Rules for Inference Based on Multiply Imputed Datasets

The 5 implicates of the SAVE data can be analyzed using standard complete data methods. Every model has to be estimated 5 times, once for each complete and imputed dataset. The results across these estimations vary, this reflects the missing-data uncertainty. Rubin (1987) has derived a method for combining the results from a data analysis performed M times, once for each of M imputed data sets, to obtain a single set of results: Suppose that Qˆ_m is the scalar point estimate of interest, obtained from data set m. Suppose further that Uˆ_m is the variance estimate associated with Qˆ_m.The overall estimate is then the average of the individual estimates,

. ˆ 1 1

∑

= = M m m Q M Q _(A13)

For the overall standard error, one must first calculate the within-imputation variance,

∑

= = M m m U M U 1 ˆ 1 (A14) and the between-imputation variance,

. ) ˆ ( 1 1 1 2

∑

= − − = M m m Q Q M B _(A15)

The total estimated variance of the multiple-imputation point estimate is then

. ) 1 1 ( B M U T = + + _(A16)

Single imputation underestimates the standard errors of the estimates because it has zero between imputation variance.

Additional methods for combining the results from multiply imputed data that hold under certain special assumptions about the data are presented in Schafer (1997).

7 References

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WORKING PAPER SERIES

Nr. Author Title

07-08 Daniel Schunk The German SAVE survey: documentation and

methodology

07-07 Hans-Martin von Gaudecker

Carsten Weber

Mandatory unisex policies and annuity pricing: quasi-experimental evidence from Germany

07-06 Daniel Schunk A Markov Chain Monte Carlo Multiple Imputation

Procedure for Dealing with Item Nonresponse in the German SAVE Survey

07-05 Hans-Martin von Gaudecker

Rembrandt Scholz

Lifetime Earnings and Life Expectancy

07-04 Christopher Koch

Daniel Schunk

The Case for Limited Auditor Liability - The Effects of Liability Size on Risk Aversion and Ambiguity Aversion

07-03 Siegfried K. Berninghaus

Werner Gueth M. Vittoria Levati Jianying Qiu

Satisficing in sales competition: experimental evidence

07-02 Jannis Bischof

Michael Ebert

Inconsistent measurement and disclosure of

non-contingent financial derivatives under IFRS: A behavioral perspective

07-01 J¨org Oechssler

Carsten Schmidt Wendelin Schnedler

Asset Bubbles without Dividends - An Experiment

06-16 Siegfried K. Berninghaus

Hans Haller

Pairwise Interaction on Random Graphs

06-15 Markus Glaser Philipp Schmitz Privatanleger am Optionsscheinmarkt 06-14 Daniel Houser Daniel Schunk Joachim Winter

Trust Games Measure Trust

06-13 Markus Glaser

Sebastian M¨uller

Der Diversification Discount in Deutschland: Existiert ein Bewertungsabschlag f¨ur diversifizierte Unternehmen?

In document A Markov Chain Monte Carlo Multiple Imputation Procedure for Dealing with Item Nonresponse in the German SAVE Survey (Page 38-43)