INFERENCE AND MISSING DATA

By Donald B. Rubin. 1975

Two results are presented concerning inference when data may be missing. First, ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are “missing at random” and the observed data are “observed at random,” and then such inferences are generally conditional on the observed pattern of missing data. Second, ignoring the process that causes missing data when making Bayesian inferences about θ is generally appropriate if and only if the missing data are missing at random and the parameter of the missing data is “independent” of θ. Examples and discussion indicating the implications of these results are included.

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Citations in the corpus

Comment: Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data. (2008, methodology): “In many applications, MAR is unrealistic.”
Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data (2007, methodology): “Strong ignorability implies that the missing yi ’s are missing at random (MAR) (Rubin, 1976; Little and Rubin, 2002).”
Application of Multidimensional Item Response Theory Models to Longitudinal Data (2006, background): “Furthermore, IRT also provides a straightforward way of handling missing item responses in the case that the missing item responses are missing at random (MAR), which means that the missing values are random within observed covariate classes (Rubin, 1976).”
Using CART to generate partially synthetic public use microdata (2005, methodology): “These proposals primarily use the leaves of trees as imputation classes, assuming the data are missing at random (Rubin 1976).”
On the Construction of Imputation Classes in Surveys (2007, unknown): “We assume that the sampling design and the non-response mechanism are ignorable (Rubin, 1976) with respect to the following imputation model m : Em(yi | z1, . . . , zN) = μi ; Covm(yi , y j | z1, . . . , zN) = 0, i = j ; Vm(yi | z1, . . . , zN) = σ 2i , (9) where Em(.)”
Handling drop‐out in longitudinal studies (2004, methodology): “We have attempted to draw what we view as a key distinction between sequential MAR, which seems naturally suited to stochastic process formulations, and MAR, which is a multivariate version of de"nitions given in References [25, 50].”
To Center or Not to Center: That Is Not the Question—An Ancillarity–Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency (2011, background): “6) to make scientific sense, we have assumed that the interval censoring mechanism is ignorable (Rubin 1976).”
Maximum Likelihood Multiple Imputation: Faster Imputations and Consistent Standard Errors Without Posterior Draws (2012, unknown): “If values are missing at random (MAR)—so that the probability of a value being missing depends only on Yobs—then we can get a consistent ML estimate θ̂ML using only Yobs, without modeling the process that causes values to be missing [24].”
Missing data techniques for multilevel data: implications of model misspecification (2011, background): “The assumption required for ML and MI is that the MD process is ignorable [23].”
Missing data and multiple imputation in clinical epidemiological research (2017, unknown): “5,6 When individuals with missing data are a random subset of the study population, the probability of being missing is the same for all cases; missing data are denoted as MCAR.”
Selection in Cultivar Trials—Is It Ignorable? (2006, methodology): “The relevant theory for missing-data patterns was developed by Rubin (1976) and further elaborated by Little and Rubin (1987, 2002).”