Journal ArticleDOI
Conditions for Ignoring the Missing-Data Mechanism in Likelihood Inferences for Parameter Subsets
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In this paper, the authors propose definitions of partially MAR and ignorability for a subvector of the parameters of particular substantive interest, for direct likelihood-based inferences from data with missing values.Abstract:
For likelihood-based inferences from data with missing values, models are generally needed for both the data and the missing-data mechanism. However, modeling the mechanism can be challenging, and parameters are often poorly identified. Rubin in 1976 showed that for likelihood and Bayesian inference, sufficient conditions for ignoring the missing data mechanism are (a) the missing data are missing at random (MAR), in the sense that missingness does not depend on the missing values after conditioning on the observed data and (b) the parameters of the data model and the missingness mechanism are distinct, that is, there are no a priori ties, via parameter space restrictions or prior distributions, between these two sets of parameters. These conditions are sufficient but not always necessary, and they relate to the full vector of parameters of the data model. We propose definitions of partially MAR and ignorability for a subvector of the parameters of particular substantive interest, for direct likel...read more
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References
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Book
Statistical Analysis with Missing Data
TL;DR: This work states that maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse and large-Sample Inference Based on Maximum Likelihood Estimates is likely to be high.
Journal ArticleDOI
Inference and missing data
TL;DR: In this article, it was shown that 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.
Journal ArticleDOI
Bayesian Inference for Causal Effects: The Role of Randomization
TL;DR: In this article, the authors make clear the role of mechanisms that sample experimental units, assign treatments and record data, and that unless these mechanisms are ignorable, the Bayesian must model them in the data analysis and confront inferences for causal effects that are sensitive to the specification of the prior distribution of the data.
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