Analysis of Incomplete Multivariate Data by J.L. Schafer PDF

By J.L. Schafer

ISBN-10: 0412040611

ISBN-13: 9780412040610

Offers a unified, Bayesian method of the research of incomplete multivariate info, masking datasets during which the variables are non-stop, specific or either. contains actual information examples and sensible recommendation.

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Cochran, 1977). Even if the model used for imputation is ©1997 CRC Press LLC somewhat restrictive or unrealistic, it will effectively be applied not to the entire dataset but only to its missing part. Multiple imputation thus has a natural advantage over some other methods of inference in that it may tend to be more robust to departures from the complete-data model, especially when the amounts of missing information are not large. Hence, even though the classes of models examined in this book may not realistically describe many of the multivariate datasets one encounters in the real world, we suspect that they will still prove useful in a wide variety of data analyses if applied within the framework of multiple imputation.

9 because its variance is lower. This reduction in variance occurs because Y1 becomes an increasingly valuable predictor of the missing 1 ©1997 CRC Press LLC values of Y2 as ρ increases. 1 for which CC appears to dominate ML are when Y1 and Y2 are unrelated (ρ = 0), in which case µˆ 2 has more variability than µ˜ 2 . Here CC enjoys an advantage because it correctly assumes that the correlation between Y1 and Y2 is zero, whereas ML uses an estimated regression line whose slope βˆ1 randomly varies about zero.

Classification of sample units by two incompletely observed binary variables x1+ =x 11 +x 12 is multinomial with parameter (θ 11 /θ 1 +,θ12/θ1+) where θ 1+ = θ 11+ θ 12; furthermore, (x 11 , x12) is conditionally independent of (x21, x22). Applying this property within parts B and C of the sample, the predictive distribution of the missing data given θ and the observed data becomes a set of independent multinomials or a product multinomial, ©1997 CRC Press LLC ( xiB1 , xiB2 )Yobs ,θ ~ M ( xiB+ , (θ i1 / θ i+ ,θ i2 / θ i+ )), i = 1, 2.

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Analysis of Incomplete Multivariate Data by J.L. Schafer

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