. 13 236–247. · Zbl 1099.62503 · doi:10.1214/ss/1028905886
[8]	Little, R. J. A. (1994). A class of pattern-mixture models for normal incomplete data. Biometrika 81 471–483. · Zbl 0816.62023 · doi:10.1093/biomet/81.3.471
[9]	Little, R. J. A. and Rubin, D. B. (2002). Statistical Analysis with Missing Data , 2nd ed. Wiley, New York. · Zbl 1011.62004
[10]	Rubin, D. B. (1976). Inference and missing data (with discussion). Biometrika 63 581–592. · Zbl 0344.62034 · doi:10.1093/biomet/63.3.581
[11]	Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data . Chapman and Hall, London. · Zbl 0997.62510
[12]	Tanner, M. A. (1993). Tools for Statistical Inference : Methods for the Exploration of Posterior Distributions and Likelihood Functions , 2nd ed. Springer, New York. · Zbl 0777.62003
[13]	Zacks, S. (1971). The Theory of Statistical Inference . Wiley, New York. · Zbl 0241.60084