Mathematics – Statistics Theory
Scientific paper
2012-04-14
Mathematics
Statistics Theory
32 pages, 3 figures, 3 tables, 2 Appendices
Scientific paper
Recent simulations have shown that widely used methods for analyzing missing data can be biased in small samples, even when the underlying statistical model is correctly specified. In an effort to understand these biases, this paper analyzes in detail the situation where a small univariate normal sample is missing values at random. Estimates are derived using either observed-data maximum likelihood (ML) or multiple imputation (MI). We distinguish two types of MI: the usual Bayesian approach, which we call posterior draw (PD) imputation, and a little-used alternative that we call ML imputation. We find that PD imputation has a large bias and low efficiency when the usual prior is used; however, modifying the prior can substantially improve both bias and efficiency. ML imputation dominates PD imputation, with greater efficiency and less potential for bias. Observed-data ML dominates both ML imputation and PD imputation.
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