By J.L. Schafer
Offers a unified, Bayesian method of the research of incomplete multivariate info, overlaying datasets during which the variables are non-stop, express or either. comprises actual info examples and functional suggestion.
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Additional info for Analysis of Incomplete Multivariate Data
Example text
This idea is so intuitively appealing that specific applications of it have appeared in the statistical literature as far back as 1926 (Little and Rubin, 1987; Meng and Pedlow, 1992). Dempster, Laird and Rubin (1977) formalized the meaning of filling in the missing data at each step and presented the algorithm in its full generality, naming it ExpectationMaximization or EM. In any incomplete-data problem, the distribution of the complete data Y can be factored as P(Y | θ ) = P(Yobs | θ ) P(Ymis | Yobs , θ ).
EM algorithm applied to victimization status of households on two occasions did not respond to the survey at either visit, we are left with a sample of n = 641 for which responses are available at one or both occasions. The EM algorithm for this example converges quite rapidly. 3 (b). One way to summarize the association between two binary variables is by the cross-product or odds ratio θ θ ω = 11 22 , θ12θ 21 with ω = 1 under independence. 57.
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.